A Hybrid Ant Colony Optimization Algorithm or Path Planning of Robot in Dynamic Environment

Transcription

1 Hao Me, Yantao Tan, Lnan Zu A Hybrd Ant Colony Optmzaton Algorthm or Path Plannng of Robot n Dynamc Envronment A Hybrd Ant Colony Optmzaton Algorthm for Path Plannng of Robot n Dynamc Envronment 1 Hao Me, Yantao Tan*, Lnan Zu School of Communcaton Engneerng, Jln Unversty, Changchun,130025, Chna hellomehao@163.com, tanyt@mal.jlu.edu.cn, zulnan-zln@163.com Abstract Ant colony optmzaton and artfcal potental feld were used respectvely as global path plannng and local path plannng methods n ths paper. Some modfcatons were made to accommodate ant colony optmzaton to path plannng. Pheromone generated by ant colony optmzaton was also utlzed to prevent artfcal potental feld from gettng local mnmum. Smulaton results showed that the hybrd algorthm could satsfy the real-tme demand. The comparson between ant colony optmzaton and genetc algorthm was also made n ths paper. Keywords. path plannng, moble robot, ant colony optmzaton, dynamc envronment, artfcal potental feld 1 Introducton Path plannng s a key step n the control of moble robot. And the qualty of path nfluences the effcency of moble robot. So desgnng an effcent path plannng algorthm s essental. Presently, there are many algorthms for path plannng, such as Artfcal Potental Feld (APF) [1], Fuzzy Logc (FL) [2], Neural Networks (NN) [3], Genetc Algorthm (GA) [4][5], Ant Colony Optmzaton (ACO) [6] and so on. However, these algorthms can t reach an deal soluton separately n complex dynamc envronment. For example, APF usually gets nto local mnmum easly. Fuzzy logc offers a possblty to mmc expert human knowledge. However, when the nput 1 Ths work was supported by the robotcs laboratory Foundaton of Chnese Academy of Scence under Grant Nos.RL * Correspondng author telephone:

2 Internatonal Journal of Informaton Technology, Vol.12, No.3, 2006 ncreases, the reasonng rules would expand rapdly, and the computaton would mount up exponentally. Neural network has the capablty to learn from exstng knowledge, but the knowledge representaton s very dffcult. GA s an evolutonary algorthm, and able to resolve composton optmzaton problems. But t updates the good ndvduals entrely and doesn t have exploted the characterstcs of the path soluton space. ACO s ft for the combnaton optmzaton problems, such as path plannng, but t can t be appled n dynamc envronment. In real system, moble robot always knows a lot of nformaton about statc obstacles n envronment, so we can explot the nformaton to mprove the algorthm effcency. Therefore, moble robot can plan the global route before movng. Ths paper combnes the characterstcs of ACO and APF, and proposes a path plannng approach n dynamc envronment that ntegrates the global planner and local planner. The basc dea s that, ACO s used to plan the global route based on statc envronment nformaton, and then APF s utlzed to program the local route. In ths paper, the pheromone nformaton obtaned from ACO s exploted to prevent t from gettng nto local mnmum. 2 Global Path Plannng For envronment part of whch s known, global planner would hghly mprove the qualty of the path. In ths paper, global planner employs ACO as a path plannng method. ACO smulates the behavor of ant colones n nature when they are foragng for food and fndng the most effcent routes from ther nests to food sources. ACO has an advantage for resolvng the large combnaton optmzaton problems, such as Travelng Salesman Problem (TSP), Flow-shop schedule and so on. These problems can t be resolved by tradtonal algorthm, such as dynamc programmng, A* algorthm. 2.1 Ant Colony Optmzaton Prncple Ants leave some chemcal substance, whch we call pheromone, on the route that they have passed. If the route s short, the ant would leave some pheromone to attract other ants, and the quantty of pheromone s n nverse proporton to the length of the path. Ants can also perceve the pheromone when they pass the route, and ther ac- 79

3 Hao Me, Yantao Tan, Lnan Zu A Hybrd Ant Colony Optmzaton Algorthm or Path Plannng of Robot n Dynamc Envronment tons could be nfluenced by the concentraton of pheromone. They would select a route wth a probablty n proporton to the concentraton of the pheromone. In ths way, the shorter of the path, the more frequent vsted by ants, the more pheromone accumulated on the path. Ths process wll be lasted untl all the ants select the shortest path. 2.2 Algorthm Improvements Tradtonal ACO exsts some lmtatons, such as requrng long tme, gettng nto local mnmum f the sze of the problem s large. In Tradtonal ACO, the pheromone concentratons of all elements are equally ntalzed. So the solutons are constructed blndly n the begnnng of evoluton phase, and t would take a long tme to fnd a better path from a great many smother paths. So we should mprove the ACO at some ponts. The frst step s the ntalzaton of pheromone concentraton. Tradtonal ACO ntalzes the pheromone concentraton equally. Ths would make the ACO take a lot of tme to converge to optmal resoluton, and also may make ACO get nto local optmal resoluton prematurely. So we can buld a pheromone feld at the begnnng of ACO. In ths feld, the shorter the dstance between current poston and obstacles, the smaller the pheromone concentraton of current poston. phe ds (1) Dfferent from TSP problem, the objectve functon of path plannng not only should nclude the length of path, but also should nclude the obstacle-avodance nformaton and the smoothness of the route. The obstacle-avodance nformaton manly relates to the least dstance between the path and the obstacles around. In addton, gven robot would slow down when t turns around, the route should be smooth. The objectve functon s m Lk 1 Fk = + w + w T L 1 2 = 1 d where L s the dstance between the startng pont and goal pont, L s the length of k the route that the k th ant agent has gone along, T s the number of the turnngs. m s the number of obstacles n the envronment, d s the dstance between the th (2) 80

4 Internatonal Journal of Informaton Technology, Vol.12, No.3, 2006 obstacle and the route that the k th ant agent has passed. w s the weght coeffcent. The smaller the value of objectve functon, the better the path. The ordnary ACO usually updates the pheromone of the best soluton or all of the solutons. The former method s only ft for the lmt soluton space, but not ft for the space when the soluton number s very large, because t would lose the dversty of solutons. The later method would occupy a lot of tme to update the pheromone when the ant populaton s very large. So after each teraton, we update the best 1/3 of all solutons. Smultaneously, because of the smoothness of soluton, namely, the qualty of soluton s as well as that of the solutons nearby, so we not only update the pheromone of elements of the selected soluton, but also update the pheromone of the elements that near the elements of the soluton selected to be updated. NUM k (3) τ ( t+ 1) = ρτ ( t) + τ j j j k= 1 τ () t s the pheromone concentraton of grd (,j). NUM s the number of ant j k agents. ρ s the evaporate coeffcent. τ s the pheromone ncrement left by ant j agent k on grd (,j). 2.3 Algorthm Descrpton The descrpton of the ACO employed n ths paper s as follows. Step1: Intalze the pheromone accordng to the method stated above. Step2: Construct a route soluton from the startng pont to the goal pont based on the pheromone nformaton. Frst generate a random number p, f p > q ( 0 q 0 s a number defned n advance). Then select the element whose pheromone concentraton s largest, namely j = max( τ ) (4) where j s the element to be selected, s the element whch s next to current element. If p q, then select a node as the next element wth a probablty computed 0 by followng formula P = wτ w τ (5) 81

5 Hao Me, Yantao Tan, Lnan Zu A Hybrd Ant Colony Optmzaton Algorthm or Path Plannng of Robot n Dynamc Envronment where w s the weght of drecton, ts computaton notaton s w 3 π / 2 θ (6) = π where θ s the angle between the drecton of goal poston relatve to current element poston and the drecton of the next element poston relatve to current element poston. θ [0, π ], so w [0.5, 1.5]. Because the bgger the θ, the probablty of the correspondng grd to be selected s smaller. Step3: Update pheromone. Update the pheromone of elements of the routes accordng to the method stated above. Step4: Ext and output the optmal soluton f the solutons have converged or reach the up lmt of teraton, otherwse jump to Step2. 3 Local Path Plannng Local planner determnes the navgaton ablty of moble robot and obstacle-avodance n unknown envronment or n dynamc envronment. In ths paper, the local planner s trggered only when the moble robot fnds that the poston whch s planned by global planner and t s about to pass by has been occuped or to be occuped by other dynamc obstacles. The local planner adopts Artfcal Potental Feld (APF) as ts path plannng algorthm, because t s a good method for real-tme obstacle-avodance, and can also utlze the pheromone generated by ACO to avod local mnmum. 3.1 Artfcal Potental Feld Artfcal potental feld was ntroduced by Khatb [7][8]. He defned obstacles as repellng force sources, and goals as attractng force sources. Moble robot s drven by the composton of the two forces. The nfluencng scope of attractng force s larger than repellng force. The repellng s effectve only n a small scope, so ths method s also called local algorthm. 82

6 Internatonal Journal of Informaton Technology, Vol.12, No.3, 2006 In ths paper, the moble robot receves three sorts of forces: the repellng force F r, the attractng force from the goal r F r and the attractng force from the pheromone generated by ACO F r. Then the drvng force of robot a p F r = F r r + F r a + F r (7) The value of repellng force F r s n reverse proporton to the dstance between r current poston and the poston of obstacles around t, and n proporton to the densty of obstacles near moble robot. The value of attractng force F r a s n proporton to the dstance between the moble robot and the goal. And the value of another attractng force F r s n proporton to the concentraton of pheromone and the dstance to the nearest obstacle. p p r (8) F phe ds p 3.2 Local Path Plannng APF s proptous to path plannng of moble robot n dynamc envronment. It can easly be mplemented, and has characterstcs for real-tme obstacle-avodance and route smoothness. So applyng APF as a local path plannng method s very sutable. In ths paper, moble robot frst goes forward accordng to the path planned by global planner. When fndng there are some dynamc obstacles on ts way or near the poston where t s about to pass, the robot employs the nformaton of dynamc obstacle and the pheromone generated by ACO to buld an APF. Tradtonal APF algorthm usually gets nto local mnmum because of not enough nformaton about global envronment. The pheromone generated by ACO can provde useful global nformaton. So employng the pheromone nformaton would help APF avod gettng nto local mnmum. The algorthm stated above has a bug. Suppose there are two postons A and B, and A s next to B. If moble robot fnds that B has the smallest value among all postons next to A and A also has the smallest value among all postons next to B, then the moble robot would wander between A and B. To remedy ths fault, we set a taboo 83

7 Hao Me, Yantao Tan, Lnan Zu A Hybrd Ant Colony Optmzaton Algorthm or Path Plannng of Robot n Dynamc Envronment table, whch records all postons the robot has passed. If the robot dscovers that the poston, whch has the smallest force value among all postons next to current poston, has already been n the taboo table, t would select an poston whose value s the second smallest of all postons next to current poston. 4 Smulaton Results and Analyss We mplement the hybrd algorthm n smulaton system developed by ourselves. Fg.1 The result of hybrd algorthm n smple envronment Fg.2 The result of hybrd algorthm n complex envronment Fg.3 GA and ACO smulaton results n smple envronment Fg.4 GA and ACO smulaton results n smple envronment 84

8 Internatonal Journal of Informaton Technology, Vol.12, No.3, 2006 Fg.5 GA and ACO smulaton results n complex nonstructural envronment The smulaton results shown n Fg.1 and Fg.2. In the fgures, S and E stand for the start pont and the end pont respectvely, and letter D stands for the dynamc obstacle. The s compose the path planned by global planner, and the small crcles compose the real route passed along by moble robot when t comes across dynamc obstacle. From the smulaton results above, we can conclude that the path plannng method based on ACO and APF together can fnd a near optmal path and avod obstacles tmely both n smple and complex envronment. We also compare the performance of ACO and that of GA. Fg 3~5 show the smulaton results of these two algorthms. In these fgures, the sold rectangles represent the path planned by ACO, and the hollow crcles represent the path planned by GA. We defne Performance = ρ tme + ρ length + ρ turnngs (7) as an evaluaton functon to estmate the performance of the two algorthms, where parameter tme s the runnng tme of the algorthm, length s the length of the path, and turnngs s the number of turnngs n the path planned by the algorthm. ρ, 1 ρ and 2 ρ 3 are the coeffcent weghts of tme, length and turnngs respectvely, and they are dependng on the mportance of the parameters. In ths paper, we set ρ 1 = 3, ρ 2 = 1 and ρ 3 = 5. The comparson results are shown n Table 1. From Table 1, we can see that the performance of ACO overmatches that of GA obvously. No mature tme, length and turnngs, the ACO excellent over GA n the gross. The reason for ths s that ACO explot the characterstc of soluton space n path plannng. In the path plannng, the solutons near best soluton are also good 85

9 Hao Me, Yantao Tan, Lnan Zu A Hybrd Ant Colony Optmzaton Algorthm or Path Plannng of Robot n Dynamc Envronment ones, whch we call the smoothness of soluton. ACO can reach good performance because t updates the pheromone concentraton around the elements of current best soluton. Whereas GA ntensfes the current best soluton as an ndvdual, and the solutons near t can t get ntensfed. GA ACO Table 1 Comparson between ACO and GA Fg 3 Fg 4 Fg 5 Length Tme (ms) Turnngs Performance Length Tme (ms) Turnngs Performance Conclusons In ths paper, a new hybrd method for path plannng of moble robot s developed and tested very well. It employs ACO as global path plannng algorthm and APF as local planner method. We also explot pheromone generated by ACO as global nformaton to gude the APF to jump to local mnmum. From the smulaton results, we can see that by syntheszng APF and ACO algorthm, global optmal and real-tme obstacle avodance can be both satsfed. We also compare the performance between ACO and GA, and nduce that ACO outmatches GA n path plannng. In the future, we wll consder the velocty of dynamc obstacles, and forecast the probablty of collson between dynamc obstacle and moble robot. References 1. Zhye L, Xong Chen and Wendong Xao. A New Moton Plannng Approach Based on Artfcal Potental Feld n Unknown Envronment. PDCAT 2004, LNCS 3320, pp ,

10 Internatonal Journal of Informaton Technology, Vol.12, No.3, Hee Rak Beom and Hyung Suck Cho, A Sensor-Based Navgaton for Moble Robot Usng Fuzzy Logn and Renforcement Learnng, IEEE Trans. On SMC, 1995,25(3),464~ N Bn, Chen Xong, Zhang Lmng, and Xao Wendong. Recurrent Neural Network for Robot Path Plannng. PDCAT 2004, LNCS 3320, pp , Luo Xong, Fan Xao-png, Y Sheng, Zhang Heng. A Novel Genetc Algorthm for Robot Path Plannng n Envronment Contanng Large Numbers of Irregular Obstacles. ROBOT, Vol.26, No.1, Jan Shuhua Lu, Yantao Tan, Jnfang Lu. Mult Moble Robot Path Plannng Based on Genetc Algorthm. Proceedngs of the 5 th World Congress on Intellgent Control and Automaton, 2004, John E. Bell, Patrck R. McMullen. Ant colony optmzaton technques for the vehcle routng problem. Advanced Engneerng Informatcs 18 (2004) Khatb. Real-tme obstacle avodance for manpulators and moble robots [J]. The Internatonal Journal Robotcs Research, 1986, 5(1): Koren Y. and Borensten J., Potental Feld Methods and Ther Inherent Lmtatons for Moble Robot Navgaton, Proc of IEEE Int. Conf. On Robotcs and Automaton, 1991, 1398~ Marco Dorgo, Erc Bonabeau, Guy Theraulaz. Ant algorthms and stgmergy. Future Generaton Computer Systems, 16 (2000): S.H.Lu, Y.T.Tan. Mult-Agent Learnng Methods n an Uncertan Envronment. IEEE Int. Conf. On Machne Learnng and Cybernetcs, p , Lnan Zu, Yantao Tan and Jnfang Lu. Algorthms of Task-Allocaton and Cooperaton n Mult Moble Robot System. Proceedngs of the 5 th World Congress on Intellgent Control and Automaton, 2004, We Hong, Yantao Tan, Zal Dong. The Approach of Extractng Features From the Local Envronment for Moble robot. Proceedngs of 2002 Internatonal Conference on Machne Learnng and Cybernetcs Vo2, pp , B. Denby, S. Le Hegarat-Mascle. Swarm ntellgence n optmsaton problems. Nuclear Instruments and Methods n Physcs Research A 502 (2003) Ana Crstna Matos and Ru Carvalho Olvera. An Expermental Study of the Ant Colony System for the Perod Vehcle Routng Problem. LNCS 3172, pp ,

11 Hao Me, Yantao Tan, Lnan Zu A Hybrd Ant Colony Optmzaton Algorthm or Path Plannng of Robot n Dynamc Envronment Hao Me (1983- ), male, master, man research: dstrbuted ntellgent system and mult-robot system. Yantao Tan (1958- ) receved hs M.S. degree n Control Theory and Engneerng and Ph.D. degree n Communcaton and Electroncs from Jln Unversty of Technology, ROC n 1987 and Currently, he s a professor n the school of Communcaton Engneerng and the Insttute of Automaton, Jln Unversty. Hs current research nterests nclude modelng and optmal control of complex systems, dstrbuted ntellgent system and mult-robot system, actve machne vson and the confluence of vson and control. Lnan Zu (1979- ) female, doctor, man research: dstrbuted ntellgent system and mult-robot system. 88