Post on 05-Jan-2016
description
Path-Finding with Motion Constraints Amongst Obstacles
in Real Time StrategiesBy Jeremiah J. Shepherd
Committee:Jijun Tang
Roger DougalJason O’Kane
Introduction
• Most video games have some form of path-finding
• Methods for finding paths are primitive– Motion Constraints not easily implemented– Agent movement is not realistic
• Some games fabricate path realism
Introduction
• Real Time Strategies (RTS) are notorious for simple path-finding
• “In an RTS, as in other wargames, the participants position and maneuver units (agents) and structures under their control to secure areas of the map and/or destroy their opponents' assets.” (Gervk)
Introduction
• Path-finding in RTS’s generally involves these steps:– A unit and destination for the unit is selected– An obstacle free path is the calculated by
using an algorithm like A*– The path is followed by a “move-rotate-move”
method
Introduction
• These paths can be created in this fashion because of the structure of the environment
• The environment is generally a grid– The size an number of cells are known– Obstacles exist in the environment and are
known– Each grid cell has an occupancy flag
Introduction
Old Game Path-finding Example
• Command and Conquer
New game path-finding example
• Halo Wars
Introduction
• A problem emerges when adding motion constraints to these paths– Paths found may not reach the destination– Paths are no longer guaranteed to be
obstacle free
Introduction
Introduction
• The method I propose uses an algorithm found in motion planning and path-finding for robotics
• Combines plans and paths found with the algorithm with carefully crafted data structures
• Paths with motion constraints could be calculated in real-time
Related Work
• Rapidly Exploring Random Trees (RRT) is an algorithm that can find a path and a motion plan that adheres to motion constraints
Related Work
• Goal biased RRT’s work by:1. Choose the point nearest to the goal state in the
tree and attempt to connect the two2. If it succeeds in connecting then a path and a plan
is found3. Else choose a random point in the configuration
space 1. Find the point in the tree nearest to the random point2. Choose actions that will incrementally move toward the
new point, creating new points in the tree
4. Repeat until goal is reached or it is determined that the goal is unreachable
Related Work
Related Work
• Why not use RRT’s?– They are inconsistent in regards to speed– In previous tests, the range of time it took to
find a path and motion plan was from six seconds to two minutes
Related Work
• Previous Attempts (Trail of Tears)– Tube Guided RRT– Preprocessing with Motion Planning Matrix
and Environment Matrix (MPM&EM)
Related Work
• Tube Guided RRT– Use a tube to constrict sampling– The less samples the faster it will find a path
• Algorithm– Draw a Probablistic Road Map (PRM)– Find the shortest path on the PRM– Construct a tube with the width the size of the
turning radius around the path– Run the RRT, only sampling points in the tube
Related Work
Related Work
• Tube Guided RRT Problems– It ran on par with a regular RRT– Some cases it took much longer than a
regular RRT– More inconsistent than a regular RRT
Related Work
• MPM&EM– The broad idea is to piece together small
paths and motion plans to create a large motion plan and path
– There are two stages to this algorithm• Offline Stage• Online Stage
Related Work
• The Smallest Turning Radius Square (STRS) is important to both stages
• Contains a full turn to the left and right
Related Work
• Offline Stage– Create the environment matrix (EM)– Create an initial motion plan matrix (MPM)– Add references in the environment matrix (EM) and
the calculate the final (MPM)
• Online Stage– Traverse the EM from the starting state to the goal
state– Follow the motion plans stored in the MPM as
referenced by the information in the EM cells
Related Work
Related Work
Related Work
• Create an initial motion plan matrix (MPM)– 3D data structure based on the x, y and in
the configuration space– Contains potential motion plans that can be
used when the STRS is obstacle free – A special environment is used for this step
• All paths are contained inside of the STRS
Related Work
Related Work
The Algorithm – Offline Stage
Related Work
• Create the EM continued– For all the points in the EM and for all the
points in the STRS at that EM find and store a motion plan and path
– If a motion plan is collision free in the MPM then a reference to that plan is stored in the EM
– Else calculate a new motion plan store that in the MPM and store a reference to that in the EM
Related Work
Related Work
Related Work
• From the starting point calculate a path using A*– The points that lay on the outer edge of
the STRS are given higher priority
• Traverse the EM using the path
• Create a full motion plan with the references in the EM to the MPM
Related Work
Related Work
Related Work
• Problems with MPM&EM– Uses too much memory
– Paths can look very unnatural
New Algorithm
• Principles– Similar idea of piecing together smaller
paths
– FORGET RRT’s!
– Use Dubin’s curves to find paths
New Algorithm
• Dubins Car– It finds the shortest path for a
nonholonomic model in an obstacle free environment
– The car that only moves forward
– The car can only steer all the way right, all the way left, or not at all
– Paths and plans are very small
New Algorithm
• Dubins Car’s 6 motion primitives
New Algorithm
• Algorithm Overview– Create an album of motion-plans and
paths (AMAP)
– Create a collision set (CS) containing colliding edges
New Algorithm
• AMAP Construction– Create paths for all cells to the right of
the center STRS using Dubin’s Curves
– We can do this because the left side will mirror the right
– Cuts the memory consumption in half
Related Work
Related Work
New Algorithm
• CS Construction– For every cell in the environment check
to see if an edge collides
– If so add it to the CS
New Algorithm
• Online Portion– Use a slightly modified version of A* to
traverse AMAP
– Includes a short circuit
New Algorithm
New Algorithm
Results
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Conclusion
• It is consistently gooder
Questions?