VILNIUS GEDIMINAS TECHNICAL UNIVERSITY

Tomas LUNECKAS

ANALYSIS OF HEXAPOD ROBOT

LOCOMOTION OVER ROUGH

TERRAIN

SUMMARY OF DOCTORAL DISSERTATION

TECHNOLOGICAL SCIENCES, ELECTRICAL AND ELECTRONIC ENGINEERING (01T)

Vilnius 2013

Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2009–2013. Scientific Supervisor

Assoc Prof Dr Dainius UDRIS (Vilnius Gediminas Technical University, Technological Sciences, Electrical and Electronic Engineering – 01T).

The dissertation is being defended at the Council of Scientific Field of Electrical and Electronic Engineering at Vilnius Gediminas Technical University: Chairman

Prof Dr Habil Roma RINKEVIČIENĖ (Vilnius Gediminas Technical University, Technological Sciences, Electrical and Electronic Engineering – 01T).

Members: Assoc Prof Dr Domantas BRUČAS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T), Assoc Prof Dr Eleonora GUSEINOVIENĖ (Klaipėda University, Technological Sciences, Electrical and Electronic Engineering – 01T), Prof Dr Vygaudas KVEDARAS (Vilnius Gediminas Technical University, Technological Sciences, Electrical and Electronic Engineering – 01T), Assoc Prof Dr Arūnas LIPNICKAS (Kaunas University of Technology, Technological Sciences, Informatics Engineering – 07T).

Opponents: Prof Dr Algirdas BAŠKYS (Vilnius Gediminas Technical University, Technological Sciences, Electrical and Electronic Engineering – 01T), Prof Dr Habil Rimvydas SIMUTIS (Kaunas University of Technology, Technological Sciences, Informatics Engineering – 07T).

The dissertation will be defended at the public meeting of the Council of Scientific Field of Electrical and Electronic Engineering in the Senate Hall of Vilnius Gediminas Technical University at 2 p. m. on 19 December 2013. Address: Saulėtekio al. 11, LT-10223 Vilnius, Lithuania. Tel.: +370 5 274 4952, +370 5 274 4956; fax +370 5 270 0112; e-mail: doktor@vgtu.lt The summary of the doctoral dissertation was distributed on 18 November 2013. A copy of the doctoral dissertation is available for review at the Library of Vilnius Gediminas Technical University (Saulėtekio al. 14, LT-10223 Vilnius, Lithuania).

© Tomas Luneckas, 2013

VILNIAUS GEDIMINO TECHNIKOS UNIVERSITETAS

Tomas LUNECKAS

ŠEŠIAKOJO ROBOTO JUDĖJIMO

NELYGIU PAVIRŠIUMI TYRIMAS

DAKTARO DISERTACIJOS SANTRAUKA

TECHNOLOGIJOS MOKSLAI, ELEKTROS IR ELEKTRONIKOS INŽINERIJA (01T)

Vilnius 2013

Disertacija rengta 2009–2013 metais Vilniaus Gedimino technikos universitete. Mokslinis vadovas

doc. dr. Dainius UDRIS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, elektros ir elektronikos inžinerija – 01T).

Disertacija ginama Vilniaus Gedimino technikos universiteto Elektros ir elektronikos inžinerijos mokslo krypties taryboje: Pirmininkas

prof. habil. dr. Roma RINKEVIČIENĖ (Vilniaus Gedimino technikos universitetas, technologijos mokslai, elektros ir elektronikos inžinerija – 01T).

Nariai: doc. dr. Domantas BRUČAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimų inžinerija – 10T), doc. dr. Eleonora GUSEINOVIENĖ (Klaipėdos universitetas, technologijos mokslai, elektros ir elektronikos inžinerija – 01T), prof. dr. Vygaudas KVEDARAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, elektros ir elektronikos inžinerija – 01T), doc. dr. Arūnas LIPNICKAS (Kauno technologijos universitetas, technologijos mokslai, informatikos inžinerija – 07T).

Oponentai: prof. dr. Algirdas BAŠKYS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, elektros ir elektronikos inžinerija – 01T), prof. habil. dr. Rimvydas SIMUTIS (Kauno technologijos universitetas, technologijos mokslai, informatikos inžinerija – 07T).

Disertacija bus ginama viešame Elektros ir elektronikos inžinerijos mokslo krypties tarybos posėdyje 2013 m. gruodžio 19 d. 14 val. Vilniaus Gedimino technikos universiteto senato posėdžių salėje. Adresas: Saulėtekio al. 11, LT-10223 Vilnius, Lietuva. Tel.: (8 5) 274 4952, (8 5) 274 4956; faksas (8 5) 270 0112; el. paštas doktor@vgtu.lt Disertacijos santrauka išsiuntinėta 2013 m. lapkričio 18 d. Disertaciją galima peržiūrėti Vilniaus Gedimino technikos universiteto bibliotekoje (Saulėtekio al. 14, LT-10223 Vilnius, Lietuva). VGTU leidyklos „Technika“ 2194-M mokslo literatūros knyga.

© Tomas Luneckas, 2013

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Introduction

Topicality of the problem. Terrain feature identification and evaluation is one of the most important robotics tasks. Solving this problem will allow to use mobile robots more widely. Main goals for solving this problem are development of new terrain identification and evaluation methods. Literature analysis shows possibility to group terrain features. Such classification allows easier terrain feature and traversability evaluation. Yet there is no exact definition on what physical attributes specify certain terrain features. So it is uncertain what terrain is complex for robot. So one of the problems is definition of terrain feature physical attributes and their relation with robot’s dimensions. Currently, most widely used systems for terrain feature identification are stereo camera and laser range finder (LIDAR) systems. In order to obtain information about terrain from stereo camera or LIDAR systems’ data complex algorithms. Consequently between data acquisition, processing and decision making a delay may arise that will influence robot operation in real time and limit robot’s ability to react to sudden changes in the environment. Also visual systems are dependent on image clearness and can poorly perform (or don’t work at all) in poor visibility conditions. These reasons impel creation of terrain identification and evaluation methods that could be processed by embedded robot controller. After detecting terrain features it is important to evaluate and interpret them correctly. Most of the time obstacles or terrain is described as traversable, difficult or impassable. Usually only impassable obstacles or terrain features are excluded. However walking robots are capable of moving over more difficult terrain than wheeled or tracked robots so terrain features should be categorized into more groups or directly influence robot’s locomotion and behavior.

Research object. Hexapod walking robot and its locomotion control over

unknown rough terrain. Aim of the work. Main task of this work is analysis of hexapod robot

locomotion on rough terrain, development and investigation of terrain feature identification and evaluation algorithm.

Tasks of the work. The following tasks have to be solved to achieve the

aim of the work: 1. Develop robot’s imitation and physical models and compose trajectory

generation mathematical expressions for adaptive locomotion.

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2. Investigate robot’s locomotion over flat terrain using adaptive gait and evaluate deviations of terrain roughness identification.

3. Develop and investigate method for identifying terrain features according to robot’s feet coordinates.

4. Develop and investigate hexapod walking robot’s algorithm for gait selection according to terrain features.

Methodology of research includes inverse kinematics, homogenous

transformation, trajectory generation, statistical analyses methods. Robot‘s kinematic model is imitated using MATLAB® software, experiments are conducted using physical robot model.

Scientific novelty 1. Developed hexapod walking robot control algorithm with real-time

feet trajectory generation that allows robot to adapt to terrain roughness.

2. Developed novel terrain roughness identification and evaluation method that allows terrain roughness evaluation only using known robot feet coordinates and robot body inclinations.

3. Developed novel robot’s decision making algorithm for selecting robot’s gait depending on terrain features and defined requirements for robot’s task.

Practical value. Research results can be used in hexapod robot control

systems to identify and evaluate terrain features. This allows to exchange complex environment identification systems and evaluation algorithms or proposed method can be used as a redundant system to ensure better terrain evaluation. Developed decision making algorithm allows selecting robot’s gait according to terrain features ensures stable robot locomotion over rough terrain. Developed imitation and physical hexapod robot models can be used for hexapod robot locomotion over various terrain and their control algorithms’ analyses.

Defended propositions

1. Feet coordinate deviations that appear due to adaptive gait compensation in control system allows to reduce uncertainties 65% for tripod, 31% for tetrapod, 77% for wave and 85% for ripple gaits on the average in comparison with not using compensation.

2. Feet z coordinate deviation compensation depending on robot’s body inclinations allows increasing terrain height evaluation accuracy to 2.7

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times and reducing uncertainties to 2.2 times. Standard deviation conformity increases to 9.25 times and uncertainties reduce to 1.5 times.

3. Developed and experimentally tested hexapod robot imitation and physical models along with developed gait selection algorithm allows hexapod robots use adaptive locomotion over unknown rough terrain and select gait according to terrain features.

The scope of the scientific work. The dissertation is written in Lithuanian. The dissertation layout consists of three main chapters, list of references and list of author‘s publications on the subject of dissertation. The work consists of 103 pages, 40 figures, 8 tables, 63 numbered formulas, 79 bibliographic sources. 1. Overview of terrain feature evaluation methods

Terrain can be described with three main features: terrain condition, terrain roughness and terrain slope.

• Terrain condition: describes terrains bearing capacity which depends on soil texture and its moisture.

• Terrain roughness: describes obstacles that could obstruct movement. • Slope: describes terrain inclination. • All three features can be combined into one parameter – terrain

traversability.

Table 1. Groups of terrain features

Terrain condition Terrain roughness Slope

1 Very good 1 Very even 1 Level

2 Good 2 Slightly even 2 Gentle

3 Average 3 Uneven 3 Moderate

4 Poor 4 Rough 4 Steep

5 Very poor 5 Very rough 5 Very steep

Each feature is grouped into categories in order to better describe terrain

(Table 1). Each category is described by physical attributes that describe terrain

features. Terrain condition categories illustrate terrains rigidity, viscosity, the

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lower the category more viscous or soft terrain is. Terrain condition is directly connected to moisture or annual rainfall and soil solidity.

Terrain roughness is related to obstacle height and their density. Higher roughness category indicates high and densely distributed obstacles.

Terrain slope is quite self-explanatory and its categories are related to terrain inclination, usually given in percentage. 45–50% (21.8–26.6º) terrain inclinations are assigned to very steep slope category.

Although terrain description and categorization can be an easy task but identification and evaluation of these features can be a very challenging task. Though such features as terrain roughness and slope can be measured using rather simple sensors but terrain condition is extremely difficult to identify and evaluate. Current equipment is able at least approximately identify and evaluate terrain features however this requires specialized sensor systems and (or) complex algorithms are used to process data.

One of the most common ways to identify terrain features is by using stereo cameras. By using appropriate algorithms and methods stereo cameras allow to obtain most of the needed information about surrounding terrain. Second most widely used method for obtaining information about surroundings is by using laser range finders (LIDAR). Information obtained using LIDAR does not need to be processed in order to obtain the distance to terrain features. But still require a lot of effort for processing data.

After obtaining data about surrounding terrain features it is necessary to process and evaluate this data in order for robot to take certain actions. Most common parameter for evaluating terrain roughness is root-mean square error (RMSE) or standard deviation.

This parameter allows to evaluate terrain roughness with only one number and it is very easily calculated. One of the biggest disadvantages of this method is that a lot of data points are needed in order to obtain good accuracy.

It is common that along with RMSE parameter terrain roughness is described with root-mean-square deviation, root-mean-square slope, autocorrelation length, effective slope and median and absolute slope.

It is also possible to evaluate terrain features by calculating terrain roughness index, terrain inclination index, path length index or terrain danger factor. 2. Hexapod robot model development methodology

It is easier to analyze hexapod robot kinematics by separating body

kinematics from leg kinematics. To correctly create a kinematic model coordinate frames must be assigned to robot. Main coordinate frame is body

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coordinate frame, coordinate frames also are assigned to leg bases and each foot.

Leg base coordinate frames are transformed into robot’s body coordinate frame using homogenous transformation matrices (1)–(3). Each leg’s base coordinate frame is transformed using three rotations and one translation.

i XYZ i= ⋅B T T , (1)

here:

11 12 13 0

21 22 23 0

31 32 33 00 0 0 1

0 0 0 1

XYZ XYZ

XYZ

r r r X

r r r Y

r r r Z

≡ =

R d

T , (2)

0

0

0

, ,

1 1

i i

i i

i i

B B

B B

i i XYZ

B B

X xX

Y yY

Z zZ

= = =

B T d . (3)

Fig. 1. Leg projections into xy (a) and xz (b) planes

After calculating leg base coordinate frame coordinates in robot’s body

coordinate frame, inverse kinematics calculations must be done for each leg. Because each leg has three degrees of freedom the easiest way to calculate actuator angles is by using geometrical approach for inverse kinematics that requires leg projections into xy (Fig. 1, a) and yz (Fig. 1, b) planes.

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Then each actuator’s angles can be calculated using (4)–(8) expressions.

1

3

θ arctany

x l

=

+ , (4)

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2 2 2

1 2

2

1

θ arccos arcsin2

qq

l l B z

l B B

− + = +

⋅ ⋅ ��������������

, (5)

2 2 2

1 2

3

1 2

θ arccos2

l l B

l l

+ −=

⋅ ⋅ , (6)

2 2

4B l z= + , (7)

2 2

4l x y= + . (8)

For successful and fluent robot’s locomotion it is important to synchronize

all six leg movements to achieve propulsion. Depending on gait one full step could take longer than the other, time that is needed to perform a full step is called step period (T) and leg swing moments are called phases ( φ

i). Gait

periods and leg phases are provided in Table 2.

Table 2. Gait periods and leg swing phases

Gait T LFφ

LMφ

LHφ

RFφ

RMφ

RHφ

Wave 6 0 1 2 3 4 5

Ripple 6 0 2 4 5 3 1

Tetrapod 3 0 1 2 1 2 0

Tripod 2 0 1 0 1 0 1

It is required to have option to change step’s length, height and robot

walking direction. Wanted feet trajectory is shown in Fig. 2.

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Fig. 2. Robot‘s leg trajectory projections into yz (a) and xz (b) planes. l – step length,

h – step height, ε – stride direction

Each leg‘s trajectory can be decomposed into three coordinate

dependences from time and must be written for three time periods: • φ

it ≤ ;

• φ φ 1i i

t< ≤ + ;

• φ 1i

t > + .

Then leg trajectories can be generated for each leg using (9)–(11) expressions.

( )

( ) ( )

( )

( ) ( )

( ) ( )

( )

sin ε 2 φ 2 1, t φ ,

2 1

φ 0,5 sin ε , φ φ 1,

sin ε 2 φ 2 1, φ 1.

2 1

i

i

i

f i i i

i

i

l T t

T

x t l t

l T tt

T

⋅ ⋅ − ⋅ + ⋅ −− ≤

⋅ −

= ⋅ − ⋅ < ≤ + ⋅ ⋅ + ⋅ − ⋅ + > + ⋅ −

(9)

( )

( ) ( )

( )

( ) ( )

( ) ( )

( )

cos ε 2 φ 2 1, t φ ,

2 1

φ 0,5 cos ε , φ φ 1,

cos ε 2 φ 2 1, φ 1.

2 1

i

i

i

f i i i

i

i

l T t

T

y t l t

l T tt

T

⋅ ⋅ − ⋅ + ⋅ −− ≤

⋅ −

= ⋅ − ⋅ < ≤ + ⋅ ⋅ + ⋅ − ⋅ + > + ⋅ −

(10)

( ) ( )( )0, t φ ,

sin φ , φ φ 1,

0, φ 1.

i

i

f i i i

i

z t h t t

t

≤

= ⋅ − ⋅ < ≤ + > +

π (11)

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Hexapod robot movement complexity dictates that all system was first tested by simulation prior building and testing physical robot model. MATLAB® was chosen as simulation software in order to develop hexapod robot imitation model to test kinematic calculations and leg trajectory generation. Model development is carried out with control program in mind so that it was easier to translate simulation program to robot control program. Also for better analyses robot movements are animated. Robot simulation program algorithm is shown in Fig. 3.

While developing robot control program it is important to organize it so that robot control was simple, that is could be controlled using simple commands but at the same time ensured total robot movement control freedom.

As in simulation program all variables are stored in arrays for easier accessibility. Also hexapod robot can be decomposed into several parts. Robot body that is described with its pose (body rotation and translation) and six legs that are described with feet coordinates, actuator angles and speeds, leg base coordinates and their offsets. For this purpose two structures are composed in program, one for robot and one for legs. Robot structure consists of leg array, three translation variables and three rotation variables. Leg structure consists of five arrays for feet coordinates, leg base coordinate frame coordinates, leg base coordinate offsets, actuator angles and speeds and one leg phase variable.

For terrain roughness evaluation feet z coordinate standard deviation σ is used. Proposed terrain roughness evaluation method is based on that that it is calculated only at given moments and only for limited terrain area. This way σ value represents terrain roughness in feet restricted area. Standard deviation σ value is calculated with expression (12).

( )( )2

1

1σ

n

fi

z i zn

=

= −∑ , (12)

( )1

n

fi

z i

zn

=

=

∑. (13)

The other proposed method allows to evaluate terrain roughness and

terrain gradient (slope) by calculated angles between two planes drawn over each three feet (Fig. 4).

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Fig. 3. Robot simulation program algorithm

Fig. 4. Planes that are used to calculate terrain gradient

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Plane angles are calculated using (14) and (15) expressions.

1 2

1 2

1 2

atan , atana a

c c

α = − α = − , (14)

1 2

1 2

1 2

atan , atanb b

c cβ = − β = − , (15)

here:

1 2,α α – inclination angles around x axis for first and second planes,

1 2,β β – inclination angles around y axis for first and second planes.

1 2 1 1 2, , , , ,

ba a b b c c are obtained by solving planes equations using three known

points. If

1α and 2α are positive, slope is on the right side of the robot, if

negative – left. If 1

β and 2β is positive, robot is climbing into hill, if negative –

descending. These angles along with the vertical feet displacements 1c and 2c

can also describe terrain roughness. If 1 2 0α = α = and (or) 1 2 0β = β = robot

is standing on a flat terrain. If 1 2 0α = α ≠ and (or) 1 2 0β = β ≠ robot is

standing on flat but inclined terrain. And if 1 2α ≠ α and (or) 1 2β ≠ β robot is

standing on rough terrain.

3. Imitational and experimental hexapod robot locomotion analyses

To test terrain roughness evaluation method experiments with robot walking over rectangular obstacle with known dimensions (length 400 mm, height 40 mm) were made. Each experiment is repeated five times with each gait.

Fig. 5 shows feet z coordinate average values when robot is walking over rectangular obstacle using constant feet coordinate deviation compensation coefficients. It is noticeable that coordinates start to increase and reach approximately 40 mm. Then after 400 mm distance coordinates start to decrease. But large deviations are noticed when robot is climbing down from obstacle. Largest deviation reached 43±9mm. Similarly standard deviation values start to deviate from real values due to feet z coordinate deviations resulting in incorrect terrain roughness interpretation (Fig. 6). Largest σ deviation reaches 37±3 mm. This tells that constant deviation compensation coefficients are not very appropriate for rough terrain.

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Fig. 5. Feet z coordinate average values during locomotion over rectangular obstacle

using different gaits, uncertainty ±9 mm. a) left front, b) right front, c) left middle,

d) right middle, e) left hind, f) right hind legs

Unequal different feet z coordinate deviations show that robot’s body

deviates from horizontal position. It is noticeable that z coordinates of left front and left middle feet deviate less than other legs’ coordinates (Fig. 5, b, d–f). This indicates that robot’s body tilts back and to the right. Therefore a relation between robot body inclination and feet coordinate deviation could be seen.

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Thus there is possibility to compensate feet coordinate deviations according to robot body inclination. It is needed to know robot’s body inclination around x and y axes in degrees that can be measured with accelerometer. Feet z coordinate deviations according to robot’s body inclination can be calculated using expressions (16)–(21).

( ) ( ) ( )

,RF

2 cos sin1 sin

2 2

x yx

e

LLz z

⋅ α ⋅ α⋅ α

= + − , (16)

( ) ( )

,RM

2 cos sin

2

x y

e

L

z z

⋅ α ⋅ α

= − , (17)

( ) ( ) ( )

,RM

2 cos sin1 sin

2 2

x yx

e

LLz z

⋅ α ⋅ α⋅ α

= − − , (18)

( ) ( ) ( )

,LF

2 cos sin1 sin

2 2

x yx

e

LLz z

⋅ α ⋅ α⋅ α

= + + , (19)

( ) ( )

,LM

2 cos sin

2

x y

e

L

z z

⋅ α ⋅ α

= + , (20)

( ) ( ) ( )

,LH

2 cos sin1 sin

2 2

x yx

e

LLz z

⋅ α ⋅ α⋅ α

= − + . (21)

Fig. 6. Standard deviation variation during robot locomotion over rectangular obstacle

using different gaits, uncertainty ±3 mm

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Fig. 7. Feet z coordinate average values during locomotion over rectangular obstacle

using different gaits with deviation compensation using robot body inclinations,

uncertainty ±4 mm. a) left front, b) right front, c) left middle, d) right middle,

e) left hind, f) right hind legs

Same experiments are repeated this time using feet coordinate

compensation according to robot body inclinations. From Fig. 7 it is clear that this method increases feet coordinate accuracy and obstacle representation is

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closer to real. Largest deviation reaches 16±4 mm which is 2.7 times lower than previously.

Fig. 8. Standard deviation variation during robot locomotion over rectangular obstacle

using different gaits with deviation compensation using robot body inclinations,

uncertainty ±2 mm

Standard deviation σ (Fig. 8) varies as it should, that is increases if robot

is climbing up or down the obstacle and is close to 0 when all feet coordinates are almost on the same plane. σ largest deviation reduces to 9.25 times, uncertainties reduce to 1.5 times.

General conclusions 1. Hexapod robot kinematics is easily described using homogenous

transformation matrices and inverse kinematics for one leg. Combining derived leg trajectory generation expressions for adaptive locomotion with robot’s kinematic model allows to develop a simplified robot control algorithm that ensures ability to control robot’s motions without disturbing its locomotion.

2. Proposed method for terrain roughness evaluation by using standard deviation parameter, which is calculated from feet z coordinates, allows simple solution to evaluate terrain roughness. Though it is very sensitive to feet deviations and can drastically distort terrain evaluation.

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3. Novel method for evaluating terrain roughness and slope by measuring angles between two planes drawn over each three feet is presented. Calculated angles between normal, estimated by accelerometer data, and these two planes give terrain roughness and their mean – slope.

4. Feet z coordinate deviations can be compensated by additionally lowering each feet coordinates in control system. This allows to reduce feet coordinate deviations by 65% for tripod, 31% tetrapod, 77% for wave and 85% for ripple gaits on the average in comparison with not using compensation.

5. Experiments showed that by compensating feet z coordinates using constant coefficients terrain roughness height evaluation deviation reaches 43±9 mm and standard deviation value – 37±3 mm. By compensating deviations according to robot’s body inclinations, that are measured using accelerometer, roughness height evaluation deviation reduces to 2.7 times, uncertainties reduce to 2.2 times, standard deviation inadequacy reduces to 9.25 times, uncertainties – to 1.5 times.

6. Proposed robot gait selection method allows to disassociate from terrain roughness categories. Also this method ensures that gait selection depends on requirements for robot’s task such as speed, stability or cautiousness. Main disadvantage of this method is that gait must be selected after several steps in order to avoid frequent gait changes due to rapid roughness changes. On the other hand such gait selection reduces standard deviation sensitivity to single high terrain roughness changes.

List of published works on the topic of the dissertation

In the reviewed scientific periodical publications

Luneckas, T.; Udris, D. 2009. Research of hexapod robot motion in irregular terrain. In 5th International conference on mechatronic systems and materials MSM 2009. Stafa-Zurich: Trans Tech Publications Ltd. 431–434. ISSN 1012-0394.

Luneckas, T. 2010. Šešiakojo roboto eisenos tyrimas. Mokslas – Lietuvos ateitis=Science – future of Lithuania:Elektronika ir elektrotechnika=electronics

and electrical engineering. T. 2, Nr. 1: 36–39. Vilnius: Technika. ISSN 2029-2341.

Luneckas, T. 2011. Paviršiaus netolygumo vertinimas pagal roboto padėtį. Mokslas – Lietuvos ateitis=Science – future of Lithuania:Elektronika ir

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elektrotechnika=electronics and electrical engineering. T. 3, Nr. 1: 96–99 Vilnius: Technika. ISSN 2029-2341.

Luneckas, T. 2012. Roboto eisenos parinkimas pagal pėdų koordinačių vidutinę standartinę nuokrypą. Mokslas – Lietuvos ateitis=Science – future of Lithuania:Elektronika ir elektrotechnika=electronics and electrical

engineering. T. 4, Nr. 1: 47–50. Vilnius: Technika. ISSN 2029-2341.

Luneckas, T.; Udris, D. 2013. Terrain evaluation method for hexapod robot. World Academy of Science, Engineering and Technology. Vol. 7, Nr. 1. Zurich. 59–62. ISSN 2010-376X.

In other editions

Luneckas, T.; Udris, D. 2010. The simplified hexapod robot control metod. In proceedings of the 5th international conference on electrical and control

technologies ECT-2010. Kaunas: Technologija. 37–40. ISSN 1822-5934.

Luneckas, T.; Udris, D. 2011. Hexapod robot motion simulation. In proceedings of the 6th international conference on electrical and control

technologies ECT-2011. Kaunas: Technologija. 31–34. ISSN 1822-5934.

Luneckas, T.; Udris, D. 2012. Hexapod kinematic model optimization for control system. In proceedings of the 7th international conference on electrical and control technologies ECT-2012I. Kaunas: Technologija. 113–116. ISSN 1822-5934.

Luneckas, M.; Luneckas, T.; Udris, D. 2013. Hexapod walking robot energy consumption dependence on the number of legs set on the surface. In proceedings of the 8th international conference on electrical and control

technologies ECT-2013. Kaunas: Technologija. 25–28. ISSN 1822-5934.

About the author

Tomas Luneckas was born in Vilnius, in 1984. Received Bachelor degree in Electrical Engineering at the faculty of Electronics of Vilnius Gediminas Technical University. In 2009 received Master’s degree in Electrical Engineering at the faculty of Electronics of Vilnius Gediminas Technical University. In 2006–2009 worked as drawer, later as programmer in company Eltera. Since 2008 works as assistant in Vilnius Gediminas Technical University Electronics faculty department of automation. In 2009–2013 PhD student of Vilnius Gediminas Technical University. Commissioner in National contest for young scientists’ technology section. Author of chapter in the book “Jaunojo tyrėjo vadovas”.

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ŠEŠIAKOJO ROBOTO JUDĖJIMO NELYGIU PAVIRŠIUMI TYRIMAS Mokslo problemos aktualumas. Paviršiaus savybių atpažinimas ir vertinimas yra viena iš svarbiausių robotų inžinerijos problemų, kurios išsprendimas nulems gerokai platesnį mobilių robotų taikymą. Dėl šios priežasties reikia tobulinti esamus ir kuri naujus paviršiaus savybių atpažinimo ir vertinimo metodus. Literatūroje galima rasti paviršiaus savybių suskirstymo į kategorijas aprašymų. Toks suskirstymas leidžia lengviau įvertinti paviršiaus savybes ir praeinamumą. Tačiau nėra aiškiai įvardijamas paviršiaus savybių fizinių dydžių pagrįstumas. Todėl viena iš problemų yra konkrečių paviršiaus savybių fizinių dydžių apibrėžimas ir santykio su roboto matmenimis nustatymas. Viena iš didžiausių neišspręstų problemų yra paviršiaus savybių atpažinimas ir vertinimas. Šiuo metu, paviršiaus savybių atpažinimui, plačiausiai naudojamos vaizdo kamerų ir lazerinių atstumo jutiklių sistemos. Norint su šiomis sistemomis išgauti duomenis apie paviršių, reikalingi sudėtingi algoritmai. Todėl tarp duomenų gavimo, jų apdorojimo ir sprendimo priėmimo gali susidaryti laiko delsos, kurios įtakos roboto veikimą realiu laiku ir robotas negalės reaguoti į staigiai besikeičiančias aplinkos sąlygas. Be to vaizdinės aplinkos atpažinimo sistemos yra priklausomos nuo matomo vaizdo ryškumo (aiškumo) ir gali prastai veikti (arba išvis neveikti) esant blogam matomumui. Dėl šių priežasčių yra svarbu sukurti metodus, kurie leistų atpažinti paviršiaus savybes naudojant ne vaizdinę informaciją bei paprastus algoritmus, kuriuos galėtų vykdyti įterptinis roboto valdiklis.

Atpažinus paviršiaus savybes, svarbu juos įvertinti ir teisingai interpretuoti. Šiuo metu, aplinkos objektai arba paviršius skirstomas į robotui praeinamą, sunkiai praeinamą arba visiškai nepraeinamą. Stengiamasi išskirti tik tokias kliūtis, kurios trukdo robotui judėti. Tačiau, žingsniuojantys robotai gali judėti kur kas nelygesniu paviršiumi, nei važiuojantys, todėl paviršiaus savybės turėtų būti skirstomi į gerokai daugiau kategorijų arba turi tiesiogiai įtakoti roboto judėjimą ir elgseną.

Tyrimų objektas. Šešiakojis žingsniuojantis robotas ir jo judėjimo nežinomu nelygiu paviršiumi valdymas.

Darbo tikslas. Šio darbo pagrindinis tikslas yra sudaryti paviršiaus savybių atpažinimo, vertinimo bei roboto eisenos parinkimo metodus ir ištirti šešiakojo roboto judėjimą nelygiu paviršiumi.

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Darbo uždaviniai. Darbo tikslui pasiekti darbe reikia spręsti šiuos uždavinius:

1. Sudaryti roboto imitacinį ir fizinį modelius bei sudaryti trajektorijų generavimo matematines išraiškas adaptyviam roboto judėjimui.

2. Ištirti roboto judėjimą lygiu paviršiumi, taikant adaptyvią eiseną ir įvertinti paviršiaus atpažinimo nuokrypas.

3. Sudaryti ir ištirti metodą, leidžiantį atpažinti paviršiaus savybes pagal esamas roboto pėdų koordinates.

4. Sudaryti ir ištirti šešiakojo žingsniuojančio roboto eisenos parinkimo pagal paviršiaus savybes algoritmą.

Tyrimų metodika apima atvirkštinės kinematikos, homogeninių

transformacijų, trajektorijų generavimo, statistinės analizės metodus. Roboto kinematinis modelis imituojamas MATLAB® aplinkoje, eksperimentiniai tyrimai atliekami su fiziniu roboto modeliu.

Mokslinis naujumas 1. Sudarytas šešiakojo žingsniuojančio roboto valdymo algoritmas,

kuriame realizuotos realiu laiku generuojamos pėdų trajektorijos, leidžiantis robotui prisitaikyti prie paviršiaus nelygumų.

2. Sudarytas naujas paviršiaus savybių atpažinimo ir vertinimo metodas, kuris leidžia įvertinti paviršiaus savybes naudojantis tik žinomomis roboto pėdų koordinatėmis ir roboto kūno pokrypiais.

3. Sudarytas naujas roboto sprendimų priėmimo algoritmas, kuris leidžia parinkti roboto eiseną, priklausomai nuo paviršiaus savybių ir iš anksto apibrėžtų reikalavimų roboto atliekamai užduočiai.

Praktinė vertė. Tyrimų rezultatai gali būti naudojami šešiakojų

žingsniuojančių robotų valdymo sistemose paviršiaus savybių atpažinimui ir vertinimui. Tai leidžia praplėsti esamų aplinkos atpažinimo sistemų galimybes ir užtikrinti patikimesnį paviršiaus atpažinimą ir vertinimą. Sudarytas sprendimų priėmimo algoritmas leidžia parinkti eiseną priklausomai nuo paviršiaus savybių, taip užtikrinant sėkmingesnį roboto judėjimą nelygiu paviršiumi. Sudaryti šešiakojo roboto imitacinis ir fiziniai modeliai gali būti taikomi šešiakojų robotų judesių ir valdymo algoritmų tyrimui, robotui judant įvairiais paviršiais.

Ginamieji teiginiai 1. Pėdų koordinačių nuokrypų, atsirandančių taikant adaptyvią eiseną,

kompensavimas valdymo sistemoje leidžia nuokrypas vidutiniškai

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sumažinti 65 % trikojei, 31 % keturkojei, 77 % banguojančiai ir 85 % pulsuojančiai eisenoms, lyginant su ėjimu netaikant kompensavimo.

2. Pėdų z koordinačių nuokrypų kompensavimas pagal roboto kūno pokrypius leidžia paviršiaus nelygumų aukščių atpažinimą pagerinti iki 2,7 karto, neapibrėžtis sumažinti iki 2,2 karto, standartinės nuokrypos neatitikimą sumažinti iki 9,25 karto, o standartinės nuokrypos neapibrėžtis sumažinti iki 1,5 karto.

3. Sudaryti ir eksperimentiškai patikrinti šešiakojo roboto imitacinis ir fizinis modeliai bei sudarytas eisenos parinkimo algoritmas leidžia šešiakojams robotams taikyti adaptyvų judėjimą nežinomu nelygiu paviršiumi ir parinkti eiseną pagal paviršiaus savybes.

Darbo apimtis. Disertaciją sudaro įvadas, trys skyriai ir rezultatų apibendrinimas. Darbo apimtis yra 103 puslapiai, tekste panaudotos 63 numeruotos formulės, 40 paveikslų ir 8 lentelės. Rašant disertaciją buvo panaudota 79 literatūros šaltiniai. Pirmame skyriuje apžvelgiami paviršiaus parametrų atpažinimo ir vertinimo metodai. Antrame skyriuje pristatomas kinematinio ir imitacinio roboto modelio sudarymas bei paviršiaus parametrų atpažinimo ir vertinimo metodai. Trečiajame skyriuje pristatomi roboto judėjimo nelygiu paviršiumi modeliavimo ir eksperimentiniai rezultatai.

Bendrosios išvados

1. Šešiakojų žingsniuojančių robotų kinematiką patogu nagrinėti taikant homogenines transformacijų matricas bei atvirkštinės kinematikos metodą vienai kojai. Sudarius pėdų trajektorijų generavimo matematines išraiškas ir apjungus jas su roboto kinematiniu modeliu galima sudaryti supaprastintą roboto valdymo algoritmą, užtikrinantį labai paprastą šešiakojo roboto valdymą, leidžiantį roboto judesius valdyti realiu laiku.

2. Pateikiama paviršiaus nelygumų vertinimo metodika taikant standartinės nuokrypos parametrą, kuris suskaičiuojamas pagal esamas roboto pėdų aukščio koordinates, leidžia labai paprastai įvertinti paviršiaus nelygumus, tačiau yra jautrus kiekvienos kojos koordinačių nuokrypoms, kurios gali iškreipti paviršiaus įvertinimą.

3. Pasiūlytas naujas paviršiaus nelygumo ir pokrypio įvertinimo metodas skaičiuojant kampus tarp dviejų plokštumų nubrėžtų per roboto pėdas. Apskaičiavus kampus tarp vertikalės, nustatytos pagal akcelerometro duomenis, ir šių plokštumų, kampų skirtumas įvardina paviršiaus nelygumą, o vidurkis – pokrypį.

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4. Pėdų koordinačių nuokrypas galima sumažinti kompensuojant esamas mechanines paklaidas valdymo sistemoje nurodant papildomai nuleisti kiekvieną koją žemiau. Tai leidžia pėdų koordinačių nuokrypas, einant lygiu paviršiumi, vidutiniškai sumažinti 65 % trikojei, 31 % keturkojei, 77 % banguojančiai ir 85 % pulsuojančiai eisenoms.

5. Eksperimentiškai nustatyta, kad kompensuojant pėdų z koordinačių nuokrypas taikant pastovius kompensavimo koeficientus, paviršiaus nelygumų aukštis įvertinamas su 43±9 mm nuokrypa, o standartinės nuokrypos verčių neatitikimai siekia 37±3 mm. Nuokrypas kompensuojant pagal roboto kūno pokrypius, išmatuojamus akcelerometru, nelygumų aukščio neatitikimas pagerėja iki 2,7 karto, neapibrėžtys sumažėja iki 2,2 karto, standartinės nuokrypos neatitikimas sumažėja iki 9,25 karto, neapibrėžtys – iki 1,5 karto.

6. Sudarytas roboto eisenos parinkimo metodas leidžia neapsiriboti iš anksto apibrėžtomis paviršiaus nelygumo kategorijomis. Šis metodas taip pat užtikrina, kad roboto eisenos keitimas priklausys ir nuo roboto užduočiai keliamų reikalavimų, tokių kaip greitis, stabilumas ar atsargumas. Kaip pagrindinis šio metodo trūkumas gali būti įvardijamas eisenos keitimas po kelių žingsnių, kas užtikrina, kad paviršiaus nelygumas tikrai tapo didesnis ar mažesnis, nei anksčiau. Bet tuo pačiu ir užtikrina, kad roboto sprendimų priėmimo sistema nereaguos į vienetinius, didesnius nelygumo pokyčius, tai sumažina standartinės nuokrypos jautrumą į vienetinius didelius pėdų koordinačių pokyčius.

Trumpos žinios apie autorių

Tomas Luneckas gimė 1984 m. rugsėjo 18 d. Vilniuje. 2007 m. įgijo elektros inžinerijos bakalauro laipsnį Vilniaus Gedimino technikos universiteto Elektronikos fakultete. 2009 m. įgijo elektros inžinerijos magistro kvalifikacinį laipsnį Vilniaus Gedimino technikos universiteto Elektronikos fakultete. 2006–2009 m. dirbo UAB Eltera braižytoju vėliau programuotoju. Nuo 2008 m. Vilniaus Gedimino technikos universiteto Elektronikos fakulteto Automatikos katedros asistentas. 2009–2013 Vilniaus Gedimino technikos universiteto doktorantas. Buvo Nacionalinio jaunųjų mokslininkų konkurso technologijų sekcijos komisijos narys, knygos „Jaunojo tyrėjo vadovas“ skyriaus autorius.