Master by Research Thesis - QUT · Master by Research Thesis By Hui Miao Student No.: 06478689...

Master by Research Thesis

By

Hui Miao

Student No.: 06478689

submitted to the

Faculty of Science and Technology Queensland University of Technology

Project Title:

Robot Path Planning in Dynamic Environments using a Simulated Annealing Based Approach

March 2009

Supervisor: Associate Professor Yu-Chu Tian Associate Supervisor: Associate Professor Yanming Feng

III

Abstract

Mobile robots are widely used in many industrial fields. Research on path planning for

mobile robots is one of the most important aspects in mobile robots research. Path planning

for a mobile robot is to find a collision-free route, through the robot’s environment with

obstacles, from a specified start location to a desired goal destination while satisfying certain

optimization criteria. Most of the existing path planning methods, such as the visibility graph,

the cell decomposition, and the potential field are designed with the focus on static

environments, in which there are only stationary obstacles. However, in practical systems

such as Marine Science Research, Robots in Mining Industry, and RoboCup games, robots

usually face dynamic environments, in which both moving and stationary obstacles exist.

Because of the complexity of the dynamic environments, research on path planning in the

environments with dynamic obstacles is limited. Limited numbers of papers have been

published in this area in comparison with hundreds of reports on path planning in stationary

environments in the open literature.

Recently, a genetic algorithm based approach has been introduced to plan the optimal path

for a mobile robot in a dynamic environment with moving obstacles. However, with the

increase of the number of the obstacles in the environment, and the changes of the moving

speed and direction of the robot and obstacles, the size of the problem to be solved increases

sharply. Consequently, the performance of the genetic algorithm based approach deteriorates

significantly. This motivates the research of this work.

This research develops and implements a simulated annealing algorithm based approach to

find the optimal path for a mobile robot in a dynamic environment with moving obstacles.

The simulated annealing algorithm is an optimization algorithm similar to the genetic

algorithm in principle. However, our investigation and simulations have indicated that the

simulated annealing algorithm based approach is simpler and easier to implement. Its

performance is also shown to be superior to that of the genetic algorithm based approach in

both online and offline processing times as well as in obtaining the optimal solution for path

IV

planning of the robot in the dynamic environment.

The first step of many path planning methods is to search an initial feasible path for the robot.

A commonly used method for searching the initial path is to randomly pick up some vertices

of the obstacles in the search space. This is time consuming in both static and dynamic path

planning, and has an important impact on the efficiency of the dynamic path planning. This

research proposes a heuristic method to search the feasible initial path efficiently. Then, the

heuristic method is incorporated into the proposed simulated annealing algorithm based

approach for dynamic robot path planning. Simulation experiments have shown that with the

incorporation of the heuristic method, the developed simulated annealing algorithm based

approach requires much shorter processing time to get the optimal solutions in the dynamic

path planning problem. Furthermore, the quality of the solution, as characterized by the

length of the planned path, is also improved with the incorporated heuristic method in the

simulated annealing based approach for both online and offline path planning.

V

List of Tables

Table 1: Four testing environments ----------------------------------------------------------------- 56

Table 2: Control parameters for the simulated annealing algorithm----------------------------- 56

Table 3: Results for environment one --------------------------------------------------------------- 58

Table 4: Results for environment two -------------------------------------------------------------- 59

Table 5: Results for environment three ------------------------------------------------------------- 61

Table 6: Results for environment four -------------------------------------------------------------- 63

Table 7: Processing time of online planning on each case --------------------------------------- 64

Table 8: Three environments for performance evaluation --------------------------------------- 68

Table 9: Comparison of execution time base on same vertices number ------------------------ 68

Table 10: Comparison of the length of the final path --------------------------------------------- 68

Table 11: Results of comparison in case one ------------------------------------------------------- 79

Table 12: Results of comparison in case two ------------------------------------------------------ 80

Table 13: Results of comparison in case three ----------------------------------------------------- 81

Table 14: Results of comparison in case four ------------------------------------------------------ 82

Table 15: Conclusion of the improvements -------------------------------------------------------- 84

VII

List of Figures

1. Classifications of the robot path planning methods -------------------------------------------- 12

2. Visibility graph -------------------------------------------------------------------------------------- 14

3. Complete visibility graph -------------------------------------------------------------------------- 14

4. Quadtree decomposition --------------------------------------------------------------------------- 15

5. Cell decomposition --------------------------------------------------------------------------------- 16

6. Potential field --------------------------------------------------------------------------------------- 18

7. Obstacle is out of the vision zone ---------------------------------------------------------------- 19

8. Obstacle partially occupies the vision zone ----------------------------------------------------- 20

9. Obstacle impedes the main line between robot and target ------------------------------------ 20

10. Obstacle fully occupies the vision zone -------------------------------------------------------- 20

11. Path planning rule 2 ------------------------------------------------------------------------------- 21

12. Path Planning Rule 3 ----------------------------------------------------------------------------- 22

13. The representation of the chromosome in GA planner --------------------------------------- 25

14. Genetic planners ----------------------------------------------------------------------------------- 26

15. Regular grids representation --------------------------------------------------------------------- 30

16. The D* algorithm --------------------------------------------------------------------------------- 31

17. The Focussed D* algorithm --------------------------------------------------------------------- 31

18. Framed-Quadatree Structure --------------------------------------------------------------------- 33

19. Procedure of the simulated annealing algorithm ---------------------------------------------- 36

20. Structure of Player -------------------------------------------------------------------------------- 38

21. Player/Stage architecture ------------------------------------------------------------------------- 39

22. Scenario one of moving obstacle ---------------------------------------------------------------- 43

23. Scenario two of moving obstacle --------------------------------------------------------------- 44

24. Online path planning ------------------------------------------------------------------------------ 44

25. State transformation diagram of the simulated annealing algorithm ----------------------- 44

26. Enlarged obstacles -------------------------------------------------------------------------------- 45

27. Procedure of simulated annealing approach for path planning ----------------------------- 49

28. The initial path selection process --------------------------------------------------------------- 51

VIII

29. Deleting operator --------------------------------------------------------------------------------- 52

30. Offline path planning in case one --------------------------------------------------------------- 57

31. Online path planning in case one --------------------------------------------------------------- 57

32. Offline path planning in case two --------------------------------------------------------------- 58

33. Online path planning in case two 1 ------------------------------------------------------------- 58

34. Online path planning in case two 2 ------------------------------------------------------------- 59

35. Offline path planning in case three ------------------------------------------------------------- 60

36. Obstacles appears on different times ----------------------------------------------------------- 60

37. Online path planning in case three -------------------------------------------------------------- 60

38. Offline path planning in case four -------------------------------------------------------------- 62

39. Obstacles appears on different times ----------------------------------------------------------- 62

40. Online path planning in case four 1 ------------------------------------------------------------- 62

41. Online path planning in case four 2 ------------------------------------------------------------- 62

42. Convergence of the SA approach --------------------------------------------------------------- 63

43. Representation of the chromosome in GA approach ----------------------------------------- 65

44. The repair operator -------------------------------------------------------------------------------- 66

45. Comparison of execution time base on same vertices number ------------------------------ 69

46. Comparison of final path length base on same vertices number ---------------------------- 69

47. Convergence comparison in environment one ------------------------------------------------ 70

48. Convergence comparison in environment two ------------------------------------------------ 70

49. Convergence comparison in environment three ----------------------------------------------- 71

50. Environment one ---------------------------------------------------------------------------------- 72

51. Environment one from [17] ---------------------------------------------------------------------- 72

52. Process of the heuristic selection method ------------------------------------------------------ 76

53. Random picking method ------------------------------------------------------------------------- 77

54. Heuristic picking method ------------------------------------------------------------------------ 77

55. Random picking method in case one ----------------------------------------------------------- 78

56. Heuristic picking method in case one ---------------------------------------------------------- 78

57. Random picking method in case two ----------------------------------------------------------- 79

58. Heuristic picking method in case two ---------------------------------------------------------- 79

59. Random picking method in case three --------------------------------------------------------- 80

IX

60. Heuristic picking method in case three --------------------------------------------------------- 80

61. Random picking method in case four ---------------------------------------------------------- 81

62. Heuristic picking method in case four ---------------------------------------------------------- 81

63. Path solution comparison -------------------------------------------------------------------------84

64. Offline processing time comparison ------------------------------------------------------------ 84

65. Online processing time comparison ------------------------------------------------------------ 84

66. The comparison of the three methods in processing time ----------------------------------- 85

67. The comparison of the three methods in finding path length -------------------------------- 86

XI

Contents

Chapter 1 Introduction 1

1.1 Background ------------------- ------------------------------------------------------------ 1

1.2 Research Gap Statements and Motivation -------------------------------------------- 3

1.3 Aim of the Project ------------------------------------------------------------------------ 5

1.4 Significance of the Research ------------------------------------------------------------ 6

1.5 Contributions of the Thesis ------------------------------------------------------------- 7

1.6 Structure of the Thesis ------------------------------------------------------------------- 8

1.7 Related Publication ---------------------------------------------------------------------- 9

Chapter 2 Background and Literature Review 11

2.1 The Classification of the Path Planning Methods ---------------------------------- 11

2.2 Path Planning in a Static and Known Environment -------------------------------- 13

2.2.1 Visibility Graph -------------------------------------------------------------------- 13

2.2.2 Cell Decomposition Method ----------------------------------------------------- 15

2.2.3 Artificial Potential Field -----------------------------------------------------------16

2.3 Path Planning in a Static and Unknown Environment ------------------------------18

2.4 Path Planning in a Dynamic and Known Environment ----------------------------23

2.5 Path Planning in a Dynamic and Unknown Environment -------------------------27

2.6 The Simulated Annealing Algorithm and SA Based Approach -------------------35

2.6.1 The Simulated Annealing Algorithm --------------------------------------------35

2.6.2 Simulated Annealing Based Approach ------------------------------------------36

2.7 Robot and Environment Simulators -------------------------------------------------- 38

Chapter 3 The Simulated Annealing Algorithm Based Approach 41

3.1 Structure and Assumptions of the method ------------------------------------------ 42

3.2 Mathematic Modelling ----------------------------------------------------------------- 45

3.2.1 Environment Modelling ---------------------------------------------------------- 45

3.2.2 Algorithm Structure and Expressions --------------------------------------------46

XII

3.2.3 Initial Path Selection Process -----------------------------------------------------50

3.2.4 Random Path Planning ------------------------------------------------------------52

3.2.5 Online Path Planning --------------------------------------------------------------53

3.3 Platform for the Research --------------------------------------------------------------54

Chapter 4 Simulation Results and Performance Evaluation 55

4.1 Simulation Environments and Algorithm Parameters ------------------------------55

4.2 Simulation Results ----------------------------------------------------------------------57

4.2.1 Case One ----------------------------------------------------------------------------57

4.2.2 Case Two ----------------------------------------------------------------------------58

4.2.3 Case Three -------------------------------------------------------------------------- 60

4.2.4 Case Four --------------------------------------------------------------------------- 61

4.3 Performance Evaluation --------------------------------------------------------------- 63

4.3.1 The Genetic Based Approach ---------------------------------------------------- 64

4.3.2 Results Comparison ----------------------------------------------------------------67

Chapter 5 Heuristic Search Method for the Simulated Annealing Approach 73

5.1 The Structure and Implementation of the Heuristic Selecting Method ----------73

5.2 Performance Evaluation of the Heuristic Method ----------------------------------78

5.2.1 Environment One ----------------------------------------------------------------- 78

5.2.2 Environment Two ----------------------------------------------------------------- 79

5.2.3 Environment Three --------------------------------------------------------------- 80

5.2.4 Environment Four ---------------------------------------------------------------- 81

5.3 Discussion of the Evaluation Results ----------------------------------------------- 82

5.3.1 Offline Planning ------------------------------------------------------------------ 82

5.3.2 Online Planning ------------------------------------------------------------------- 83

5.3.3 The Length of the Path ----------------------------------------------------------- 83

5.3.4 Comparison with the Genetic Algorithm Based Approach ------------------ 85

Chapter 6 Conclusion 87

6.1 Summary --------------------------------------------------------------------------------- 87

XIII

6.2 Research Limitations ------------------------------------------------------------------- 88

6.3 Future Work ----------------------------------------------------------------------------- 89

Acknowledgement 91

References

XV

Statement of Original Authorship The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution.

To the best of my knowledge and belief, the thesis contains no material

previously published or written by another person except where due

reference is made.

Signature:

Date:

XVII

Acknowledgement

I would like to express my gratitude to my supervisor Associate Professor Yu-Chu Tian and

my associate supervisor Associate Professor Yanming Feng, who have given me excellent

supervision and guidance. I would also like to thank them for helping me to gain experience

on research study, which will be very helpful for my future study. I also wish to thank my

friends who helped me through all the difficult times.

1

Chapter 1 Introduction This thesis develops and implements a simulated annealing algorithm based approach with a

heuristic search method for path planning for a mobile robot in dynamic environments. The

approach uses the vertices of the static and dynamic obstacles as search space. Using the

heuristic search method, it searches an initial feasible path for the robot in the environment.

Then, the approach applies the simulated annealing algorithm to find the optimal path for the

robot. When a moving obstacle is detected with possible collision with the robot, this

two-step planning process is activated for dynamic path planning. This chapter introduces

some background information about robot path planning, the motivation of the project,

research gaps, and research significance. It also highlights the contributions of this thesis.

1.1 Background

At present, research on various algorithms for mobile robot path planning is a hot topic.

Mobile robots are widely used in many hazardous industrial fields where there may be

dangers for people, such as aerospace research, the nuclear industry, and the mining industry.

2

To find a safe path in a dangerous environment for the mobile robot is an essential

requirement for the success of any mobile robotic systems. Therefore, research on path

planning algorithms to make the robot move from the start point to the termination point

without collision with obstacles is a fundamental requirement for the mobile robot safety in

such environments. Moreover, to reduce the processing time, communication delay and

energy consumption, the planned path is naturally required to be optimal with the shortest

length.

At the initial stage of the robot industry, a robot was simple constituted by mechanical arms

controlled by motor engines. Path planning for the robot was often in stationary obstacle

environment. As an example of the robot, path planning in static environments were

discussed in [1]. However, with the development of the robot technology, robots have been

used in many industrial fields such as aerospace research, marine research, and mining

industry, to just mention a few. A lobster-like underwater walking robot [2] is one of these

new types of robots. Recently, Australian researchers have developed an unmanned

underwater vehicle robot for reef surveying [3]. The robot is equipped with sonar and vision

systems, and works at the platform of the sea. Thus, how to response quickly to the changing

environment to avoid the stationary rocks in the seabed and big moving fish is a primary

issue in the design and operation of the robot.

Recently, the genetic algorithm based approach has been developed for robot path planning

in dynamic environments, but the efficiency is not sufficient for large-scale path planning

problems. Therefore, more efficient path planning methods in dynamic obstacle

environments need to be developed for adapting the development of robots research.

The simulated annealing algorithm is similar to the genetic algorithm in solving general

optimization problems. It has been implemented for robot path planning in static

environments. What’s the performance of the simulated annealing based approach in

dynamic path planning? This is a question yet to be answered and this research gives a

positive answer to the question.

3

1.2 Research Gap Statements and Motivation

Because the entire information of a dynamic environment will change along with the

movement of obstacles, the complexity and uncertainty of the path planning problem

increase greatly in dynamic environments. Therefore, traditional path planning methods,

such as Visibility Graph [4], Voronoi diagrams [5] and Grids [6], are not suitable for planning

path in dynamic environments. Recently, Wang, Sillitoe and Davide [14] introduced a genetic

algorithm based navigation method to deal with the path planning problem in an environment

with moving obstacles. However, this method still has drawbacks: local minima results may

occur in some cases [14] and the calculating time for finding the first feasible path increases

greatly while the number of the obstacles increases [14]. The result (feasible path)

convergence rate is high using genetic algorithms, making the method lose the mechanism

for exploration. If the method has a low convergence rate, it could raise the mutation

probability and reduce the crossover probability [22]. Nevertheless, research in [9] shows

that large mutation rates improve the quality of the algorithm. Therefore, an improved

method for path planning in dynamic environment needs to be designed.

The A* algorithm [10] is another path planning method to help the robot to find the optimal

path in grid decomposed static maps. The environment with free space and obstacles is

presented by a set of uniformed regular grids. The A* algorithm uses heuristic based Dijkstra

algorithm to obtain the optimal result for the robot. The drawback is that the A* uses

uniformed grids representation which must allocate large amounts of memory for regions

that may never be traversed or may not contain any obstacles. This drawback may affect the

efficiency of the method. Quadtree representation can be used to enhance the efficiency of

the method, but it sacrificed the optimality for the efficiency. The above drawbacks also

happen in the D* method [11] which is the dynamic version of the A* method. The D* helps

robot to find the optimal path in uncertain environments. Besides, in dynamic environments

with moving obstacles, the environment changes the planning problem from fixed obstacles

to moving ones; changes the problem from a geometric one to a dynamic one; equally the

environment changes the problem from a deterministic problem to a stochastic problem [12].

4

Therefore, a vertices based stochastic optimisation method can be applied to the dynamic

environments for robots.

The simulated annealing algorithm is a generic probabilistic meta-algorithm for the global

optimization problem, namely locating a good approximation to the global optimum of a

given function in a large search space. It was independently invented by Kirkpatrick, Gelatt

and Vecchi in 1983, and by Cerny in 1985 [13].

The reasons of choosing the simulated annealing algorithm to plan the shortest path for

robots are listed below:

1) Recently, the genetic algorithm was implemented to find the optimal path for a robot in a

dynamic environment [14]. According to [9], the simulated annealing algorithm is an

optimization algorithm similar to the genetic algorithm, and can provide similar results in

optimization searches. The simulated annealing algorithm has been already used in

searching the optimal path in stationary path planning methods [15], [16] and [17].

Therefore, it is expected to work successfully in planning path for a robot in dynamic

environments.

2) The simulated annealing algorithm based methods use vertices as search space. The

reason to use the vertices as search space is the solution constituted by the vertices of

obstacles can be the optimal result. If the search space is represented by quadtree grids,

suboptimal result will be obtained. The robot can obtain the optimal path in a short time

in a dynamic environment, if the developed simulated annealing based method is

efficient.

3) According to [18], the performance of the genetic algorithm deteriorates greatly as the

problem size increases. However, the simulated annealing algorithm performs better than

the genetic algorithm in this case [18, 19]. Thus, it is worth researching this issue if the

simulated annealing approach could perform better in searching the optimal path in an

environment with large number of obstacles. Implementing the simulated annealing

algorithm in dynamic environment can provide a convincing answer. Until now, limited

work has been reported in the open literature on using the simulated annealing algorithm

in path planning in dynamic environments. Therefore, the research in this area is original

5

and can make useful contribution to the research field.

4) The genetic algorithm uses a population that contains a collection of chromosomes rather

than a single solution, implying that it is more complicated and harder to implement than

the simulated annealing algorithm. The processing time of the simulated annealing

algorithm based approach can be shorter than that of the genetic algorithm based approach.

Compared with the genetic algorithm based approach, the simulated annealing algorithm

based approach may give better trade-offs among simplicity, far-field accuracy and

computational cost in some cases as those in [20].

1.3 Aims of the Project

The research focuses on planning path for robots in dynamic environments. The aims of this

project are summarized below:

To develop and implement a simulated annealing algorithm based approach for path planning

for mobile robots in dynamic environments; the approach is expected to be able to determine

the optimal feasible path quickly for a robot in an environment with dynamic obstacles and

to give a result comparable or better than those results in the previous approach [21], which

is a typical path planning method that uses the vertices of the obstacles as search space.

1) The simulated annealing based approach could quickly determine an alternative path for

the robot if the sensor of the robot detects a moving obstacle. The alternative path

generated should also be the optimal result for the robot. The online processing time is

expected to be shorter than those of previous works.

2) To develop a heuristic method for searching the initial feasible path efficiently and to

incorporate the heuristic method to the developed simulated annealing algorithm based

approach.

3) To incorporate the heuristic method into the simulated annealing algorithm based

approach for further improvement of the performance of the approach.

6

1.4 Significance of the Research

The project contributes novelty in implementing a simulated annealing based approach for

robot path planning in dynamic environment that contains moving obstacles. The simulated

annealing based approach solves drawbacks occurred in some previous methods such as:

1) The simulated annealing based approach takes the shape of every obstacle into calculation

that can provide more precise result than other methods. Some methods like [22], [23] and

[24] ignore the dimension of the obstacles. Obstacles in [22], [23] and [24] are considered

as points or simple square blocks which could generate the repulsive force to robots. The

methods are not suitable for optimal path searching in an environment with a variety of

sharp obstacles. For searching the optimal path, the dimensions of the obstacles cannot be

ignored in such a situation. In fact, most of the published researches that use artificial

potential field neglect the dimensions of the static and dynamic obstacles. This

simplification will generate imprecise route for the robot, and the optimal solution is hard

to obtain in the artificial potential field based method. The simulated annealing based

approach takes the vertices of any different sharp obstacles as search space, therefore the

approach takes the shape of the obstacles into account that overcomes the drawback of the

artificial potential field based method.

2) Compared with some methods like [11], [25], [26], [27] and [28], the simulated annealing

based approach reduce the calculation consumption of updating the dynamic environment.

The methods in [11], [25], [26], [27] and [28] focus on dynamic uncertain environments,

in which the change of the environment caused by the absence of obstacles or the

appearance of the unexpected obstacles detected by the sensor of the robot. D* based

methods are used to re-plan path in dynamic environments where the unexpected obstacle

appears or disappears caused by the incorrect information. However, the obstacles

described in the environments are not purely dynamic with speed and moving directions.

Compared with the grids representation methods, it is easier to use vertices to represent the

moving obstacles. Updating the positions and directions of the vertices of the moving

obstacles can be easier than updating every grids in the moving obstacles. In this project,

7

the simulated annealing based method is proposed to do one-time online calculation to

generate an alternative optimal path for robot once a moving obstacle is detected.

According to [29] and simulation result of [27], the computational time of the searching

process in grids based method increases exponentially with the number of the vertices in

the map. The large number of vertices in the map may affect the performance of the D*

based methods. Therefore, the simulated annealing based approach can give a better

performance than grids based methods in dynamic environments with moving obstacles.

3) The simulated annealing based approach provides a more efficient result than previous

approaches which also use the vertices as a search space for path planning. The

performance of the new simulated annealing based approach is all-better than the previous

method [14] and [21] in calculating the optimal path for robot. As the method is able to

quickly determine the optimal path for robots in dynamic environments, it could be used in

industrial research robots such as [3] and [2]. Also, the heuristic method to search initial

path in the simulated annealing based approach in dynamic environments can greatly

improve the performance of the simulated annealing based approach in calculation time

and convergence in online and offline calculation. The heuristic method could also be used

in other optimisation methods which need to generate initial solutions for calculations.

1.5 Contributions of the Thesis

With the completion of the project, the aims of the research have been fully achieved, and an

integrated framework has been successfully developed for robot path planning in dynamic

environments. Main contributions of the Thesis are:

1) Main contribution 1: The simulated annealing algorithm based approach to search

feasible path for robot in static environments with improved performance over existing

methods. Genetic algorithm based path planning method in [21] is a typical path planning

method that uses the vertices of the obstacles as search space and it is the fundamental

algorithm used by [14] in dynamic path planning. Because the genetic algorithm based

method used in [14] and [21] uses the same algorithm mechanism, and the mechanism is

8

stated clearly in [21], so the performance of the simulated annealing algorithm based

approach is compared with that of the genetic algorithm based approach in [21]. The

calculation time for obtaining the optimal path is all-better than genetic algorithm based

approach in [21]. The simulated annealing based approach successfully generates

collision free path for the robot in dynamic environments. The simulated annealing based

approach can quickly determine an alternative path for the robot if the sensor of the robot

detects a moving obstacle. The alternative path generated is also the optimal result for the

robot in the dynamic environment.

2) Main contribution 2: A heuristic selection method for selecting the initial feasible path

more efficiently. It can be used in different types of optimisation methods. Compared

with the random picking method, the heuristic method uses a more intelligent way to

search the initial feasible path for robots. The heuristic method is incorporated into the

simulated annealing algorithm based approach to further improve the efficiency of the

approach. The simulation results show that the new heuristic selection method can greatly

improve the performance of the simulated annealing approach in searching the optimal

path in dynamic environments.

1.6 Structure of the Thesis

The following are the descriptions of the structure of the thesis. Chapter One states the main

issues of the thesis, including a general introduction to the problem and aims and outcomes

of the research. Chapter Two provides detailed literature review and background information

for robot path planning. As one of the main contributions of this thesis, Chapter Three

discusses the implementation details of the simulated annealing based approach. It illustrates

the methodology of the simulated annealing based approach to calculating the optimal path

for a robot in dynamic environments. In Chapter Four, the simulation results of the approach

are compared with the genetic algorithm based approach to test the efficiency of the

simulated annealing based approach. As another main contribution, Chapter Five proposes a

heuristic method to search the initial feasible path. The method is incorporated into the

simulated annealing based approach to further improve the performance of the approach.

Simulation results are also given to demonstrate the effectiveness and high efficiency of the

9

approach with integrated heuristic initial path search method. Chapter Six concludes the

thesis, and briefly discusses future directions on the research topic.

1.7 Related Publications

The following papers are published or in preparation in support of this thesis:

(1) “Robot Path Planning in Dynamic Environments using a Simulated Annealing based

Approach”, accepted for presentation at IEEE 10th International Conference on Control,

Automation, Robotics and Vision (ICARCV 2008), Hanoi, Vietnam, Dec 2008.

This conference is ranked by Core (www.core.edu.au) as a Tier A+ conference in 2007

and a Tier A conference in 2008.

(2) A Journal paper “Path Planning in Dynamic Environment Using a Heuristic Simulated

Annealing Approach” is being prepared to be submitted. It reports the outcomes of the

entire Masters research project.

11

Chapter 2 Background and Literature Review The mobile robot path planning task is to find a collision-free route, through an environment

with obstacles, from a specified start location to a desired goal destination while satisfying

certain optimization criteria [30]. This chapter classifies various robot path planning methods

in different ways and gives some general information about traditional path planning

methods in different environments such as the Visibility Graph method, Grid method, and

Artificial Potential Field method.

2.1 Classifications of Robot Path Planning Methods

Path planning for mobile robots is one of the most important aspects in robot navigation

research. The robot path planning methods could be classified into different kinds based on

different situations. Depending on the environment where the robot is located in, the path

planning methods can be classified into the following two types:

12

(1) Robot path planning in a static environment which only contains the static

obstacles in the map; and

(2) Robot path planning in a dynamic environment which has static and dynamic

obstacles in the map.

Each of these two types could be further divided into two sub-groups depending on how

much the robot knows about the entire information of the surrounding environment:

(1) Robot path planning in a clearly known environment in which the robot already

knows the location of the obstacles before it starts to move. The path for the robot

could be the global optimised result because the entire environment is known.

(2) Robot path planning in a partly known or uncertain environment in which the robot

probes the environment using sensors to acquire the local information of the

location, shape and size of obstacles, and then uses the information to proceed

local path planning.

Fig 1 shows the hierarchy of the classifications of the robot path planning methods:

Fig 1: Classifications of the robot path planning methods.

13

2.2 Path Planning in a Static and Known Environment

In a static and known environment, the robot knows the entire information of the

environment before it starts travelling. Therefore the optimal path could be computed offline

piror to the movement of the robot.

The path planning techniques for a static and known environment are relatively mature.

Representative path planning methods for a clearly known static environment include the

Visibility Graph method [4], Voronoi diagrams method [5], the Grids method [6], the Cell

Decomposition method [31], and the Potential Field method [32].

Moreover, the genetic algorithm, the simulated annealing algorithm, and some other

optimisation methods have also been used to obtain the optimal path for the robot. Davidor

[33] developed a tailored genetic algorithm with a modified crossover operator to optimize

robot path. Nearchou [29] used the number of vertices produced in visibility graphs to build

fixed length chromosomes in which the presence of a vertex within the path is indicated by

setting of a bit at the appropriate locus. The method applied a reordering operator for

performance enhancement, and the algorithm was capable of determining a near-optimal

solution. Cai and Peng [34] developed a fixed-length decimal encoding mechanism to

replace the variable-length encoding mechanism and other fixed-length binary encoding

mechanisms used in the genetic approach for robot path planning.

2.2.1 The Visibility Graph Method

In this method, a visibility graph is used in robot motion planning when the geometry of the

environment is known. The main idea of the visibility graph method is that if there is a

collision-free path between two points, then there is a polygonal path that bends only at the

obstacles vertices [31]. As Fig 2 shows, collision-free path (in curves) could be transformed

into line segments (straight line).

14

Fig 2: Visibility graph.

A visibility graph is constituted by nodes and edges. Nodes are the start point, destination

point and the vertices of all obstacles. Edges are strait-line segment between two nodes

which do not path through obstacles. Fig 3 shows the complete visibility graph base on Fig 2.

Fig 3: Complete visibility graph.

The following is the pseudo-code for building a complete visibility graph [31]: Output: G

(visibility graph)

1: for every pair of nodes u, v

2: if segment(u,v) is an obstacle edge then

3: insert segment(u,v) into G;

4: else

5: for every obstacle edge e

6: if segment(u,v) intersects e

7: goto (1)

15

8: insert segment(u,v) into G

Fig 3 shows that there are multiplex paths that could lead the robot from the start point to the

destination. Then, any optimisation algorithms such as the genetic algorithm [35] and the

simulated annealing algorithm [36] could be used to calculate the optimal path for the robot.

The defect of the visibility graph method is that the efficiency of the algorithm is low. From

the pseudo-code for building a complete visibility graph, it can be seen that the visibility

algorithm requires O(n3) time. Furthermore, the obtained path is often very close to obstacles

and thus, may lead to crashing of the robot. However, the problem can be fixed by enlarging

the obstacles by a value according to the dimension of the robot. In this way, the robot can

approaches obstacles without collision.

2.2.2 The Quadatree Method

The Quadatree method is another algorithm for searching the collision free path for a robot.

It uses small non-overlapping grid cells to represent the entire environment. The cells usually

are simple squares. There are three types of cells: empty cell, mixed cell and full cell. An

empty cell is a free space, where the robot could go through, in the environment. A mixed

cell contains obstacles and free space. A full cell is the block of the obstacles. In a

two-dimensional map, a Quadtree is used to decomposition the map, as shown in Fig 4:

Fig 4 [16]: Quadtree decomposition.

16

The cell decomposition method is briefly outlined below [31]:

1. Decompose the map into cells.

2. Search for a sequence of mixed or free cells that connect the initial and goal positions.

3. Further decompose the mixed cells.

4. Repeat (2) and (3) until a sequence of free cells is found.

Then, the method uses an optimisation algorithm, such as A* algorithm, to find the optimal

path for the robot. The A* algorithm [37] is first described early in 1968 by Hart, Nilsson and

Raphael. The algorithm is a best-first, tree search algorithm, and could find the shortest path

from the start point to the destination point. Lingelbach in [38] used the cell decomposition

method combined with probabilistic sampling to plan path for a robot in high-dimensional

static configuration spaces. In [39], a combined artificial potential field and probabilistic

sampling cell decomposition method was proposed. The potential field approach based on

harmonic function is computed over a non-regular grid decomposition of a high-dimensional

space obtained with the probabilistic sampling of cells.

Fig 5 [40]: Cell decomposition

2.2.3 The Artificial Potential Field Method The potential field method was initially proposed by Khatib in 1986 for mobile robot path

planning. The main idea of the method is to imagine that all obstacles can generate repulsive

force to the robot, while the destination point has attractive force to the robot. The robot

applies a force proportional to the negated gradient of the composition of the attractive and

repulsive force. The position and direction vector [ ], TX x y= of robot are fixed on by

composite of attractive force and repulsive force.

17

The attractive potential field function is given by

( ) ( )21 ,2att gU X k X Xρ=

k : positive scaling factor X : position of the robot

gX : goal of the robot

( ), g gX X X Xρ = − : distance from robot to goal Attractive force Fatt is negative grads of the attractive potential field function:

( ) ( ),att att gF U X k X Xρ= −∇ =⎡ ⎤⎣ ⎦ The repulsive potential field function is described by

( ) ( ) ( )

( )

00

0

1 10.5 ,,

0 ,

oorep

o

X XX XU X

X X

η ρ ρρ ρ

ρ ρ

⎧ ⎛ ⎞− ≤⎪ ⎜ ⎟⎜ ⎟= ⎨ ⎝ ⎠

⎪ >⎩

η : positive scaling factor ( ), oX Xρ : the shortest distance between the robot and obstacles

Constant 0ρ : distance of influence imposed by the obstacle; its value depends on the

condition of the obstacle and the goal of the robot, and is usually less than half distances

between the obstacles or shortest length from the destination to the obstacles.

When the robot is not at the goal, the repulsive force is

( ) ( )

( ) ( ) ( )

( )

02

0

1 1 1 ,, ,

0 ,

rep rep

oo o

o

F X U X

X XX X X X

X X

η ρ ρρ ρ ρ

ρ ρ

⎡ ⎤= −∇ ⎣ ⎦⎧ ⎛ ⎞

− ≤⎪ ⎜ ⎟⎜ ⎟= ⎨ ⎝ ⎠⎪ >⎩

The resultant force is att repF F F= +

F navigates the movement of the robot [23]. This is illustrated in Fig 6:

18

Fig 6: Potential field.

The artificial potential field method provides a simple yet effective method to plan paths for

a robot. However, it also has some drawbacks. The major problem is that robots are often

trapped into a local minimum before reaching the destination. Nowadays, the artificial

potential field method is combined with many other computational methods to improve its

efficiency. Park and Lee [41] have integrated the artificial potential field method with the

simulated annealing algorithm to escape local minimum. Zhu, Yan and Xing [15] also use the

artificial potential field method in combination with the simulated annealing algorithm for

similar scenarios. In addition, as will be discussed later, the potential field method is also

used in planning path in dynamic environment, as demonstrated in [8] and [23].

2.3 Path Planning in Static and Unknown Environment

In a static and unknown environment, robot navigation is more difficult than that in static and

known environment. This is due to the uncertainty of the information in the environment,

such that the optimal result is difficult to obtain and the robot has to use local information to

calculate the path. Some path planning methods in static and unknown environment will be

reviewed below.

19

In Ying and Eicher [42], a sensor-based path planning method was proposed to help

underwater robotic vehicles perform real-time path planning in a static and unknown

environment. The environment is constituted by various shaped static obstacles. A

three-dimensional path planning algorithm is developed for the robot in such an environment.

Using sonar to detect the static obstacles in the environment, the robot is controlled by a

group of thrusters. The simulation results show that the on-line path planning method can

plan a collision free path for the robot. The calculation time in the simulations is acceptable

for real-time online planning application.

In [42], the relationships among the robot position, vision zone, obstacles and target position

are described as the following situations:

1) No obstacle is inside the vision zone of the robot, shown as Fig 7:

Fig 7: Obstacle is out of the vision zone.

2) An obstacle partially occupies the vision zone but it does not impede the main line VTuuur

between robot and target. This is shown in Fig 8.

20

Fig 8: Obstacle partially occupies the vision zone.

3) As shown in Fig 9, obstacle partially occupies the vision zone and it impedes the main

line VTuuur

between the robot and the target.

Fig 9: Obstacle impedes the main line between robot and target.

4) Obstacle fully occupies the vision zone, as shown in Fig 10:

Fig 10: Obstacle fully occupies the vision zone.

21

Several path planning rules are used to plan path against above mentioned situations:

(1) Path planning rule 1: If no obstacles exist inside the vision zone or the obstacles

partially occupy the vision zone but do not impede the main line VTuuur

, the robot will

follow the main line VTuuur

to the target.

(2) Path planning rule 2: The best gate rule. If an obstacle partially occupies the vision

zone and it impedes the main line VTuuur

between robot and target, then the robot

search for the best path based on the currently known information. The path is

obtained by the current robot position and the edge point of intersected surface

produced by obstacle surface and vision zone of the robot. The best gate A and the

shortest VATuuuur

are selected, which can be determined by ( )MIN VA AT+uur uuur

. The

following figure demonstrates that:

Fig 11: Path planning rule 2.

(3) Path planning rule 3: The possible shortest path rule. If Obstacle fully occupy the

vision zone, the current location of the robot V, the target position T and the puncture

point G are used for calculating the feasible path:

a): Find puncture point G produced by the VTuuur

and the intersected surface of

the obstacle.

b): Find the minimum gradient direction PGuuur

at the puncture point P on the

intersected surface. G is on the edge of intersected surface.

22

c): The path VGTuuuur

= ( )MIN VG GT+uuur uuur

.

Fig 12: Path planning rule 3.

The path planning algorithm applies each planning rule against each situation robot

encounter until the robot reaches the destination point T.

In [43], Park and Lee proposed a modified virtual hill concept based on the artificial potential

field method to escape local minimums in the local environment. A virtual hill with extra

potential is added at the trapping obstacle when the robot is trapped in a local minimum

position. The extra potential is added to the global potential, which can repel the robot from

the local minimum. However, due to the insufficient information of the obstacles in the

environment, the global optimization result can not be acquired and only the local optimal

result is attained. Recently, Chang and Yamamoto [44] combine the Voronoi diagram

approach with the potential field method to avoid dead-lock problem in the potential field

method. The problem is solved by defining necessary sub-goals between targets on the

constructed map. Xie and Chen [45] use a virtual water-flow concept combine with potential

field method to avoid the local minimum problem in potential field method. Vanualailai and

Sharma [46] developed an asymptotically stable point-mass system to avoid the local

minimum in artificial potential field method. The Lyapunov function in the asymptotically

stable system produces artificial potential fields around the goal and the obstacle, has no

local minimum other than the target.

23

In [47], Wan, Chen and Earnshaw used a robot version hypothesis similar to that in [42] and

proposed an A* based path finding algorithm. The method allocates the points of visibility

dynamically and decentralise the view angle in each step to build state node. Paper [48]

proposed a more practical method using a virtual window in the front of the robot to

calculate the space ahead and any intersections that are done. The robot acquires a

two-dimensional image of the space ahead and processes the information to find a collision

free path. The simulation results show that path planning can be successfully implemented

using the virtual window method and that the computational time limitation can be

overcome.

In [49], an artificial immune network based path planning method is proposed. The method is

capable of obtaining an optimal or near-optimal collision free path in unknown environments

that is presented by grids. According to the simulation results, the method can give a better

performance on complex environments than the Knowledge-based Genetic Algorithm [58]

does.

Nowadays, the path planning problem is still a favorite research topic in robotic and artificial

intelligence studies. The path searching for robot in unknown static environment will still be

study in the future.

2.4 Path Planning in Dynamic and Known Environment

Research on methods that deal with the static environment path planning has been introduced

in previous sections. Currently, the path planning methods to find paths in static environment

have been well developed with hundreds of published papers. Given the entire information of

the environment, the global optimal or near-optimal result path could be found by these

algorithms, such as the genetic algorithm [50].

However, in practical applications, robots such as those described in [2] and [3], often face

obstacles that are not all static in the environment; the status and the movement of the

obstacles change continuously in the map. Moving obstacles in a dynamic environment

24

increase the difficulty of planning path for the robots in the map.

Unlike the situation for path planning in a static environment, limited reports have been

found in the open literature to discuss optimal path planning in dynamic environments.

Complexity and uncertainty increase with the number of the dynamic obstacles. Therefore,

traditional path planning algorithms, such as the visibility graph, the voronoi diagrams and

the grids method, do not perform well in dynamic environments. It is also difficult to gain the

optimal path for the robot using these methods. Robot path planning in a dynamic

environment is thereby an issue for further research. In a dynamic environment, how to

manipulate the robot so that it can travel to the destination safely and optimally without

collision is an important issue of concern.

In 2005, Chestnutt, Lau and Cheung [51] used a modified A* algorithm to calculate path for

a Honda ASIMO humanoid robot. The path planning method is applied to real robots rather

than simulated on software. A grid of cells is employed to represent the environment. Colour

cells represent the obstacles. The cells create a bitmap representing the free spaces and

obstacles in the map. The algorithm plans a sequence of footstep positions to navigate toward

a goal location based on known static and moving obstacles with predictable trajectories. It

uses three cost functions to constrain the step nodes used by the robot.

(1): The first cost is the location cost, which evaluates the footstep location with regard

to the environment to determine if the location is safe place to step.

(2): The second cost is the step cost, which calculates the cost to the robot to make the

desired step.

(3): The last cost is the estimated remaining cost-to-go, which is calculated by planning

backwards from the goal with a standard mobile robot planner as a precomputation

step. This cost is used to avoid the local minimums.

Wang and Sillitoe [14] proposed a vertices genetic algorithm planner in 2007. The planner is

able to rapidly determine optimal or near-optimal solutions for a mobile robot in an

environment with moving obstacles. The method uses the vertices of the obstacles as search

space and produces off-line path planning through the environment with dynamic obstacles.

25

It firstly incorporates the robot speed into the genetic genes, which could optimise both the

travel time and distance of the robot. Before the robot starts movement, the complete motion

knowledge of the moving obstacles in the observed region is available for the robot. The

robot uses the genetic algorithm based planner to calculate the time or distance-optimised

solution and then starts to travel. The assumptions of this method are:

• Obstacles are bounding polygons with vertices.

• The speed of the moving obstacles is fixed value, and

• Physical dimensions of the robot are neglected and regarded as a single point.

The genetic representation of the method is outlined in Fig 13:

Fig 13: The representation of the chromosome in GA planner.

As shown in Fig 13, the possible solution paths are represented by a chromosome which is

constituted by a bunch of genes. The minimum number of genes for a chromosome is two

corresponding to the start point and the end point, and the maximum number of genes is thus

the total number of whole vertices N plus the start and the end points.

Each gene contains four parts with the first two being the x and y coordination positions of

the vertex. The third part is the robot’s speed in the segment of each gene. The robot speed is

selected from a group of predefined discrete speeds. The last part indicates the feasibility of

the path that originates from the genes; if the path segment connecting two consecutive

vertices intersects one or more obstacles, then the infeasibility bit of the gene representing

the originating node is assigned 1 to mark the infeasibility of this segment. The evaluation

functions have two types: the path length and the travel time.

26

Four genetic operators are used in the method; they are crossover operator, mutation operator,

repair operator and robot speed mutation operator. Fig 14 illustrates the first three genetic

operators.

Fig 14: Genetic planners.

The generational operation begins with the random selection of a genetic operator and a

quadratic ranking scheme is used to retain the constant selection differential after evaluation.

The parent (or parents for the crossover operation) involved in the genetic operation is

determined by a roulette wheel whose slots are sized in proportion to the fitness as scaled by

a ranking technique. To form a new generation, the newly generated offspring replace the

worst individual (or pair of individuals if crossover is applied) in terms of fitness in the

existing population. The evolutionary process continues until a termination condition is

satisfied, which can be defined to be a number of generations specified by the user or

determined by monitoring against a specified performance criterion. When the evolution

terminates, the best individual is selected as the path planning solution. The simulation

results show that the planner changes in robot speed significantly improves the efficiency of

the method especially in time management for robot in dynamic environment.

A hybrid navigation method [52] was proposed in 2003. The method consists of two modules:

global and local modules, which could combine two robot path methods to deal with the

global map information and local sensor information.

27

(1) The global module specifies the global route positions. It uses prior information on

the navigation environment and chooses critical points to pass through before actual

navigation takes place. This module uses the A* algorithm to determine the optimal

route to the specified goal position. Using the algorithm, it is possible to find the

optimal route to the goal.

(2) The local module carries out the navigation itself, relying on current sensor data,

thus making it easier to avoid static or dynamic obstacles. It uses a fuzzy neural

representation of the potential field based navigation method.

Firstly, the global planning module finds the optimal route to the goal and proposes the

positions to pass through as intermediary points. These intermediary points are then passed

one by one to the local navigator, which makes the robot reach them while reactively

avoiding the obstacles present in the environment, according to the potential function

previously supplied to the local navigator.

A dynamic environment is more complicated than a static environment in the robot path

planning issue. Several methods were proposed to solve the problem. Because the moving

information and the obstacle information can be known in advance of movement

commencing, the optimal solution can still be obtained.

2.5 Path Planning in Dynamic and Unknown Environment

Path planning in dynamic and unknown environment is the most complicated case in robot

path planning, and is also the most common situation that mobile robots will confront. In the

real world, mobile robots such as undersea unmanned vehicles often need not only to avoid

static rocks in the seabed, but also to avoid colliding with the large sea lives. Due to the

complicated and unknown environment, the robot cannot adopt one time global path

planning for the environment. The global optimised solution is thereby difficult to be

obtained. The robot has to use sensors acquiring the information of surrounding environment

and do online real-time path planning. The planning time for the robot should be short

28

because the robot needs a sufficient time interval to adjust its movement in order to avoid the

coming obstacle. In next few paragraphs, recent research in this area will be reviewed.

In 2006, Lv and Feng [53] introduced a numerical potential field for finding the path in a

dynamic environment for a robot. This research used an ant colony optimisation algorithm to

perform optimal path searching. The movement of the obstacles is taken into considerations

by changing the local potential values. The method firstly uses dynamic valued potential

field to model the dynamic environment, then employs an ant colony optimisation method to

search the path for local path planning.

In 2007, Wang, Sillitoe and Mulvaney [14] introduced a genetic algorithm planner to

determine optimal or near-optimal solutions for a mobile robot in dynamic environments.

The obstacles are described as bounding polygons and the robot dimension is neglected and

regarded as a point. The method firstly uses offline planning to generate a path for the robot,

then the robot starts to travel with its sensors. The online path planning method is activated

to calculate an alternative path for the robot if obstacles are detected. Because of the

complexity and uncertainty involved, very limited work has been conducted to develop

complete solutions for a purely uncertain dynamic environment.

Furthermore, implementing path planning algorithms in real robots in dynamic cases is also

very limited. Cao, Huang and Zhou [23] provided an evolutionary artificial potential field

method for dynamic path planning for soccer robots in RoboCup 2005. The new potential

field method is intended for path planning of mobile robots in a dynamic environment where

the target and obstacles are moving. Firstly, the new force function and the relative threat

coefficient function are defined. Then, a new potential field path planning algorithm based

on the relative threat coefficient is presented. Finally, computer simulation and experiment

are used to demonstrate the effectiveness of the dynamic path planning scheme [32].

Zheng and Zhao [54] proposed an artificial potential field based approach in 2006. The

method could handle path planning for five mobile robots in a dynamic unknown

environment. The robot will pass the intersection area in order according to their priority,

29

which is predefined before movement. The method assumes that the obstacles in the map

have identical sizes. It successfully coordinates the movements of multiple robots, and makes

the robots pass through the static obstacles and other robots without collision. The novelty of

the research is the application of the artificial potential field method to multi-robot path

planning in dynamic environment.

Tarokh [55] develops a hybrid intelligent approach to path planning for high mobility robots

operating in rough environments. Path planning consists of characterization of the

environment using a fuzzy logic framework, and a two-stage genetic algorithm planner. A

global planner determines the path that optimizes a combination of terrain roughness and

path curvature. A local planner uses sensory information, and in case of detection of

previously unknown and unaccounted for obstacles, performs an on-line re-planning to get

around the newly discovered obstacle.

Hu and Gu [56] developed an improved algorithm to solve the problem of optimum route

planning in vehicle navigation systems. The algorithm is based on the standard genetic

algorithm and the lambda-interchange local search method and has evolved from the

improved A* shortest-path algorithm. The algorithm can find the optimum route more

efficiently and quickly without any network constraint condition and can work well either in

continuous or in discrete networks.

In [57], potential field method is applied for both path and speed planning for a mobile robot

in a dynamic environment where the target and obstacles are moving. The robot’s velocity

and trajectory are determined by the relative speed and moving directions of the obstacles

and target. The simulation results verify that the method can efficiently tracking the moving

target while avoiding the obstacles along its path.

The D* (Dynamic A*) [11] method is a typical method used in path planning in dynamic

unknown environments. It plans optimal traverses in real-time by incrementally repairing

paths to the robot’s state as new environment information is known, which makes it possible

to greatly reduce the computational cost. When the robot gathers new information about the

30

environment, it will replan new paths based on the new information and produce a path for

the robot. D* does not require complete re-planning of the path every time when new

information comes in. It updates the path arc cost locally when environment changes.

However, D* still try to obtain the globally optimal path when possible.

Like A*, D* operates on a cost graph. The environment with the obstacles is represented by a

uniform grids map as in Fig 15. The main idea of the method is illustrated as following:

From the initial state, the method repeatedly selects the neighbour with the minimum cost

until propagates to the goal. Each small cell in the map is called state. Each state X has the

arc cost from the state X to the goal given by the path cost function h(X,G). From the start

point (start state), all neighbour states of the current state are listed on the open list. From the

open list, the method calculates the arc cost of the states by h(X,G). Then, select the state

with the minimum h(X,G), go to this state, and new neighbours are added to the open list. As

Fig 16 shows, from the start point, the method repeatedly propagating to neighbours and

selecting the state with the minimum h(X,G) until the goal state is propagated.

In the dynamic uncertain environment, when the robot detects new obstacles or the absence

of expected obstacles, the cost values of the states in the area change. And the adjoining

states are put on the open list for cost correction. Encountering unexpected obstacles, D* will

set off a “raise” wave, a wave of increasing cost, through neighboring states. When this wave

meets with the states that are able to lower path costs, these “lower” states are put on the

open list to recalculate new optimal paths. When it detects the absence of an expected

obstacle, the arc of the path passing through this “missing” obstacle is assigned a small cost,

denoting an empty space, and the adjoining state is put on the open list as a lower state,

setting off a “lower” wave, a wave of decreasing cost. D* is able to determine how far the

raise and lower waves need to propagate while providing the optimal path for robot traverse

continuously [26].

The basic D* method was originally proposed in 1994. However, the cost change

propagation method used in basic D* does not consider which expansions will benefit the

robot at its current location. Thus, the performance of the algorithm [25] can be affected.

31

Therefore, like A*, D* can use heuristic function to focus on the search in the direction of

the robot and reduce the total number of the state (grids) expansion. Focussed D* method [26]

uses the focussing heuristic function to estimate the estimated path cost from the current

location to the goal to help the robot to minimise its search space. In comparison with Fig 16,

Fig 17 shows that with focussed D*, robot uses fewer grids in search the optimal path.

Fig 15: Regular grids representation.

Fig 16: D* Algorithm [25]

32

Fig 17: Focussed D* Algorithm [25]

To enhance the performance of the D* algorithm, framed-quadatree D* [27] and Field D*

[28] methods were proposed.

• The Framed-quadatree method uses quadatree structure to represent the

environment. It uses different dimensions of grids to represent the environment in

order to minimize the search space, and then adding the border-cells to connect

each grid, as shown in Fig 18. The framed-quadatree structure can reduced the

search space for the robot and also the framed-quadatree uses border-cells to over

come the disadvantage of the suboptimal result in using the quadatree structure.

However, because the method has to create more sub-cells for calculation, the

performance of the framed-quadatree method deteriorates greatly as the fractal gain

increases, especially in offline planning [27].

• The Field D* method [28] uses an interpolation-based planning and re-planning

algorithm to generate smooth paths for robots through non-uniform cost grids. It

uses linear interpolation during planning to calculate accurate path cost estimates

33

for arbitrary positions within each grid cell and to produce paths with a continuous

range of headings. The method can produce a smooth optimal path for a robot to

over come the suboptimal problem in using non-uniformed girds method. However,

the method scarifies the performance for the accuracy. It reduces the path length of

the robot in offline and online planning but takes 1.8 times longer in calculation

time than previous D* method [28].

Fig 18: Framed-quadatree structure.

Recently, a grid-based distance-propagating dynamic system is proposed in [58]. The

algorithm is similar to the D* algorithm, but it does not maintain a sorted queue of points to

update. The algorithm uses only local information when computing an update at each point,

and the order of updating is predetermined. This makes the algorithm exceedingly easy to

parallelize by simply assigning a subset of points to each processor. Consequently, in

situations where obstacles and targets are moving at substantial distances from the current

robot location, the grid-based distance-propagating dynamic algorithm is more efficient than

the D* algorithm.

Until now, most research activities on robot path planning in dynamic environments have

been theoretical in focus. Some methods such as those in [11], [25], [26], [27] and [58] are

34

proposed to deal with the issue of robot path planning in uncertain environment. However,

due to the complication of dynamic environment, the methods still have limitations

concerning their assumptions, algorithm efficiency and other issues:

1) The methods in [11], [25], [26], [27], [28] and [58] focus on dynamic uncertain

environments, in which the change of the environment caused by the absence of obstacles

or the appearance of the unexpected obstacles detected by the sensor of the robot. The

robot uses D* or algorithm similar to D* based methods to re-plan path in dynamic

environments where the unexpected obstacle appears or disappears caused by the

incorrect information. However, obstacles described in the environments are not purely

dynamic with speed and moving directions. Compared with the grids representation, it is

easier to use vertices to represent the moving obstacle. Updating the positions of the

vertices of the moving obstacle can be easier than updating every grids in the moving

obstacle. In this project, a simulated annealing based method is proposed to do one-time

online calculation to generate an alternative optimal path for robot once a moving

obstacle is detected. According to [29] and simulation result of [27], the computational

time of the searching process in grids based method increases exponentially with the

number of the vertices in the map. The large number of vertices in the map may affect the

performance of the D* based methods. Therefore, it is worth implementing efficient

vertices based simulated annealing approach for robot path planning.

2) The efficiency of some methods such as that in [14] is not practically acceptable when

applying the method in real-world systems. The methods assume that in order to allow

the robot to be guided so as to avoid any potential collisions with obstacles, there is an

adequately large time interval between the detection of obstacle movements and the

implementation of new generated actions. When dealing with robot path planning in

complex environments, genetic based approach is time consuming. According to the

simulation result of [14], it requires nearly 30 seconds to find the first feasible path for

the robot in an environment with 14 static obstacles and 5 dynamic obstacles. It seems

not practical applying the approach to real robot application.

35

Addressing those drawbacks, this project develops and implements a new approach for more

efficient robot path planning in dynamic unknown environments. The proposed approach

could provide a near or better result than previous solutions like [14] and [21]. The algorithm

is able to quickly determine the optimal path for a robot in dynamic unknown environments.

The robot uses sensors to gain the information of moving obstacle, and compounding it with

the information of static obstacles to acquire the optimal path for the robot in dynamic

environments.

With the time limitation of this research, we will use a robot and environment simulator to

investigate the robot path planning problem, and, implement our algorithms in the simulator.

In this project, we use Matlab to simulate the robot with sensors and the unknown dynamic

environments. For simulating the algorithms, Matlab could be the suitable application,

because of its sophisticate math toolbox. In this paper, the simulation results show that the

approach can give a better performance in path planning than [21], and takes the dimensions

of the static and dynamic obstacles into account comparing with the artificial potential base

methods. The simulated annealing based approach with heuristic search method improves the

searching algorithm in finding the optimal solution in dynamic unknown environments. The

detailed methodology of the approach will be explained in Chapter 3.

2.6 The Simulated Annealing Algorithm and SA Based Approach

2.6.1 The Simulated Annealing Algorithm

The simulated annealing algorithm is a generic probabilistic meta-algorithm for the global

optimization problem, namely locating a good approximation to the global optimum of a

given function in a large search space. It is widely applied in many industrial fields. The

well-described application of the simulated annealing algorithm is for the Traveling

Salesman Problem (TSP) [59]. The TSP problem is that given a number of cities and the cost

of traveling form one city to another, to get the least cost round trip to visit each city exactly

once and then return to the start city.

36

The simulated annealing algorithm is analogous to metal physical cooling process, with each

step of the simulated annealing algorithm replacing the current solution by a random

"nearby" solution. The probability of choosing the random "nearby" solution depends on the

difference between the corresponding function values and on a global parameter T (called the

temperature) that is gradually decreased during the process. The dependency is such that the

current solution changes almost randomly when T is large, but increasingly "downhill" as T

goes to zero [60]. Fig 19 is the flow chart of the general steps of the simulated annealing

algorithm:

37

Fig 19: Procedure of the simulated annealing algorithm.

2.6.2 Simulated Annealing Based Approach

Before this project, the simulated annealing algorithm approach had already been applied to

the robot path planning method to deal with finding path for robot. Zhu, Yan and Xing [61]

proposed a simulated annealing based artificial potential method to deal with the robot path

planning issue in static environments. The artificial potential method is firstly used to map

the environment and find a route for the robot. The simulated annealing algorithm is applied

to the artificial potential method to overcome the local minimum problem that is caused by

obstacles in the map. Zhang and Lu [62] integrate the simulated annealing algorithm into the

artificial potential field method to solve the GNRON and local minima problems. Neachor

[19] used vertices of the static obstacles as search space and implemented the simulated

annealing based approach to find optimal path for robot. The simulated annealing based

approach is compared to genetic based approach in his paper. The performance of the

simulated annealing approach is slightly lower than the genetic approach in his experiment.

There might be two reasons that affect the performance of simulated annealing approach in

Neachor’s model.

(1) The simulated annealing algorithm is more sensitive to the control parameters such

as initial temperature and cooling rate. In Neachor’s research, only one group of

control parameters is set in dealing with three different situations. The performance of

simulated approach could be improved if suitable parameters are set.

(2) The operator that generates the new solutions is too simple. Neachor only used a

swapping operator to generate the new solution. The swapping operator only flips

some bits of the result to generate a new result. In this way, the possibility of jumping

out of the local optimal result is small. The simulation results in this Thesis proves

that adding more algorithm operators to generate the new result gives the simulated

annealing approach better performance. In this thesis, more than one operator were

38

used, the simulation results show that the performance is improved by the

multi-operator in the approach. The detailed approach description will be discussed in

Chapter 3.

Path planning in a dynamic unknown environment is the most common case in the real world.

Therefore, a more effective robot path planning method should be proposed, which can

satisfy the accuracy and the efficiency simultaneously. Our project is trying to apply the

simulated annealing method to quickly produce online calculation and efficiently defines the

optimal path for robot in a dynamic environment.

2.7 Robot and Environment Simulators

Implementing a new method on real robots is not only complicated and time consuming, but

also expensive. For the purpose of this Master research project, we use software simulators to

model both the robot and the environment. Then, the developed approach is implemented in

the simulators. There are many kinds of robot and environment simulators, such as multiple

mobile robot simulators EyeSim [63] and Player/Stage [64]. The following is an introduction

to the Player/Stage appliance.

The Player/Stage Project is an open source project for multiple, distributed robots control and

sensor network system, in which Player provides as robot device server. Stage works as a

multiple robotics simulator, plus some supporting tools. Since that Player/Stage can work

under different platforms and be easily programmed, they have been adopted, modified and

extended by researchers all around the world. In fact, Player can actually control and work in

many popular robot devices, such as Pioneer 2-DX mobile robot and etc [64]. The

Player/Stage project is carried out in Robotics Research Lab of University of Southern

California. Player is an open sourced middleware server that could run on variety of robots,

sensors and actuators. It hides the hardware detail of robots for users (like an operating

system on robots). Users could write their own control program at client to control the robot

through TCP channel.

39

Fig 20: Structure of Player

Researchers do not need to access to the real hardware and environments when they are

focusing on Player and robot research. Stage is used to simulate different kind of robots,

sensors and object for the Player. It provides two-dimensional bitmapped environments, and

also could let research to do experiments with novel devices that do not exist (By adding

library files). Stage simulates a population of simulated robots and sensors operating in a

two-dimensional bitmapped environment. The devices provided by the Stage are accessed

through Player, as if they were real hardware. Stage aims to be efficient and configurable

rather than highly accurate. In practice this means that Stage can simulate tens or hundreds of

robots on a desktop PC, and the simulated robots commonly work similarly to the real robots

in the world [65].

Fig 21: Player/Stage architecture.

40

The implementation of building the new simulated annealing approach on Player/Stage will

not only demonstrates the feasibility of approach but also provide a more practical simulated

environment for the new method. The simulated annealing based approach could be tested by

simulated robot hardware, not only exist in theoretics.

The Stage Library (libstage) provides a C code library for simulating a population of mobile

robots, sensors and environments. Stage is one product of Player/Stage project, which is a

simulating tool used in the field of mobile robot and intelligence sensor system. Stage

simulates mobile robot, sensor, obstacles and other objectives in two-dimensional bit map.

Stage could simulate different equipments and models. It could also simulate virtual robots

and sensors that have not yet been developed. Stage could simulate variety of sensors and

executor including sonar, laser scanning distance measurer, splash display, blob gripper,

mobile robot and so on.

Equipments simulated by Stage can be controlled by Player which is a network robot server.

Interface program provided by Player drives equipments like robot and sensor, and Stage

simulates these equipments. The TCP ports for controlling the real robots provided by Player

are identical with the TCP ports to control the simulated models in Stage. Therefore, Stage

could totally provide comprehensive real environments and robots for the Player and its

clients. It is expected that Stage builds the dynamic environment and simulates real robot and

real sensors for the player sever. The simulated annealing approach is implemented in client

machine, the client acquires the useful information from Player server, and then use

simulated annealing approach to acquire the optimal path.

41

Chapter 3 The Simulated Annealing Algorithm Based Approach

This chapter explains the methodological approach in details, including the modeling of

environments, structure of the approach/algorithm, the generation of the initial feasible path,

the new planner for generating the random path and the procedure of online calculation. One

of the aims of this project is to implement a simulated annealing based approach into robot

path planning in a dynamic environment. The simulated annealing based approach is

expected can quickly determine the optimal feasible path for robot in the environment with

moving obstacles. The research uses the mathematic software Matlab to simulate the

dynamic environment, real world robots and sensors. The research then implements the

simulated annealing path planning method in the environment. Therefore, the entire research

project could be separated into the following three phases:

1) Design the algorithms that could find paths and optimising the paths for the robot in

dynamic environments.

42

2) Use Matlab to build mathematic model and obtaining the simulation results proving

the feasibility of algorithm.

3) Compare the results of the new approach with the those from existing methods, and

discuss the performance and the efficiency of the new approach.

.

3.1 Structure and Assumptions of the Method

First, as in the development of many existing methods, some assumptions are made before

designing the algorithm.

1) There are stationary and moving obstacles in the dynamic environment.

2) As a traditional assumption, both the stationary and dynamic obstacles are bounding

polygons.

3) The search space is the vertices of the static obstacles plus the vertices of the detected

moving obstacles.

4) The movement trajectory of the dynamic obstacles is constituted by a series of line

segments, and is constrained by a straight line.

5) Any changes in motion parameter of the dynamic obstacle are immediately available

to the robot, if the obstacle is in the range of the sensor. The time of the robot

obtaining the moving parameter (such as speed and direction) is minimum that does

not affect the path planning calculation.

6) The robot could change its speed and direction at any time.

7) After the sensor of the robot acquires the motion information of the moving obstacle.

It is assumed that a separated module is used to monitor the movement of the

obstacles for the robot. The module will predict the next movement for the robot based

on the previous movement of the obstacle. It will report any change of direction and

speed of the obstacle. The module is separated from the robot, which can be simply

implemented by using extern sensors in real robot implementation.

The designed structure of the simulated annealing algorithm in dynamic obstacles

environments is divided into two stages: off-line calculation for stationary obstacles, and

online calculation when moving obstacles are detected.

43

Stage 1: Offline calculation for the path on stationary obstacle based on the vertices of the

static obstacles. The simulated annealing based approach firstly calculates the

optimised path for the robot base on the positions of the stationary obstacles. Once

the path is ready, the robot starts to travel through the stationary obstacles with the

sensor that could detect the 360 degree direction of the robot.

Stage 2: Online path calculation once the moving obstacles are detected by the sensor. As

moving obstacle enters the detection range of the robot, the sensor will detect the

obstacle and the robot acquire the moving information such as speed and moving

direction of the obstacle from the sensor of the robot. Then the robot uses the

motion information to calculate the possibility of the moving obstacle clashing

with the robot. If it is calculated that the moving obstacle will not collide with the

robot, the robot will use the current path plan to travel through the map. As Fig 22

shows, the sensor of robot calculates out that the L shaped moving obstacle will not

collide with the robot. Therefore, the robot will not change the current path plan. If

the moving obstacle will clash with the robot as Fig 23 shows, the robot will

activate the algorithm again to calculate a new path online for the robot (Fig 24).

Fig 25 shows that state change of the robot in path planning approach in dynamic

environments.

Fig 22: Scenario 1 of moving obstacle.

44

Fig 23: Scenario 2 of moving obstacle

Fig 24: Online path planning

Fig 25: State transformation diagram of simulated annealing approach.

45

In the actual calculation for either offline or online path planning, the algorithm consists of

two procedures:

• Firstly, using randomly selection to find one initial feasible path which could lead

robot from start point to destination.

• Secondly, based on the initial feasible route, using the optimization algorithm to

search for the optimal or near-optimal path for the robot in the static environment. In

this Thesis, the optimization algorithm used for searching the optimal path is a

simulated annealing algorithm.

3.2 Mathematic Modelling

3.2.1 Environment Modelling

The environment is represented by polygons with vertices and edges. The mathematic model

of locating the edges and vertices of the obstacles in the environment is not complicated, use

the model mentioned in Chapter 2 about visibility graph. For realistic simulations, as in [21],

all obstacles in the map are enlarged by a fixed value that the robot could approach obstacles

without collision. The dimension of the robot is neglected, and consequently the robot is

regarded as a single point. In Fig 26, the black polygons represent the static obstacles and the

hollow polygons are moving obstacles. The vertices of the enlarged polygons form the search

space for the robot.

Fig 26: Enlarged obstacles

46

A mathematic model can be developed to determine the possibility of robot colliding with a

moving obstacle. The model is described as follows:

1) The first crossing point between the robot path proposed by the planner and the

trajectory of a moving obstacle is calculated before examining the possibility of

collision;

2) Based on the time t required for the robot to cover the distance from the current

position to the first crossing point, the instantaneous location of the moving obstacle

can be calculated and. Consequently, the exclusion area for this obstacle can be

obtained;

3) If the robot path between the vertex and the crossing point across the edges of the

moving obstacle in odd times, then a collision would occur between the robot and the

moving obstacle, otherwise no collision will happen between the robot and the

obstacle;

3.2.2 Algorithm Structure and Expressions

Traditionally, the path length Ef is the evaluation criteria for the quality of the solution

derived from the algorithm. The shorter the path, the better the solution. A feasible solution is

expressed by a series of vertices linking the start point through to the end point. Each vertex

of the obstacle has its series number. The path for the robot is represented by a sequence of

vertex numbers. Thus, the feasible solution X is given by:

X = {Vstart, Vstart+1, Vstart+2…Vend-1, Vend};

The evaluation function Ef is given by:

Ef = 1

1( , )i endi i

i startD V V= −

+=∑

Where D(Vi, Vi+1) represents the direct distance from vertex Vi to Vi+1. The pseudo-code of

47

the algorithm is as following:

Step 1: Set an initial temperature T;

Step 2: Generate a initial path order randomly from the start to the destination and calculate

the path length L(initial);

Step 3: Generate a new path which also from the start to the end and calculate path length

L(new);

Step 4: If L(new) < L(initial), accept new path. Else possibly accept new order according to

some scheduling.

Step 5: Repeat step 3 and step 4 until the temperature gets down.

Step 6: Down the temperature and return to step 1.

The following are pseudo-codes for the simulated annealing algorithm:

T = Tinit;

while (T>Tterminate)

randomly generate one feasible solution Xs;

evaluate Xs, Ef = f(Xs);

count = 1;

while (count < Threshold)

generate a new feasible solution Xn base on Xs;

evaluate Xn, En = f(Xn);

if f(Xn) < f(Xs)

Xs = Xn;

else if rand(1) < (exp((f(Xs)- f(Xn))/T)

Xs = Xn;

count =count +1;

endwhile

T = cool_rate * T;

update Xs at each reduction of temperature T

endwhile

48

Xs is the optimal or near-optimal solution for the robot.

Fig 27 is the flow chart of the simulated annealing approach for searching the path for robot

in the environment.

49

Fig 27: Procedure of simulated annealing approach for path planning.

50

3.2.3 Initial Path Selection Process

It is known from Fig 27 that after each reduction of initial temperature T, a new feasible

solution Xn is selected in each new round. It is essential for the algorithm to quickly and

correctly generates a random feasible path in each round. For this purpose, the edges of the

static obstacles should be specified first. An edge is any straight-line between two points on

the edge of or within the obstacles. Any path section crosses the edge is defined as an invalid

path. In the proposed program, a separate array is used to store all the edges of the map.

At the initial stage of the program, except dynamic objects, starting point and end point; a

vertex is chosen randomly from the map, then use a strait-line to connect the start point and

the selected vertex. If the path line intersects with any edges of the obstacle in the map, the

path is recognized as invalid path. Another vertex will be randomly selected again for testing.

If the strait-line to the selected vertex does not intersect with any edges in the map, the

strait-line is recognized as part of a valid path. Then add the vertex into the path. After that,

start from the selected vertex to find next valid vertex. Keep doing the above procedure until

the end point is selected and also the path line to the end point is a valid path, i.e., the path to

the end point does not intersects with any edges. The following pseudo-codes and Fig 28

illustrate the process of the initial path selection process.

initial path IP = {start};

while (1)

randomly select Vs;

if path{IPend, Vs} intersects any obstacles;

continue;

else

IP = {IP,Vs};

endif

if Vs == destination point;

break;

51

else

continue;

endif

endwhile

Fig 28: The initial path selection process.

52

3.2.4 Random Path Planner

As discussed in Chapter 2 (Literature Review), a simpler random path planner directly

affects the performance of the path planning algorithm. Therefore, advanced and more

efficient path planner needs to be implemented. Different from the simple path planner used

in [30], a more efficient random path planner is developed in this thesis.

Additional deleting and switching operators in the planner are used to generate a new

solution by flipping some bits of the Xs. The switching operator randomly switches two

vertices in the feasible path, then check if the new generated path is a feasible path (which

does not intersect with any edge). If the new path is a feasible path, accept the new path;

otherwise, discard it. The algorithm randomly chooses one operator to generate the new path.

Fig 29 shows that the deleting operator randomly deletes one vertex from the initial Xs to

generate a new solution, while the switching operator randomly swaps two vertices in Xs. As

the same selection criteria in generating initial path, each line section generated by the

operators should be firstly tested against the edges in the map in order to generate a valid

path line. This means that the line section created does not intersect with any edges in the

map.

Fig 29: Deleting operation.

When the path length is the evaluation criterion, randomly deleting vertices could contribute

more improving the performance of the solution. Therefore, the possibility of choosing the

deleting operator is set to be higher than the possibility of selecting the switching operator. In

our simulation program that will be discussed later, the possibility of choosing the deleting

operator is set to be 0.78. After generating a new path solution by deleting or switching

53

operator, the new solution will be evaluated using the evaluation function. Ether accept the

new solution if the new solution is better than the previous one, or accept the solution in a

certain probability defined by the current temperature.

3.2.5 Online Path Planning

As stated in Chapter 1 (Introduction), while a robot uses the route generated by offline

planning to travel through static obstacles, the online path planner is triggered automatically

to calculate an alternative optimal path when a dynamic obstacle is detected. As no particular

brand or configuration of the sensor is specified, the sensor range of the robot can be

simulated by a fixed value. The distances between the robot and every vertices of the moving

obstacle real-timely get updated. If the distance between the robot and any vertex of the

moving obstacle is shorter than the fixed value, it can be defined that the moving obstacle

enters the range of the sensor, and can be detected by the sensor of the robot. Then, the

separate module as described in assumption (7) (Section 3.1) can monitor the trajectory and

the shape of the moving obstacle. The moving information of the dynamic obstacles gathered

by the sensor of the robot includes speed and moving direction. After the robot combines the

information of the dynamic obstacle with the moving parameter of itself, the robot could

infer the possibility of collision with the moving obstacles.

The simulated annealing optimization algorithm for finding optimal path is triggered when it

is calculated that the robot will collide with the moving obstacle if no change of movement

will be made in the future. The simulated annealing algorithm will be activated and reloaded

with the updated search space. The search space for the algorithm will be updated. The

current status of the robot, the current location information of the dynamic obstacle, the

location information of the dynamic obstacles that could cause the collision and the location

information of the static obstacles are all combined as a new search space for the robot. In a

realistic case, the planning time should be short enough for the robot to implement motion

changes to avoid collision. With the search space becomes larger, as a result, the time

required of planning a path becomes longer. Therefore, an efficient algorithm is required that

its planning time is relatively short for the robot to change the directions to avoid the

54

collision with the obstacles, which is one main aim of our Thesis.

3.3 Platforms for the Research

Algorithm simulating software and system: Matlab 7 and Windows XP Operating System

Hardware equipment: Pentium Core 2 Duo 1.6Ghz Process, 1G RAM

55

Chapter 4 Simulation Results and Performance Evaluation

This chapter presents the simulation results. With these results, the performance of the

simulated annealing based approach is evaluated. Four environments are tested using the

developed approach. The simulation results are compared with those presented in [21] to see

weather the new approach is efficient for path planning in dynamic environments. The

evaluation results clearly illustrate the first main contribution of the Thesis, that the

simulated annealing based approach successfully generates collision free path for the robot in

a dynamic environment. The approach gives improved performance over existing methods.

The calculation time for obtaining the optimal path all-better than genetic algorithm based

approach in [21].

4.1 Simulation Environments and Algorithm Parameters

The approach is tested in four different environments. Each environment contains static and

dynamic obstacles. The path is optimized for length. The solution derived from the algorithm

56

is optimal or near-optimal. The numbers of static and dynamic obstacles in the four testing

environments are summarized in Table 1. The numbers of the vertices for offline planning

are also given in Table 1. The dynamic obstacles in all four cases have random shapes. The

first two environments simulate simple scenarios where the dynamic obstacles appear

simultaneously and simply travel forward in the same direction. The last two environments

are more complicated scenarios where the dynamic objects do not appear simultaneously but

each appears at a random time and moves forward or backward. Also the numbers of the

moving objects and static objects are larger than those of the simple environments. All the

position information of the static obstacles in the map is known to the robot for offline

planning before it starts to travel.

Table 1: Four testing environments

Environment Number of Static

Obstacles

Number of

Dynamic Obstacles

Number of Static

Vertices

1 3 2 10

2 6 2 25

3 9 4 56

4 14 6 90

The control parameters for the simulated annealing algorithm are set in a traditional way.

According to [18], with bigger initial temperature and smaller cooling rate, it is much more

likely to find the optimal solution, but it will require longer processing time for running.

After many times of testing, we set the control parameters of the algorithm as shown in table

2:

Table 2:Control parameters for the simulated annealing algorithm.

Initial Temperature

Terminate Temperature Cooling Rate Deleting

Operator Rate Switching

Operator Rate

999999999 555555555 0.97 78% 22%

57

4.2 Simulation Results

4.2.1 Case One (Three static obstacles with two dynamic obstacles)

A simple environment that contains three static and two dynamic obstacles is tested firstly.

The total number of vertices of the static environment is ten. Fig 30 shows that the robot

firstly uses offline path planning to obtain the optimal path based on static obstacles. Fig 31

shows that if moving obstacle is detected, an alternative path is generated by the online

planner.

Fig 30: Offline Path Planning Fig 31: Online Path Planning

The black full filled blocks in the map above are the static obstacles in the environment, the

hollow triangles are the trajectories of the dynamic obstacles, the sequence of the points are

the travel trajectory of the robot from start to end point. The above figures illustrate the

optimal path has been found and the robot can perform online path planning to find

alternative path for the robot in online path planning mode. Table 3 concludes the calculation

time of online and offline planning and the optimal result for environment one. The

simulation is run for ten times, the results in the table are the median results of the simulation.

Optimised path length and offline and online calculation time are recorded since the results

will be compared with previous results for discussion.

58

Table 3: Results for environment one

Search Space

(Vertices Numbers) 10

Number of

Dynamic Obstacles 2

Number of

Static Obstacles 3

Optimised Path Length

(Base on Static Obstacles) 145.78

Calculation Time for

Offline Planning (Seconds) 0.453


Online Planning (Seconds) 0.573

4.2.2 Case Two (Six static obstacles with two dynamic obstacles)

In case two, a more complex case is presented; the environment contains six static obstacles

with two dynamic obstacles. The same strategy as case one, Fig 32 shows that the robot

firstly uses offline path planning to obtain the optimal path based on static obstacles. Fig 33

shows that if a moving obstacle is detected, an alternative path is generated by the online

planner.

Fig 32: Offline Planning Fig 33: Online Planning 1

59

Fig 34: Online Planning 2

The above figures illustrate the optimal path has been found and the robot can perform online

path planning to find alternative path for the robot in online path planning mode. Fig 34

shows that the robot will use the current route to travel if it is calculated that no collision will

happen between robot and dynamic obstacle. Results in Table 4 show that due to the

increasing search space, the approach needs more time to calculate the optimal path for the

robot.

Table 4: Results for environment two

Search Space


Number of

Dynamic Obstacles 2

Number of

Static Obstacles 6




Offline Planning (Seconds)1.201


Online Planning (Seconds)1.501

60

4.2.3 Case Three (Nine static obstacles with four dynamic obstacles)

In case three, a more complicated environment was involved. Additional four static and two

dynamic obstacles were added in the map. Other than the last two cases above, the dynamic

obstacles in the map do not appear simultaneously and the trajectory of one dynamic obstacle

is not the strait line. The dynamic obstacle can change moving direction during its movement.

Fig 36 shows that the dynamic obstacles do not appear simultaneously in the map. Fig 37

shows that one dynamic obstacle change its trajectory when it is moving.

Fig 35: Offline Planning Fig 36: Obstacles appear on different times.

Fig 37: Online Planning

61

Fig 37 shows the robot uses the online path planner twice to adjust its route safely travelling

to the final destination. Because the map is more complex, the results obtained by the

simulated annealing based approach are not the same each time. However, all the results

obtained by the approach are the optimal or near-optimal results. The following table shows

the median result of ten runs.

Table 5: Results for environment three

Search Space


Number of

Dynamic Obstacles 4

Number of

Static Obstacles 9




Offline Planning (Seconds)3. 418


Online Planning (Seconds)4. 784

4.2.4 Case Four (Fourteen static obstacles with six dynamic obstacles)

Case four is the most complicated case in all four cases. Fourteen static obstacles and six

dynamic obstacles are included in the map. Dynamic obstacles appear randomly on different

times and move in different directions. Also, the dynamic obstacles could change their

moving directions during the movement.

62

Fig 38:Offline Planning Fig 39: Obstacles appear on different times

Fig 40: Online Planning 1 Fig 41: Online Planning 2

As in case three, Fig 39 shows that the dynamic obstacles do not appear simultaneously in

the map. Fig 40 and Fig 41 shows that two dynamic obstacles change their trajectory and the

robot uses the online path planner twice to adjust its rout safely travelling to the final

destination. Table 6 below concludes the obtained path length and calculation time for case

four.

63

Table 6: Results of environment four

Search Space


Number of

Dynamic Obstacles 6

Number of

Static Obstacles 14




Offline Planning (Seconds)10.98


Online Planning (Seconds)13.57

Fig 42 below illustrates the convergence of the algorithm. It is seen from Fig 42 that the

result converges rapidly in each round of temperature reduction. The algorithm could jump

out of the local minimum and approaches to the global minimum. Table 7 concludes the

calculation time of online path planning in four environments.

Fig 42: Convergence of the simulated annealing approach.

64

Table 7: Processing time for online planning for each case.

Environment 1 (10 vertices)

2 (25 vertices)

3 (56 vertices)

4 (90 vertices)

Processing Time (Seconds) 0.57 1.201 4.784 13.57

4.3 Performance Evaluation

The efficiency of the simulated annealing based approach is discussed in this section. The

simulated annealing based approach is compared with the previous results obtained based on

genetic algorithm in [21]. The new genetic based approach in [21] will be introduced firstly

in this section. The genetic based approach is re-implemented in the same hardware on which

simulated annealing based approach is implemented. The comparison results are also

included in this section.

4.3.1 The Genetic Based Approach

Wang, Mulvaney and Sillitoe [21] proposed a genetic based path planning in 2006. The

approach also uses the vertices of the obstacles as search space. Similar to the simulated

annealing based approach, obstacles are described as polygons. The proposed genetic vertex

planning method is compared with the Evolutionary Navigator/Planner [66], and it is claimed

that the performance is better than the Evolutionary Navigator/Planner results. The rest part

of this section introduces the genetic approach; most of the details are from [21]. In genetic

approach, each gene represents a single obstacle vertex selected as an intermediate node. The

solutions are described as chromosomes in the genetic approach. The chromosome in the

genetic approach contains a total number of genes N, whose minimum value is two (a path

containing only the start and goal nodes) and whose maximum value is L + 2, where L is the

total number of vertices in the static map. The gene in the chromosome has two parts, one is

the vertices reference, and the other is the feasibility bit. The feasibility bit for each gene

65

indicates whether the path segment originating from the vertex referenced by the node is

feasible. If the path segment connecting two consecutive vertices intersects any one or more

obstacles, then the feasibility bit of the first node of the path segment is assigned to 1 to mark

this segment as infeasible. If there is no intersection, 0 is assigned to indicate the segment is

feasible. Each population contains 30 of chromosomes. The following figure [21] shows the

structure of a chromosome:

Fig 43: Representation of chromosome in GA approach [21].

The approach use two evaluation functions, one is Ef which is simply the lengths of the

generated paths. Ef is given by:

where d(Vi, Vi+1) demotes the distance between the referenced pair of vertices. The other

evaluation function Ei indicates how deeply an infeasible path segment intersects with an

obstacle and is given by:

Where denotes the number of the obstacle intersections along the entire path and

is the mean number of intersections per infeasible segment. When the population contains

both feasible and infeasible paths, the infeasible paths are all assumed to be worse than the

worst feasible path.

Three genetic operators are used in the genetic approach, crossover, mutation and repair. The

crossover operator randomly selects two crossover points; the parts after the crossover points

of the two parent individuals are swapped. The mutation operator uses another vertex to

66

replace the selected vertex. The repair operator adjusts a randomly selected infeasible

segment of an infeasible path. Fig 44 illustrates the repair operation:

Fig 44: The Repair Operator [21]

The evaluation process is as the standard GA approach; only one genetic operator is selected

to produce the offspring for the approach. Each generation contains 30 chromosomes and

evolution was terminated when there was no further improvement in the fitness of the best

individual over 300 generations. The following are the copy of the pseudo-code from [21]:

Procedure vertex planning algorithm

begin

t = 0

enlarge the obstacles

encode the vertices of the obstacles

initialise P(t)

decode P(t)

evaluate P(t)

while (not terminating condition) do

67

t = t+1

select operator Oi with probability Pj

select parent (s) from P(t)

apply the operator Oj to produce offspring

decode offspring

evaluate new offspring

replace worst member in P(t) by offspring

end

select the best individual p from P(t)

end

4.3.2 Results Comparison

Three environments are used to make comparison of the approaches. One environment is

selected from the cases in [21], and other two cases are the case 3 and case 4 in the simulated

annealing approach simulation in last chapter. The search space for the two approaches is the

number of the vertices in the map. First environment has 5 static obstacles which has total

number of 22 vertices in the map. Second environment has 9 static obstacles which has 56

vertices in the map. The last environment has 14 obstacles which are constituted by 90

vertices. The termination conditions of the two approaches are:

(1) Termination condition of the simulated annealing approach is the parameter

termination temperature terminT which is predefined at the start of the approach.

(2) As in [21], the genetic based approach terminates when noticing that there is no

improvement on path length after 300 generations.

Every approach was run 10 times on each environment. The results in the Table 9 and Table

10 are the medians obtained over 10 runs on each environment. Table 9 and Table 10 present

the comparison results of the execution time to get the final path and the final path length

from the two approaches:

68

Table 8: Three environments for performance evaluation.

Environment Number of Static

Obstacles

Number of Total

Vertices

1 5 22

2 9 56

3 14 90

Table 9: Comparison of execution time of getting the final path (Seconds).

Environment Simulated Annealing

Algorithm Based Approach

Genetic Algorithm Based

Approach

1 1.01 6.90

2 3.69 21.78

3 12.01 29.78

Table 10: Comparison of the length of the final path.

Environment Simulated Annealing

Algorithm Based Approach

Genetic Algorithm Based

Approach

1 258.477 259.455

2 291.690 351.238

3 429.022 469.580

Fig 45 compares the offline execution time of two approaches base on same vertices numbers.

It shows that the simulated annealing algorithm based approach consumes a shorter time in

path planning than the genetic algorithm based approach.

69

Fig 45:Comparism of execution time based on same vertices number.

Fig 46 compares the final optimal path lengths obtained by two approaches base on same

vertices numbers. It shows the solutions are improved in the simulated annealing algorithm

based approach.

Fig 46: Comparison of final path length based on same vertices number.

For comparing the convergence and the optimisation efficiency of the two approaches, from

each case, selecting the individual runs that produce similar path length results. And

comparing the convergence and efficiency base on the time elapses in two approaches.

70

Environment 1 (22 Vertices):

Final Path Length: 259.27

GA Processing Time: 6.969 Seconds (Dashed Line)

SA Processing Time: 1.107 Seconds (Solid Line)

Fig 47: Convergence comparison in environment one.





Fig 48: Convergence comparison in environment two.

71





Fig 49: Convergence comparison in environment three.

In paper [21], insufficient information is provided about the implementation of the genetic

operators in the approach. For example, in [21], how to implement the repair operator in the

approach is not clearly specified. Therefore, the differences of implementing the genetic

operators between this paper and [21] may slightly affect the simulation results on our

hardware. Thus, the simulation results of genetic based approach in our hardware may be

slightly different than the simulation results in [21]. However, as Fig 50 shows: environment

one with 25 vertices is established to build a mimic environment one in [21], and the

simulation result in environment one could produce similar results as in [21]. Therefore the

genetic approach implemented on our hardware could illustrate a comparative performance

to [21]. Therefore, the comparison could show that the performance of the simulated

annealing based approach is comparable or even more efficient than the genetic based

approach in [21]. The simulated annealing based approach is able to use shorter processing

time to determine the optimal path in the environment.

72

0 20 40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200

Start Point

End Point

Fig 50: Environment One Fig 51: Environment One From [21]

73

Chapter 5 Heuristic Search Method for the Simulated Annealing

Approach

This chapter proposes a heuristic search method to further improve the simulated annealing

approach for robot in dynamic environment. The simulation results show that the heuristic

method can greatly improve the efficiency of simulated annealing approach in offline and

online planning for robots in dynamic environments. The simulation results in this chapter

can totally illustrate the second main contribution of this Thesis.

5.1 The Structure and Implementation of the Heuristic Selecting Method

From Chapter 3 (Implementation of the Simulated Annealing Algorithm Approach), it is

known that in finding the optimal path, the simulated annealing approach needs firstly

selecting a random feasible path, then apply a mathematic operator to generate a new path

base on the selected feasible path. The initial selected path is the beginning of the search

point; the initial solution is replaced by the randomly generated neighbour solution. The

search goes along “down hill” movement from the initial solution. Then, as temperature goes

74

down, the algorithm accepts the “up hill” movement to avoid being stuck at local minimus.

Therefore, a better initial solution means a better initial searching point, which could enhance

the efficiency and the performance of the approach.

From Chapter 3 (Implementation of the Simulated Annealing Algorithm Approach), the way

of generating the initial path was illustrated as follows:

• Firstly, except dynamic objects, starting point and end point, a vertex is chosen

randomly from the map, use strait-line to connect the start point and the selected

vertex.

o If the path line intersects with any edges of the obstacle in the map, the path is

recognized as invalid path. Another vertex will be randomly selected again for

testing.

o If the strait-line to the selected vertex does not intersect with any edges in the

map, the strait line is recognized as part of a valid path. Then add the vertex

into the path.

• Then, start from the selected vertex to find the next valid vertex. Keep performing

the above procedure until the end point is selected and also the path line to the end

point is a valid path (i.e., the path to the end point does not intersects with any

edges).

The method just randomly picks a feasible vertex until the end point is picked. The blindly

picking is not an efficient way of producing the initial path.

To improve the efficiency of the initial solution selecting process, a heuristic process is

proposed in this Chapter. The process makes a modification on the current method. In current

method, a random vertex is selected after one feasible vertex is select, and then tests the

feasibility of the line segment between randomly selected vertex and the feasible vertex.

In the proposed heuristic method, after one feasible vertex is select, an end point feasibility

test will be carried out before selecting another vertex. Before selecting next vertex, the

method will firstly test whether the line segment between the feasible vertex and the end

point is feasible (does not interest with any obstacles). If the segment between the feasible

75

vertex and the end point is feasible, then put the end point as the next vertex and complete

the selection process. The following pseudo-codes and Fig 52 illustrates the process of the

heuristic initial path selection method.

initial path IP = {start};

while (1)

if path{IPend, Destination Point} is a feasible path

IP = {IP, Destination Point};

break;

endif;

randomly select Vs;

if path{IPend, Vs} intersects any obstacles;

continue;

else

IP = {IP,Vs};

endif

if Vs == destination point;

break;

else

continue;

endif

endwhile

76

Fig 52: Process of the heuristic selection method.

Fig 53 and Fig 54 show the difference between the random picking method in normal

simulated annealing algorithm and the proposed heuristic method. Fig 53 shows it is possible

that it requires five times of random picking to find a feasible path to the end point. And Fig

54 shows that if testing the end point feasibility before random selection, a better feasible

path may be obtained.

77

Fig 53: Random picking method. Fig 54: Heuristic picking method.

The heuristic method could improve the approach in two aspects:

• One is that the method could enhance the quality of the solution, i.e., a shorter path

length solution, obtained by the approach. Fig 54 above shows that the heuristic

method may generate a better initial path than the randomly picking method. The

better initial path means the better searching beginning, which may lead a better

solution.

• The other improved aspect is the processing time of getting the solution. After each

feasible vertex is selected, the heuristic method firstly checks the feasibility of the

line segment to the end point rather than randomly select next vertex. Therefore, the

processing time of selecting vertices could be reduced by the heuristic method.

In fact, the heuristic method could be used not only in the simulated annealing approach, but

also in any other mathematic methods which generate initial solution for calculation.

78

5.2 Performance Evaluation of the Heuristic Method

To test the performance of the heuristic method, the random picking process is replaced by

the heuristic method in the simulated annealing approach, and the modified simulated

annealing approach is tested by the same four environments as those in Chapter 4

(Simulation Results and Performance Evaluation). The simulation results of the modified

simulated annealing based approach are compared with those obtained in Chapter 4. The

following are the compared results of the two methods:

5.2.1 Environment One (Three static obstacles with two dynamic obstacles):


79

Table 11: Results of comparison in case one (3 static and 2 dynamic obstacles).

Environment One

Random

Picking

Method

Heuristic

Method Improvement

Optimal Path Length 145.78 145.78 0%

Calculation Time

(Offline Planning)

(Seconds)

0.453 0. 447 1.34%

Calculation Time

(Online Planning)

(Seconds)

0.573 0. 335 41.54%

5.2.2 Environment Two (Five static obstacles with two dynamic obstacles):


80

Table 12: Results of comparison in case two (5 static and 2 dynamic obstacles).

Environment Two

Random

Picking

Method

Heuristic

Method Improvement

Optimal Path Length 257.25 246.28 4.26%

Calculation Time

(Offline Planning)

(Seconds)

2.453 0.793 67.67%

Calculation Time

(Online Planning)

(Seconds)

2.573 0.822 68.15%

5.2.3 Environment Three (Nine static obstacles with four dynamic obstacles):


81

Table 13: Results of comparison in case three (9 static and 4 dynamic obstacles).

Environment Three

Random

Picking

Method

Heuristic

Method Improvement


Calculation Time

(Offline Planning)

(Seconds)

3.418 1.411 58.72%

Calculation Time

(Online Planning)

(Seconds)

4.784 1.562 67.35%

5.2.4 Environment Four (Fourteen static obstacles with six dynamic obstacles):

Fig 61: Random picking method. Fig 62: Heuristic picking method

82

Table 14: Results of comparison in case four (14 static and 6 dynamic obstacles).

Environment Four

Random

Picking

Method

Heuristic

Method Improvement


Calculation Time

(Offline Planning)

(Seconds)

10.98 2.796 74.54%

Calculation Time

(Online Planning)

(Seconds)

13.57 2.96 78.19%

5.3 Discussions of the Evaluation Results

From the comparison results presented above in Section 5.2, it can be seen that the heuristic

search method can greatly enhance the performance of the simulated annealing based

approach in dynamic environments. The heuristic method can accelerate the calculation in

online and offline planning modes and can reduce the optimal path length obtained,

especially in complex environments. The evaluation results clearly show the second main

contribution of the Thesis, the heuristic method is successfully incorporated in the simulated

annealing algorithm based approach and can boost the efficiency of the approach.

5.3.1 Offline Planning

In offline planning calculation,

• In the simple environment with 3 static obstacles, the heuristic method improves the

offline processing time by 1.34%.

• In the environment with 5 static obstacles, the heuristic method improves the offline

83

processing time by 67.67%.

• In the environment with 9 static obstacles, the heuristic method improves the offline

processing time by 58.72%.

• The heuristic method gives nearly 74.54% improvement in offline processing time in

finding the optimal path in the environment with 14 static obstacles.

5.3.2 Online Planning

In online planning mode, the heuristic method improves the online processing time by

• 41.54% in environment 1;

• 68.15% in environment 2;

• 67.35% in environment 3 with 9 static obstacles; and

• 78.19% in environment 4 with 14 static obstacles.

5.3.3 The Length of the Path

The heuristic method improves the obtained optimal path by 4.26% in environment 2, and it

improves the optimal path by 3.62% and 4.12% in environment 3 and environment 4

respectively.

Fig 63 compares the optimised path length solution on each case. Fig 64 and Fig 65 compare

the offline and online processing time of the two methods on each environment. Table 15

summarizes the new heuristic method improvements on the processing time and the optimal

path length base on four environments. It can be seen that the heuristic method is far superior

to the random picking method and should be used by the simulated annealing algorithm

based approach in complex environment especially in online path planning calculations.

84

Fig 63: Path solution comparison.

Fig 64:Offline processing time comparison. Fig 65: Online processing time comparison.

Table 15: Conclusion of the improvements.

Environment Improvements

(Offline Planning)

Improvements

(Online Planning)

Improvements

(Optimal Path)

1 (10 Vertices) 1.34% 41.54% 0%

2 (25 Vertices) 67.67% 68.15% 4.26%

3 (56 Vertices) 58.73% 67.15% 3.62%

4 (90 Vertices) 74.54% 78.47% 4.12%

85

5.3.4 Comparison with the Genetic Algorithm Based Approach

Finally, the performance of the heuristic simulated annealing based approach is compared

with the performance of the normal simulated annealing approach and the genetic algorithm

based approach. The heuristic based simulated annealing approach is implemented on the

three test environments in Section 4.3.2 to compare the offline processing time of three

approaches. Compared with the genetic algorithm based approach; the heuristic method

improves the offline processing time by 88.69% in environment 1 with 5 static obstacles. The

heuristic method improves the offline processing time by 93.07% and 90.03% in

environment 2 with 9 obstacles and environment 3 with 14 obstacles respectively. Fig 66

concludes the calculation time performance of the heuristic method based simulated

annealing approach, the basic simulated annealing approach, and the genetic algorithm based

method.

Compared with the genetic algorithm based approach; the heuristic method improves the

obtained optimal path by 0.38% in environment 1 with 22 vertices, and it improves the

optimal path by 20.96% and 11.33% in environment 2 and environment 3 respectively. Fig

67 concludes the performance of obtaining the optimal path in the three methods. Fig 66 and

Fig 67 clearly show that the heuristic method based simulated annealing approach gives the

best performance. Therefore, it can be concluded that the new heuristic method for simulated

annealing algorithm gives superiority to other methods in path planning on vertices based

complicate environment, and it should be used in simulated annealing based approach to deal

with the path planning issue in dynamic environment.

86

Fig 66: The comparison of the three methods in processing time.

Fig 67: The comparison of the three methods in final path length.

87

Chapter 6 Conclusion

This chapter summarizes the Thesis, and discusses the research limitations of the project.

Future research on the simulated annealing based approach will also be discussed.

6.1 Summary

This thesis has developed and implemented a simulated annealing based approach in Chapter

3 to deal with path planning issue for robots in dynamic environment – this is one of the

main contributions of the thesis. The approach uses the vertices of the static and dynamic

obstacles as search space to obtain the optimal path for robots, the approach searches the

initial feasible path for robot in dynamic environment which contains static and dynamic

obstacles, then uses simulated annealing algorithm to obtain the optimal path for the robot in

the dynamic map. Compared with the genetic based approach in [21], the simulation results

in Chapter 4 show that the simulated annealing based approach provides a better

performance in processing time, and is crucial for a robot to quickly response to avoid

88

collision with the dynamic obstacles.

The thesis has also proposed a heuristic search method in Chapter 5 to search the initial path

– this is another main contribution of the thesis. The heuristic method has been incorporated

into the developed simulated annealing algorithm based approach to greatly enhance the

performance of the path planning in both online and offline calculations. The experiment

results show that the heuristic search method can improve not only the processing time of

offline and online planning but also the quality (path length of the solution) of the solution.

The percentage of the improvement in online processing time ranges from 41% to 78% in

our simulated environments for dynamic path planning.

The novelty of the project is the implementation of a simulated annealing based approach

incorporated with a heuristic selecting method for robot path planning in dynamic

environments with moving obstacles. The approach is simpler and easier to implement than

existing genetic algorithm based methods. As the method is able to quickly determine the

optimal feasible path for robot in dynamic environments, it could be used in marine research

robot such as [3] and [2]. Also, the heuristic selecting method can enhance the efficiency of

the simulated annealing based approach. Furthermore, the heuristic selecting method can also

be used in other optimisation methods which need to generate an initial feasible solution for

calculation.

6.2 Research Limitations

The project successfully implements the simulated annealing based approach incorporated

with a heuristic selecting method to plan path for mobile robots in dynamic environments.

However, there are still some research limitations in the project. The limitations of the

project are described below:

1) The shape of the robot is ignored in the project though the dimensions of the obstacles are

considered for calculation. This is a topic that has not been systematically investigated in

the dynamic path planning for mobile robots. Saboori and Menhaj [67] proposed a robot

89

path planning method that is based on fuzzy model. The method implements Dijkstra

algorithm to find an optimum path for in an area with static obstacles for the robot. The

dimensions of the robot and the obstacles have been taken into consideration to have a

more realistic and efficient technique. However, the research and the simulation

experiments are constrained in static environments. Therefore, taking the dimension of

the robot into consideration in dynamic environments is a future issue.

2) In the project, no particular brand or configuration of the sensor is specified. The sensor

is assumed to be able to acquire the motion information such as the speed and direction of

the moving obstacles once the obstacles are in the sensor range. For a more realistic

modelling, how the sensor obtains the motion information of the dynamic obstacle should

be modelled and discussed.

6.3 Future Work

Though the simulated annealing based approach solves the issue of obtaining the optimal

path in dynamic environments, some work is still expected to be done in the future:

1) For a more realistic modelling, a more complex and realistic environment shall be used

and tested using the simulated annealing approach. The environments in the project are

described in a two-dimensional surface and the trajectories of the dynamic obstacles are

constituted by a series of line segments. For modelling a more realistic environment for

robot, a three-dimensional modelling is expected and the trajectories of the dynamic

obstacles can be curves instead of strait line segments. The three-dimensional

environment still uses vertices as search space; the only difference is that the calculation

should add Z coordinate.

2) As stated in Section 6.2 about research limitations, for a more realistic modelling, the

method used by the sensor to obtain the motion information of the dynamic obstacle

should be further investigated. More research should be done to discuss the detailed

method on how the sensor acquires the motion information of dynamic obstacles (e.g.

90

using which sensor? What is the appropriate mathematical method?).

3) Implementing the simulated annealing approach on a more realistic robot simulator, such

as the Player/Stage [65] application. Successfully implementing the simulated annealing

approach into Player/Stage provides a more practical environment than Matlab which

only uses mathematic model to demonstrate the ability of algorithm. The implementation

of the new method on Player/Stage not only demonstrates the feasibility of method but

also provides a more practical testing environment for the new method.

91

References [1] J. Cook, “Adding Intelligence to Robot Arm Path Planning Using a Graph-Match

Analogical Reasoning System” IEEE International Conference on Intelligent Robots and

Systems, vol. 1, pages 657-663, July 1992

[2] J. Ayers, “Underwater Walking”, Arthropod Structure & Development, vol. 33, pages

347-360, July 2004

[3] B. Williams and I. Mahon, “Design of An Unmanned Underwater Vehicle For Reef

Surveying”, Proceedings of IFAC 3rd Symposium on Mechatronic Systems, Sept 2004

[4] H. Mitchell, “An algorithmic approach to some problems in terrain navigation”, Artificial

Intelligence, vol. 37, pages 171–201, Dec 1988

[5] C. O’Dunlaing, and C. Yap, “A retraction method for planning the motion of a disc”,

Journal of Algorithms, vol. 6, pages 104–111, 1982

[6] D. Payton, J. Rosenblatt and D. Keirsey, “Grid-based mapping for autonomous mobile

robot”, Robotics and Autonomous Systems, vol. 11, pages 13–21, 1993

[7] N. Kalra, D. Ferguson and A. Stentz, “Incremental Reconstruction of Generalized

Voronoi Diagrams on Grids”, Robotics and Autonomous Systems, vol. 57, pages 123 –

128, Feb 2009

[8] P. Zhang, T. Lu and L. Song, “Soccer Robot Path Planning Based on the Artificial

Potential Field Approach with Simulated Annealing”, Robotica, vol. 22, pages 563-566,

Oct 2004

[9] B. Stuckman, G. Evans and M. Mollaghasemi, “Comparison of Global Search Methods

92

for Design Optimization Using Simulation”, Proceedings of the Winter Simulation

Conference, pages 937-945, Dec 1991

[10] S. Russell, P. Norvig, “Artificial Intelligence: A Modern Approach”, Prentice Hall, pages

97-104,2003

[11] A. Stentz, “Optimal and Efficient Path Planning for Partially-Known Environments”,

Proceedings of the IEEE International Conference on Robotics and Automation, pages

3310 – 3317, May 1994

[12] D. Rathbun and S. Kragelund, “An Evolution Based Path Planning Algorithm for

Autonomous Motion of a UAV Through Uncertain Environments”, IEEE International

Conference on Digital Avionics Systems Conference, vol. 2, pages 8.D.2.1 – 8.D.2.12,

Oct 2002

[13] Introduction of Simulated Annealing Algorithm, Internet Source,

<http://en.wikipedia.org/wiki/Simulated_annealing >, From Wikipedia, the free

encyclopedia, Viewed in 11th Oct. 2007

[14] Y. Wang, P. Sillitoe, J. Mulvaney, “Mobile Robot Path Planning in Dynamic

Environments”, IEEE International Conference on Robotics and Automation, pages

71-76, May 2007

[15] Q. Zhu, Y. Yan and Z. Xing, “Robot Path Planning Based on Artificial Potential Field

Approach with Simulated Annealing”, Proceedings of the Sixth International

Conference on Intelligent System Design and Applications, vol. 2, pages 622-627, Oct

2006

[16] P. Zhang and T. Lv, “Soccer Robot Path Planning Based on Artificial Potential Field

Approach with Simulated Annealing”, Mechanical Science and Technology, vol. 22,

pages 624-629, Oct 2003

93

[17] Y. Peng and W. Wei, “A New Trajectory Planning Method of Redundant Manipulator

Based on Adaptive Simulated Annealing Genetic Algorithm”, Proceedings of IEEE the

Sixth International Conference on Intelligent System Design and Applications, vol. 1,

pages 262-266, Nov 2006

[18] J. Park, D. Nam and C. Park, “An Empirical Comparison of Simulated Annealing and

Genetic Algorithms on NK Fitness Landscapes”, Proceeds of IEEE the Sixth

International Conference on Evolutionary Computation, pages 147-151, Apr 1997

[19] E. Burke and G. Kendall, “Comparison of Meta-Heuristic Algorithms for Clustering

Rectangles”, Proceedings of the 24th International Conference on Computers and

Industrial Engineering, vol. 3, pages 383-386, Sept 1999

[20] J. Perez and J. Basterrechea, “Comparison of Different Heuristic Optimization Methods

for Near-Field Antenna Measurements”, IEEE Transaction on Antennas and

Propagation, vol. 55, pages 549 – 555, March 2007

[21] Y. Wang; D. Mulvaney; I. Sillitoe, “Genetic-based Mobile Robot Path Planning using

Vertex Heuristics”, IEEE International Conference on Cybernetics and Intelligent

Systems, pages 1 – 6, June 2006

[22] P. Tang, Q. Zhang, Y. Yang, “Studying on path planning and dynamic obstacle avoiding

of soccer robot” Proceedings of the 3rd World Congress on Intelligent Control and

Automation, vol. 2, pages 1244- 1247, July 2000

[23] Q. Cao, Y. Huan and J. Zhou, “An Evolutionary Artificial Potential Field Algorithm for

Dynamic Path Planning of Mobile Robot” International Conference Proceedings on

Intelligent Robots and System, pages 3331-3336, Oct 2006

[24] P. Zhang, T. Lu, “Soccer Robot Path Planning based on the Artificial Potential Field

94

Approach with Simulated Annealing”, Robotica, vol 22, pages 563 – 566, Oct 2004

[25] A. Stentz, “The Focussed D* Algorithm for Real-Time Replanning”, Proceedings of the

International Joint Conference on Artificial Intelligence, pages 1652-1659, Aug 1995

[26] A.Yahja, S. Singh and A. Stentz, “An Efficient Online Path Planner for Outdoor Mobile

Robots Operating in Vast Environments”, Robotics and Autonomous Systems, vol 22,

pages 129-143, 2000

[27] A. Yahia, A.Stentz, S. Singh and B. Brummit, “Framed-Quadatree Path Planning for

Mobile Robots Operating in Sparse Environments”, IEEE Conference on Robotics and

Automation, vol. 32, pages a129-143, May 1998

[28] D. Ferguson and A. Stentz, “Field D*: An Interpolation-based Path Planner and

Replanner”, Intermational Symposium on Robotics Research, vol. 8, pages 239-253, Oct

2005

[29] A. Nearchou, “Path planning of a mobile robot using genetic heuristics”, Robotica, vol.

16, pages 575–588, Sept 1998.

[30] C. Yap, “Algorithmic motion planning” in Advances in Robotics vol. 1: Algorithmic and

Geometric Aspects of Robotics, Eds. Hillsdale, New Jersey: Lawrence Erlbaum, pages

95-143, 1987

[31] W. Regli, “Robot Lab: Robot Path Planning”, Lecture Notes of Department of Computer

Science, Drexel University, Viewed at 20th Oct 2007

[32] O. Khatib, “Real-time Obstacle Avoidance for Manipulators and Mobile Robots”, IEEE

Conference on Robotics and Automation, vol. 2, pages 500-505, Jan 1985

[33] Y. Davidor, “Genetic algorithms and robotics: a heuristic strategy for optimization”,

95

Singapore: World Scientific Publishing, vol. 1, pages 220-225, 1991

[34] J. Cai, M. Peng and S. Ma, “RL-ART2 Neural Network Based Mobile Robot Path

Planning”, Proceedings of the IEEE Sixth International Conference on Intelligent

System Design and Applications, vol. 2, pages 581-585, Oct 2006

[35] M. Scott, “An introduction to genetic algorithms”, Journal of Computing Sciences in

Colleges, vol. 20, pages 115-123, Oct 2004

[36] C. Edelman, M. Franklin, and M. Witte, “Simulated Annealing on a Multiprocessor”,

Proceedings of the 1988 IEEE International Conference on Computer Design: VLSI in

Computers and Processors, pages 540 – 544, Oct 1988

[37] P. Hart, N. Nilsson and B. Raphael, “A Formal Basis for the Heuristic Determination of

Minimum Cost Paths”, IEEE Transaction on Systems Science and Cybernetics, vol. 4,

pages 100–107, July 1968

[38] F. Lingelbach, “Path planning for mobile manipulation using probabilistic cell

decomposition”, Intelligent Robots and Systems, 2004. (IROS 2004). Proceedings,

IEEE, vol 3, pages 2807-2812, 2004

[39] J. Rosell and P. Iniguez “Path planning using Harmonic Functions and Probabilistic Cell

Decomposition”, Proceedings of IEEE International Conference on Robotics and

Automation, pages 1803-1808, Apr 2005

[40] Lecture Note, “Robot Motion Planning”, Department of Computer Science, University

of Mcgill, Viewed at 20th Oct 2007

[41] M. Park and M. Lee, “Experimental evaluation of robot path planning by artificial

potential field approach with simulated annealing”, Proceedings of SICE 2002 Annual

Conference, vol. 4, pages 2190-2195, Aug 2002

96

[42] N. Ying and L. Eicher, “Real-time 3D path planning for sensor-based underwater

robotics vehicles in unknown environment”, OCEANS 2000 MTS/IEEE Conference and

Exhibition, vol 3, pages 2051-2058, Sept 2000

[43] M. Park and M. Lee, “Real-time path planning in unknown environment and a virtual

hill concept to escape local minima”, IEEE Conference on Industrial Electronics Society,

vol 3, pages 2223-2228, Nov 2004

[44] Y. Chang, Y. Yamamoto, “Online Path Planning Strategy Integrated with Collision and

Dead-lock Avoidance Schemes for Wheeled Mobile Robot in Indoor Environment”,

Industrial Robot-An International Journal, vol 35, pages 421 – 434, 2008

[45] L. Xie, H. Chen, “Solution to Reinforcement Learning Problems with Artificial Potential

Field”, Journal of Central South University of Technology, vol 15, pages 552 – 557,

Aug 2008

[46] J. Vanualailai and B. Sharma, “An Asymptotically Stable Collision-avoidance System”,

International Journal of Non-linear Mechanics, vol 43, pages 925 – 932, Nov 2008

[47] T. Wan; H. Chen and R. Earnshaw, “Real-time path planning for navigation in unknown

environment”, International Conference on Theory and Practice of Computer Graphics,

pages 138-145, June 2003

[48] M. Mansor and A. Morris, “Path Planning in Unknown Environment With Obstacles

Using Virtual Window”, Journal of Intelligent and Robotic Systems, vol 24, pages 235 –

251, Mar 1999

[49] X. Hu, Q. Xu, “Robot Path Planning based on Artificial Immune Network”, IEEE

International Conference on Robotics and Biomimetics, pages 1053 – 1057, Dec 2007

97

[50] X. Hu, C. Xie “Niche Genetic Algorithm for Robot Path Planning” The Third IEEE

International Conference on Natural Computation, vol. 2, pages 600-605, Aug 2007

[51] J. Chestnutt and M. Lau, “Footstep Planning for the Honda ASIMO Humanoid”, IEEE

International Conference on Robotics and Automation, pages 629-634, Apr 2005

[52] S. LBszlo and K. Annamiria, “Autonomous navigation in a known dynamic

environment”, The 12th IEEE International Conference on Fuzzy Systems, vol. 1, pages

266-271, May 2003

[53] N. Lv and Z. Feng, “Numerical Potential Field and Ant Colony Optimization Based Path

Planning in Dynamic Environment”, The Sixth IEEE World Congress on Intelligent

Control and Automation, vol 2, pages 8966- 8970, Oct 2006

[54] T. Zheng and X. Zhao, “A Novel Approach for Multiple Mobile Robot Path Planning in

Dynamic Unknown Environment”, IEEE Conference on Robotics, Automation and

Mechatronics, pages 1-5, Dec 2006

[55] M. Tarokh, “Hybird Intelligent Path Planning for Articulated Rovers in Rough Terrain”,

Fuzzy Sets and Systems, vol 159, pages 2927 – 2937, Nov 2008

[56] L. Hu, Z. Gu, “Research and Realization of Optimum Route Planning in Vehicle

Navigation Systems based on a Hybrid Genetic Algorithm”, Proceedings of the

Institution of Mechanical Engineers part D-Journal of Automobile Engineering, vol 22,

pages 757 – 763, May 2008

[57] L. Huang, “Velocity Planning for a Mobile Robot to Track a Moving Target – A

Potential Field Approach”, Robotics and Autonomous Systems, vol 57, pages 55 – 63,

Jan 2009

[58] A. Willms, S. Yang, “Realtime Robot Path Planning via a Distance-Propagating

98

Dynamic System with Obstacle Clearance”, IEEE Transactions on System, Man, and

Cybernetics, vol 38, pages 884 – 893, Jun 2008

[59] J. Schneider, S. Kirkpatrick, “Stochastic Optimization”, Springer Berlin Heidelberg,

pages 299 – 314, 2006 [60] Z. Lo and Z. Bavarian, “Job scheduling on parallel machines using simulated annealing”,

IEEE International Conference on Decision Aiding for Complex Systems, vol. 1,

pages 391-396, Oct 1991

[61] Y. Zhu, S. Yan, “A Knowledge based Genetic Algorithm for Path Planning of a Mobile

Robot”, IEEE International Conference on Robotics and Automation, vol 5, pages 4350

– 4355, May 2004

[62] R. Zhang and P. Lu, “Beyond quadtrees: Cell decompositions for path planning using

wavelet transforms”, The 46th IEEE International Conference on Decision and

Control, pages 1392-1397, Dec 2007

[63] EyeSim: EyeBot Simulator, Free Internet Source,

<http://robotics.ee.uwa.edu.au/eyebot/doc/sim/sim.html>, Viewed in 11th Feb. 2008

[64] X. Yan, W. Li and D. Chen “A New Mechanism for Robots Control Based on

Player/stage” Proceedings of International Conference on Robotics and Biomimetics,

pages 750-754, Dec 2006

[65] P. Gerkey, T. Vaughan, A. Howard, “The Player/Stage Project: Tools for Multi-Robot

and Distributed Sensor Systems” Proceedings of the International Conference on

Advanced Robotics, pages 317-323, July 2003

[66] J. Xiao, “Evolutionary planner/navigator in a Mobile Robot Environment”, Handbook of

Evolutionary Computation, IOP Publishing Ltd, pages G3.11: 1 – G3.11: 13, Jan 1995

99

[67] I. Saboori and M. Menhaj, “Optimal Robot Path Planning Based on Fuzzy Model of

Obstacles”, IEEE 32nd Annual Conference on Industrial Electronics, pages 383-387,

Nov 2006

Master by Research Thesis - QUT · Master by Research Thesis By Hui Miao Student No.: 06478689...

Documents

Transcript of Master by Research Thesis - QUT · Master by Research Thesis By Hui Miao Student No.: 06478689...