Robot Control using Genetic Algorithms

Transcription

1 Robo Conrol using Geneic Algorihms Summary Inroducion Robo Conrol Khepera Simulaor Geneic Model for Pah Planning Chromosome Represenaion Evaluaion Funcion Case Sudies Conclusions

2 The Robo Conroller Problem Given a robo and a descripion of an environmen, provide commands (moor speeds) o he robo, in order o achieve a pah beween wo specified locaions, which is collision-free and saisfies cerain opimisaion crieria. (x f, y f ) (x i, y i ) Opimisaion Crieria Robo should: aemp near-opimal pahs avoid obsacles perform sraigh moion Conroller should be independen of: he robo s environmen arge locaion 2

3 The Khepera Simulaor Freeware mobile robo simulaor (designed by Olivier Michel, Universiy of Nice Sophia-Anipolis) User designed worlds Conrol algorihms can be wrien in C/C++ Robo s posiion and angle reading Colourful Graphical Inerface S 8 sensors (S0-S7): [0, 023] S0 2 moors (M, M2): [-0, +0] S2 S3 Fron idenificaion S4 S5 M M2 S7 S6 Simulaor Readings: sensors, posiion and angle Y S0 S S2 S3 S4 Fron idenificaion S5 000 Robo s World M M2 S2 S S3 S4 S7 S6 S0-S7: [0, 023] y S0 S5 Fron idenificaion M M2 S7 S6 angle of he robo wih he world a : [-p, p] obsacle no obsacle very deeced closed 0 x 000 X 3

4 Conrol Mode To evolve he robo s aiudes as i ineracs wih he exernal environmen Each robo acion deermines: how well he conroller performs wih respec a given ask; he nex inpu simuli o he conroller. The conroller should learn as he robo ineracs wih he environmen Conroller Model Khepera Simulaor Moor 2 Moor Geneic Algorihm evolves robo s aiudes Sensors Posiion Robo s Angle Goal Locaion 4

5 Proposed Model IF Obsacle deeced THEN Avoid collision, forge arge ELSE Sraigh o he arge according o he arge direcion END Sensors Reading Simplificaion Slef Srigh S 0 S S 2 S 3 S 4 S5 S lef = ( S 0 + S + S 2 ) / 3 S righ = ( S 3 + S 4 + S 5 ) / 3 S back = ( S 6 + S 7 ) / 2 S 7 S 6 Sback 5

6 Deermining he Targe Direcion Direcion = β - α arrival posiion: (xf,yf) p/2 3p/4 Goal poin o lef side p/4 β p Goal poin behind Goal poin in fron 0 α = π/2 (x,y) β = an - [(yf - y)/(xf - x)] -3p/4 Goal poin o righ side -p/4 -p/2 Model IF ((S lef > L) or (S righ > L) or (S back > L)) THEN Obsacle deeced, avoid collision, forge arge Proximiy-sensor = highes value (S lef, S righ, S back ) ELSE Obsacle no deeced (collision-free), sraigh o he arge END Targe direcion = b - a L=collision hreshold=900 6

7 Geneic Algorihm Modelling Chromosome Represenaion Evaluaion Funcion Geneic Operaors Techniques Parameers Chromosome Represenaion Which speed should be imposed o each moor in each siuaion he robo is? Targe Direcion(collision free) Obsacle deeced M,M2 M,M2 M,M2 M,M2 M,M2 M,M2 M,M2 Fron Lef Righ Back Lef Righ Back Aiudes (Genes) 7

8 Three objecives: Evaluaion Funcion (V) speed (D) sraigh moion (A) acion: reach a arge and avoid obsacles Calculaed for each gene [,7] a each sep F 7 = i= ( Vi* Di* Ai) 0 Vi ;0 Di ;0 Ai Speed Vi = ( M + M 2 ) /(2* M max) Normalised sum of he absolue value of he moors speeds; Whaever he robo does, i does quickly. 8

9 Sraigh Moion Di = ( + (( M+ M 2) (2* M max))) 2, i = [2,3,4], i = [,5,6,7] I favours high posiive speeds o boh moors When he robo is no oriened o he arge, D= avoids conradicory learning Acion I considers he benefi of each gene regarding o: obsacle avoidance arge closeness 0 = TPi Ai ( = AAi ) TPi, TPi = 0, TPi 0 TPi = oal of seps execued by aiude i AAi=acion s finess a sep of aiude i AAi di d max = gi g max S S max, if ( i = ) and( di 0), if ( i = [2,3,4]) and( gi 0), if i = [5,6,7], elseaai, elseaai = 0 = 0 9

10 Acion I considers he benefi of each gene regarding o: obsacle avoidance arge closeness 0 = TPi Ai ( AAi ) = Raes he disance variaion o he arge beween wo consecuive, TPi = 0 TPi seps, = oal and of seps execued by aiude i he maximum disance in one sep, for collision free/fron, TPi 0 AAi=acion s finess a sep of aiude i TPi AAi di d max = gi g max S S max, if ( i = ) and( di 0), if ( i = [2,3,4]) and( gi 0), if i = [5,6,7], elseaai, elseaai = 0 = 0 Acion I considers he benefi of each gene regarding o: obsacle avoidance arge closeness 0 = TPi Ai ( AAi ) = Raes he angle variaion beween wo, TPi consecuive = 0 TPi seps, = oal andof seps execued by aiude i he maximum angle in one sep,, TPi for collision 0 AAi=acion s free finess a sep of aiude i lef, righ, back TPi AAi di d max = gi g max S S max, if ( i = ) and( di 0), if ( i = [2,3,4]) and( gi 0), if i = [5,6,7], elseaai, elseaai = 0 = 0 0

11 Acion I considers he benefi of each gene regarding o: obsacle avoidance arge closeness 0 = TPi Ai ( AAi ) = TPi di d max AAi = gi g max S S max, TPi = 0, if ( i = ) and( di 0), if ( i = [2,3,4]) and( gi 0), if i = [5,6,7] TPi = oal of seps execued by aiude i Increases, TPi 0 as AAi=acion s he disance o he proximiy-sensor increases finess a sep of aiude i in he sep, elseaai, elseaai = 0 = 0 Improving he Targe Direcion Model 4 possible arge direcions Â2 - Â 3π/4 π/4 Targe a LEFT 8 possible arge direcions π/2 3π/4 π/4 Targe Behind Targe in FRONT π/2 0 Targe a RIGHT -3π/4 - π/4-3π/4 -π/4 Firs Targe Direcion Model -π/2

12 Chromosome Represenaions Cada esado corresponde a uma única aiude (par de velocidades Targe Direcion (collision free) Obsacle deeced M e M2), e cada aiude corresponde a um gene do cromossoma. M, M2 M, M2 M, M2 M, M2 M, M2 M, M2 M, M2 Fron Lef Righ Back Lef Righ Back Chromosome wih 7 aiude Genes Targe Direcion (collision free) Obsacle deeced M,M2 M,M2 M,M2 M,M2 M,M2 M,M2 M,M2 M,M2 M,M2 M,M2 M,M2 Fron Fron Lef Lef Righ Righ Back Back Lef Righ Back lef righ fron back fron back lef righ Chromosome wih aiude Genes Geneic Algorihm Real number chromosome Populaion Size =00 Generaions = 50 Crossover Rae = 80 % Muaion Rae = 4% Roulee Wheel Reproducion Eliism Linear scaling of finess 300 Evaluaion Seps for each chromosome Average of 25 Experimens 2

13 Geneic Algorihm Performance 7 Genes Chromosome Bes Chromosomes in experimen 4,5 4 3,5 FITNESS 3 2,5 2,5 0,5 0 Number of Generaions Geneic Algorihm Performance 7 Genes Chromosome Average of Bes Chromosomes in 25 experimens 4,5 4 3,5 3 2,5 2,5 0, FITNESS Number of Generaions

14 Geneic Algorihm Performance Genes Chromosome Bes Chromosomes in experimen 5 4,5 4 3,5 FITNESS 3 2,5 2,5 0, Number of Generaions Geneic Algorihm Performance Genes Chromosome Average of Bes Chromosomes in 25 experimens 5 4,5 4 3,5 FITNESS 3 2,5 2,5 0, Number of Generaions 4

15 Pahs Achieved in World Case Sudy SITUAÇÃO 7 Genes Chromosome Genes Chromosome CROMOSSOMA DE 7 GENES CROMOSSOMA DE GENES Pahs Achieved in World Case SITUAÇÃO Sudy 42 7 CROMOSSOMA Genes Chromosome DE 7 GENES CROMOSSOMA Genes Chromosome DE GENES 5

16 Speed Comparison Numbe of Seps Genes Chromosome 7 Genes Chromosome Case Sudies Pahs Achieved in World 2 Case Sudy SITUAÇÃO 7 Genes Chromosome Genes Chromosome CROMOSSOMA DE 7 GENES CROMOSSOMA DE GENES 6

17 Pahs Achieved in World 2 Case SITUAÇÃO Sudy Genes Chromosome Genes Chromosome CROMOSSOMA DE 7 GENES CROMOSSSOMA DE GENES Speed Comparison Number of Seps Genes Chromosome 7 Genes Chromosome Case Sudies 7

18 Speed Comparison (%) 24,29% 84,62% Case Sudy Case Sudy 2 Case Sudy 3 40,00% Pahs Achieved in World 3 Case SITUAÇÃO Sudy 7 Genes Chromosome Genes Chromosome CROMOSSOMA DE 7 GENES CROMOSSOMA DE GENES 8

19 Pahs Achieved in World 3 Case SITUAÇÃO Sudy 2 7 Genes Chromosome Genes Chromosome CROMOSSOMA DE 7 GENES CROMOSSOMA DE GENES Pahs Achieved in World 3 SITUAÇÃO 3 Case Sudy CROMOSSOMA 7 Genes Chromosome DE 7 GENES Genes Chromosome CROMOSSOMA DE GENES 9

20 Pahs Achieved in World 3 Case Sudy 4 SITUAÇÃO 4 7 Genes Chromosome Genes Chromosome CROMOSSOMA DE 7 GENES CROMOSSOMA DE GENES Speed Comparison Speed Comparison World 3 7 Genes Cromosome Genes Cromosome Case Sudy arge no reached 729 Case Sudy Case Sudy 3 arge no reached arge no reached Case Sudy 4 arge no reached

21 Conclusions A simple GA could gradually evolve he robo conrol The robo achieved near opimal pah owards he goal, avoiding obsacles Reraining is no necessary when he environmen changes Conroller improved performance wih he genes model The robo has no memory abou previous unsuccessful pahs and may ge los Oher asks can be included in he model (e.g. energy supply) Chromosome codificaion is limied for few robo s siuaions 2