Virtual force field based obstacle avoidance and agent based intelligent mobile robot

Transcription

1 Virual force field based obsacle avoidance and agen based inelligen mobile robo Saurabh Sarkar *a, Sco Reynolds b, Ernes Hall a a Dep of Mechinical Engineering, Universiy of Cincinnai b Dep. of Compuer Science, Univ. of Cincinnai 2600 Clifon Ave., Cincinnai, OH USA Inerne: hp:// ABSTRACT This paper presens a modified virual force based obsacle avoidance approach suied for laser range finder. The modified mehod akes advanage of he polar coordinae based daa sen by he laser sensor by mapping he environmen in a polar coordinae sysem. The mehod also uilizes a Gaussian funcion based cerainy values o deec obsacle. The mehod successfully navigaes hrough complex obsacles and reaches arge GPS waypoins. Keywords: Virual force field, laser ranger finder, agens. 1. INTRODUCTION Real-ime obsacle avoidance algorihms are imporan for mobile robos. Khaib demonsraed he realime obsacle avoidance wih his concep of arificial poenial field in Moravec and Elfes came ou he widely popular concep of cerainy grids. I is especially useful for daa accumulaion and sensor fusion 2. Borensein and Koren developed he Virual Force Field by merging he las wo conceps 3. A cerainy grid divides he robo s work area ino small cells. Each cell hen assigned a cerainy value. The cerainy value is he measure of confidence of an obsacle being in he cell. The greaer he cerainy values of he cell he more probabiliy of an obsacle being in he cell. The moving robo keeps updaing he cerainy values in he grid around iself. Each of he cells applies a repulsive force on he robo and pushes i away from cell. The force is proporional o he cerainy value of he cell and inversely proporional o square of disance beween he obsacle and he robo. F cr = Force Consan d(i,j) = Disance beween robo and cell (i,j) C(i,j) = Cerainy Level of cell (i,j) x, = Robo s presen coordinaes o y o x i, y j = Coordinaes of cell (i,j) FcrC( i, j) x x0 y y0 F( i, j) = xˆ + yˆ 2 (1) d ( i, j) d( i, j) d( i, j) The resulan repulsive force is he vecor sum of all he repulsive forces from he cells * sarkarsh@ .uc.edu V. 4 (p.1 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

2 F r = F i, j (2) i, j Simulaneously he robo is aced upon by an aracive force, which pulls he robo owards he arge. The aracive force F originaes from he arge. The arge may be waypoin whose coordinaes are known o he robo. The magniude of he force is given by F x y y x0 y 0 = F xˆ + yˆ c d d (3) F c = Force Consan (aracion o arge) d = Disance beween arge and he robo x, y = Targe coordinaes The final resulan force R is he vecor sum of resulan and repulsive forces. R = F + F r (4) The direcion of he resulan R, δ where F F ( cos( δ ) i.sin( δ )) seering rae command Ω of he robo. =., is used o deermine he r r + [ min( θ δ )] Ω = K (5) s K s = Proporional consan for seering (in sec -1 ) θ = Curren direcion of ravel min(a-b) is he shores roaional difference beween wo angles. The resul is always beween -180 and 180. Some modificaions have been made in he original algorihm o make i more suied for use wih a laser scanner sensor. A novel feaure of his approach is dividing he robo s work area ino radial secors insead of using a grid sysem. The secors are 0.5 degrees wide and heir origin is locaed a he cener of he laser sensor. Anoher novel feaure is he equaion used o deermine he cerainy value of each of hese radial secors. The deails of each of he conribuions will be described in he following secions. 2. SYSTEM OVERVIEW Our robo sysem is designed as a disribued muli agen sysem. Muli agen sysems have been idenified by many including 4 as a promising approach o sofware engineering in a complex domain. Our sysem is designed o be open and always on. In hese sysems, sofware modules are modeled as auonomous agens. In our sysem, each sensor is represened as an agen ha communicaes wih he cenral summaion agen module. The individual agen acs as if i is he sole agen on he sysem and i is responsible for where he robo goes. For insance, he GPS sensor agen will always reurn o he summaion module he angle correcion he robo mus ake in order o drive down a sraigh line o he nex way poin. In his paper, we presen a simple wo agen sysem in which each sensor agen makes is decisions and demonsrae how hese decisions are fused ino one by he summaion module V. 4 (p.2 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

3 Each sensor agen perceives and undersands only a limied par of he environmen in which he robo exiss. This allows each agen o be solely focused on wha i is rying o achieve. In his sysem, a sensor can fail and our robo will sill be able o operae. This approach grealy simplifies he proocol in which he agens communicae and allows for a simple ye robus sysem. Figure 1Bearca Cub he robo using he algorihm 3.1 Working principle 3. LASER RANGE SCANNER SYSTEM Sonar sensors were predominan in mobile robos before he laser range scanner became commercially viable. Laser scanners are more reliable and give much beer resoluion compared o he sonar. Laser range scanner works on a similar ime of fligh principle ha is used by sonar or radar. I shoos ou a highly focused laser beam ino space. When he beams his an obsacle i ges scaered and par of i reurns o he scanner. The sensor deecs boh he changes in ampliude and phase and his is used o deermine he disance he beam was refleced back calculaing he ime difference beween release of he beam and arrival of he refleced beam. The sensor pans is laser beam in a 180 degree span using a roaing mirror. As he laser sensors shoos ou laser beams a differen angles i calculaes disance of obsacle laying in is field of view. Thus a 2- dimensional map of obsacles in-fron of he laser sensor can be obained. The laser sensor used here is a SICK TM LMS 200. I uses as infrared laser beam of 835 nm wavelengh. I has a span radius of 180 degrees. The resoluion of scan be 0.25, 0.5, 1 degree. I can communicae wih he compuer using a RS 422 or 232 pors. The daa ransfer rae varies from 96 K o 500 K Baud. Figure 2 SICK LMS V. 4 (p.3 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

4 3.2 Algorihm Figure 3 Laser measuremen sysem oupu The space in-fron of he mobile robo is broken ino radial secors. Each secor is 0.5 degrees in widh. Each of he secors is given a cerainy value. The cerainy value is depends on a Gaussian funcion of disance a which he obsacle is from he robo. The reading from he laser range finder gives disances in each of he secor. C = Consan C (θ ) = Cerainy value of secor a θ x (θ ) = Disance of obsacle a secor θ µ (θ ) = Mean value a secor θ σ = Sandard deviaion ( x( θ ) µ ( θ )) 2 (2σ ) e C ( θ ) = C if ( θ ) > µ ( θ ) σ 2π C (θ ) = C if x ( θ ) µ ( θ ) 2 x (6) By using µ (θ ) he shape of he mean curve around he robo can be conrolled. I can be eiher any 2-D shape like semi-circle or semi-ellipse. This will enable us o conrol how near o an obsacle a robo should be when passing i V. 4 (p.4 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

5 Figure 4 Mean Curve As he robo keeps moving ahead i updaes he cerainy values of each secor. Each of he secors applies a virual repulsive force on he robo. The magniude of he force depends on he cerainy value of he secor. F( θ ) = F C( θ ) (7) F c = Force consan C (θ ) = Cerainy of secor θ The resulan repulsive force is he vecor sum of all he repulsive forces from he cells c F r = F(θ ) (8) θ The direcion of he resulan seering angle is deermined from he resulan force. The angle of he F = F cos( δ ) i.sin( δ ). resulan force is given byδ where ( ) r r + ψ δ (+) β = (9) ψ = Seering angle of robo wih respec o curren heading δ = Angle of resulan repulsive force β π = Consan wih a value of 2 α (+)β is a special funcion which equals α + β when α is less han π 2 and α β when α more π han equal o V. 4 (p.5 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

6 Figure 5 Deermining seering angle when δ π < Special cases The value of δ varies under cerain special cases. Figure 6 Deermining seering angle when δ π > 2 δ = 0 If F < γ (10) r γ = Threshold. This is for he case when here is no obsacle in fron of he robo. By seing δ = 0 he final seering angle π he resulan seering angle becomes 2 and he robo does no change direcion V. 4 (p.6 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

7 Figure 7Seering direcion when δ = 0 Figure 8 Seering direcion when δ π 2 Simulaneously he robo is aced upon by an aracive force, which pulls he robo owards he arge. The aracive force F originaes from he arge. The arge may be waypoin whose coordinaes are known o he robo. The magniude of he force is given by F x y y x0 y 0 = F xˆ + yˆ c d d (11) V. 4 (p.7 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

8 F c = Force Consan (aracion o arge) d = Disance beween arge and he robo x, y = Targe coordinaes The final resulan force R is he vecor sum of resulan and repulsive forces. The direcion of he resulan R, δ = robo. R = F + F r (12) R R, is used o deermine he seering rae command Ω of he [ min( θ δ )] Ω = K (13) s K s = Proporional consan for seering (in sec -1 ) θ = Curren direcion of ravel min(a-b) is he shores roaional difference beween wo angels. The resul is always beween -180 and GPS SENSOR MODEL Our robo sysem is designed o find a pah o various way poins using only local informaion. Our robo uses a GPS sysem and a compass ac as a sof sensor o deermine he heading correcion needed from he curren posiion o reach he way poin in a sraigh line. The robo reads in he GPS informaion from he sensor and calculaes he heading change needed based on he heading i is currenly on and he heading needed from he curren posiion o drive sraigh o he way poin. This informaion is hen sen o our summaion module. This module is responsible for fusing hem ogeher. 5. SUMMATION MODULE This module is responsible for making he final decision on he heading correcion he robo underakes. Each sensor on our robo makes a decision on he change and sends is local decision o he summaion module. The summaion module receives his informaion and fuses i ogeher by mahemaically combining he sensors suggesions. The suggesion each sensor model sends is in he form of wheel commands, w, where i is he corresponding robo wheel. The basic formula is below i k w i = s sw =1 s, i = λ (14) w i is he wheel command for wheel i, s is he sensor model, k is he number of sensors weigh applied o ha sensor and w s, i is he wheel command for wheel i from sensor s. λ i is he This mehod allows for all daa coming ino he summaion module o be fused ogeher ino one cohesive command o he moion conroller. Theλ s for each sensor is deermined hrough experimenaion and i ranges from 0-1. When λs is se o one he sensor has full conrol over he robos acions, when λs is se o V. 4 (p.8 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

9 0 i has no conrol over he robos acions. The λs works as a parameer o deermine he behavior of he robo. A low λs on he GPS sensor will resul in a less opimal pah o he way poin bu sronger obsacle avoidance. And he converse is rue for applying a small λs on he laser sensor. The iniial experimens wih his formulaion were mixed. I was deermined ha he sensors were fighing each and one sensor would essenially negae he oher sensor. In paricular his would happen when one sensor would indicae a change ha was a negaion of anoher sensor. This would hen resul in a fused wheel command ha was near 0 even hough he sensor had suggesed had suggesed a change in direcion. This causes major issues when he robo is approaching an obsacle and he laser suggess a hard urn in one direcion and he GPS suggess a hard urn in he opposie direcion. The end resul is essenially no change in direcion for he robo. This is illusraed in following figure. Figure 9 Sensor conflic V. 4 (p.9 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

10 Figure 10 Pah aken by robo Our soluion o his problem adds anoher level of decision o he summaion module. The summaion module has o look a he daa provided by he wo sensors and compare he values. If he wheel commands are no in he same direcion, as shown above, hen he decision is made o jus use he laser sensors values and ignore he GPS sensor. This circumvens he issue of conflicing wheel commands and pushes he decision o find he pah o he way poin ino he fuure. This mehod allows he robo o use reacive conrol law o guide is moion and creae a plan of acion. All compuaion is based around wha is happening now locally. Our sysem has removed he emporal dimension and grealy reduced he complexiy of pah planning. And i scales o any number of heerogeneous sensors. 6. TEST RESULTS The algorihm was esed in obsacle course wih various GPS waypoins. The robo running on he algorihm success navigaed hrough he course. One of he obsacles was a GPS coordinae enclosed in a circular fence wih wo openings V. 4 (p.10 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

11 Figure 11 GPS waypoin enclosed in a fence Figure 12 Approximae pah aken by robo 7. CONCLUSION Our work presened here presens a new mehod for obsacle avoidance. I uilizes he polar coordinae sysem which is far more suiable for laser range finders. This paper also presens our summaion module which fuses sensors suggesed moion commands ino one direcion. This mehod presens a more scalable approach and allows for any number of sensors. REFERENCE 1. O. Khalib, Real-Time Obsacle Avoidance for Manipulaors and Mobile Robos:, IEEE In. Conf. On Roboics and Auomaion, (1985). 2. H.P. Moravec, High resoluion maps from wide angle sonar, IEEE In. Conf. On Roboics and Auomaion, (1985). 3. J. Borensein and Y. Koren, Real-ime Obsacle Avoidance for Fas Mobile Robos, IEEE V. 4 (p.11 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM

12 Transacions on Sysems, Man, and Cyberneics 19(5) (1989). 4. F. Zambonelli, N.R. Jennings and M. Wooldridge, Developing muliagen sysems: The Gaia mehodology, ACM Trans. Sofware Eng. Mehodologies 12(3) (2003). 5. D. Weyns, e al. Environmens for Muliagen Sysems: Sae-of-he-Ar and Research Challenges, Environmens for Mul-Agen Sysems, Springer Berlin/Heidelberg 1-47 (2005) V. 4 (p.12 of 12) / Color: No / Forma: Leer / Dae: 7/16/2007 8:55:42 AM