2nd Internatonal Conference on Autonomous obots and Agents Prorty based Dynamc Multple obot Path Plannng Abstract Taxong Zheng Department of Automaton Chongqng Unversty of Post and Telecommuncaton, Chna zhengtaxong@163.net D. K. Lu AC Centre of Excellence for Autonomous Systems (CAS), Faculty of Engneerng Unversty of Technology, Sydney, Australa dklu@eng.uts.edu.au Png Wang Department of Automaton Chongqng Unversty of Post and Telecommuncaton, Chna wangpng@cqupt.edu.cn Path plannng has been a topc of research n multple robot coordnaton and control. The purpose of ths paper s to nvestgate the path plannng problem of a group of robots wth communcaton between each other to perform a set of prortzed tasks n a dynamc envronment. Unlke tradtonal path plannng approaches that a path does not change once the path has been planned, the approach nvestgated n ths paper plans each robot s path dynamcally,.e., the path wll change accordng to the envronment. When one robot starts to perform or fnshes a task, t broadcasts the task s start poston or goal poston to other robots. Then other robots wll change ther paths f the broadcast poston has nfluence on ther planned paths. Keywords: multple robots, path plannng, collaboratve control 1 Introducton Path plannng s one of the fundamental problems n multple moble robotc systems. Varous algorthms have been proposed and nvestgated to solve ths problem. These algorthms can be roughly categorzed as centralzed and decentralzed accordng to the nformaton handlng structure among robots. Centralzed path plannng algorthms normally assgn prortes to robots n advance. They can guarantee optmal path f the envronment s statc and the number of robots s small. In a dynamc envronment wth large number of robots, decentralzed path plannng algorthms are more preferable. Decentralzed path plannng algorthms often apply traffc rules and thus are sutable for route network. They fnd the optmal paths and solve conflct problems by assgnng prortes dynamcally and negotatng among robots. They allow each robot to search ts own path n advance wthout consderng other robots. If there exts a potental collson, they can negotate to solve the conflct problem. Soluton of the negotaton could be that one robot stops and wats untl the potental collson dsappears. In the case of a large number of tasks wth dfferent prorty levels n a dynamc envronment, each robot has to perform many tasks wth dfferent prorty levels n the order of prorty. The current algorthms, ether centralzed or decentralzed, cannot guarantee that the planned path for each robot s always optmal because all the tasks are consdered as statc obstacles at the plannng stage. For example, contaner handlng n a contaner termnal, f one robot removes the contaner from a place before the other robots reaches that place, the contaner should not be consdered as a statc obstacle to other robots. Other robots need not move around the place to avod collson. On the other hand, f a contaner s placed at another robot s path before t passes the poston, the task wll be an obstacle. Ths research wll focus on these two cases and solve the problem by proposng an effectve approach. 2 Lterature evew Dfferent approaches for multple moble robot path plannng have been proposed and studed by researchers. The approaches to avod plannng path n a hgh-dmensonal composte confguraton space are prorty assgnment and decouplng technques. Hu et al [1] proposed a trackng controller for moble robots by ncorporatng neural dynamcs equatons nto a conventonal non-tme based controller, whch 373
2nd Internatonal Conference on Autonomous obots and Agents resolves the collson problem for mult-robot systems by settng a set of control rules for every case. For dfferent envronment or stuaton, the control rules have to be set dfferently. Bennewtz[2] proposed a path plannng approach to mult-robot systems by optmzng prorty schemes for prortzed and decoupled technques. Every robot generates ts path wthout consderng the paths of others. Possble conflct n the traectores of robots s then checked. The conflct between robots s resolved by ntroducng a prorty scheme that determnes the order of prorty. The path of a robot s planned n ts confguraton tme space based on the map of the envronment and the paths of the other robots wth hgher prortes. Aronov et al [3] studed the moton-plannng problem for pars and trples of robots operatng n a shared workspace contanng n obstacles. They showed that t s suffcent to consder a constant number of robot systems whose number of degree of freedom s at most d-1 for pars of robots and d-2 for trples. They d presented a O ( n ) tme algorthm to solve the motonplannng problem for a par of robots, whch s one order of magntude faster than what the standard method would gve. For a trple of robots the runnng tme becomes d 1 O ( n ), whch s two orders of magntude faster than the standard method. Gulherme [4] addressed the problem of plannng the moton of a team of moble robots subect to constrants mposed by sensors and the communcaton network. The goal was to develop a decentralzed moton control system that leads each robot to ther ndvdual goals whle keepng connectvty wth ts neghbours. Expermental results wth a group of car-lke robots equpped wth omn drectonal vson systems were presented. LaValle et al[5] ntroduced a form of optmalty that s consstent wth concepts from mult-obectve optmzaton and game theory research by consderng ndependent performance crtera. They mplemented mult-robot moton plannng algorthms derved from the prncple of optmalty for three cases: ) coordnaton along fxed and ndependent paths; ) coordnaton along ndependent roadmaps; and ) unconstraned moton plannng. It can be seen that the method n [1] s to set dfferent control rules for dfferent envronments or stuatons to solve collson problem but not deal wth the path plannng problem. The algorthm n [2] needs to compute the possble collson zones n advance, and t s obvous that the compute cost wll ncrease rapdly wth the ncrease of the number of robots. The algorthm n [3] wll gve a good performance only f t s appled n the stuaton wth a small quantty of robots, such as the stuaton wth two or three robots. The algorthm n [5] optmzes each robot s path by consderng ndependent performance crtera. All the methods or algorthms mentoned n the lteratures cannot guarantee an optmal path for each robot consderng the dynamc change of the envronment. 3 An approach for path plannng 3.1 Problem descrpton Gven n prortzed tasks are assgned to m robots and communcatons are exsted among the robots. Each robot knows the envronment n advance. For 1 2 3 robot, ts tasks r = { r k, r, r, Lr }, where r denotes the th task of robot, are arranged n the order of prorty. The robot executes the tasks from the one wth hghest prorty to the one wth lowest prorty. For the task r of robot, ts start poston and goal poston are respectvely. To execute the task r, 1 g s and g need to move from the destnaton of the predecessor 1 task r to s, then from s to g. For the frst 1 task r, s assumed to move from ts ntal 0 1 1 1 poston s to s, then from s to g. For undertakng each task, the robot needs to plan a path from ts current poston to the start poston of the next task, and to the destnaton based on the envronment. For example, to execute task r, robot wll plans ts path P n advance accordng to the statc obstacles n the envronment when t fnshes 1 the task r. When obot executes the task r along the planned path P, three cases mght happen: (1) The goal postons of other robots tasks are on the path P and other robots put ther obects on the way of P before robot passes t. If robot moves along ts orgnal path P, a collson wll occur. (2) The start postons of other robots are orgnally on the way of path P and are consdered as statc obstacle(s) when the robot plans ts path. But these obstacles wll be moved before the robot moves around t. In these cases, robot does not need to move around the obstacle. A straght path at that poston should be generated. (3) obots paths are crossed, collson among the robots may happen when they undertake ther tasks. 374
2nd Internatonal Conference on Autonomous obots and Agents 3.2 Path plannng An envronment s represented by occupancy grds, whch separate the envronment nto a grd of equally spaced cells. Then the path plannng for each robot becomes a graph search problem, shown n Fgure 1. task robot robot task Fgure 1: The occupancy grd expresson of an envronment Gven that robot ust fnshes ts task 1 r, t 1 plans ts path P from g to s then to g base on the current envronment. The path P satsfes the condton that the robot does not collde wth any obect f all the obects keep statc when execute the task r. The path P wll then be adusted n the followng cases: Case 1: meets other robots at the ntersecton area of ther paths. The robot performng the task wth hgher prorty s endowed wth hgher prorty. If the robots have the same prortes, the robot closer to ts goal poston of the current task wll be assgned hgher prorty. That s to say, the robot wth lower prorty wll stop and wat tll the robot wth hgher prorty passes the ntersecton. Case 2: The task s goal poston of robot s on the path of robot and has located the task at ts goal poston before passes the poston. In ths case, need to re-plan the path around the obstacle. Case 3: One task s removed by robot from ts poston whch s on the way of other robot, ths task wll no longer be as obstacle to robot. Then the path P of robot s not the optmzed path any more. The robot wll plan a new path from ts current poston to ts goal poston. 4 Smulaton esults In order to verfy the method presented above, two smple examples, each of whch conssts of two robots and four tasks, are used. Each robot s assgned two tasks respectvely, and each task s to move a box from a start poston to a destnaton. The tasks start postons and goal postons, and the robots start postons n example one s shown n Fgure 2. A* algorthm was appled as the path plannng algorthm. Fgure 3 shows dfferent states of operaton when the two robots are movng the boxes n the example one. In Fgure 3(a) and 3(b), obot 2 (whte) wats at the ntersecton untl obot 1 (green) passes the ntersecton because obot 1 s task prorty s hgher than that of obot 2. In Fgure 3(c) and 3(d), As obot 1 has moved the second box from ts start poston and the box s no longer the obstacle of obot 2, obot 2 re-planed ts path to pass ths start poston. Fgure 3(c) shows the moment ust before obot 1 reaches the start poston of ts second task. In Fgure 3(c) the blue curve shows the current path of obot 2 and the yellow lne shows the changed path after obot 1 take ts second task away from the start poston. Fgure 3 (d) shows that obot 2 goes drectly through the orgnal poston of obot 2 s second task s start poston. That s to say, obot 1 s second task s no longer an obstacle for obot 1. Fgure 3(e), 3(f) and 3(g) shows the Case 2 stated n Secton 3.2,.e., obot 1 moved a box to ts goal poston, but the goal poston of obot 2 s second task s on the way. obot 1 re-planed ts path to avod collson wth the box by takng a way around the box. Fgure 3(e) shows the moment obot 1 locates the box at the goal poston and the box becomes an obstacle of obot 2. obot 2 re-plans ts path at ths moment. The blue lne and yellow curve n Fgure 3(e) shows the orgnal path and the changed path of obot 2 respectvely. Fgure 3(f) and 3(g) shows obot 2 move around the obstacle. Fgure 3(h) shows the fnal state of the two robots when they fnsh ther tasks. Fgure 4 shows the tasks start postons and goal postons and the robots start poston n example 2. Smlar to Fgure 3 n example 1, Fgure 5 shows dfferent states of operaton when the two robots are movng the boxes n ths example. Fgure 5(a) and 5(b) shows the Case 1 n ths example that obot 1 and obot 2 have the same prorty. But obot 2 must wats at the ntersecton untl obot 1 passes the ntersecton because the dstance from obot 1 s current poston to ts goal poston s shorter than that of obot 2, therefore hgher prorty s assgned to obot 1. Fgure 5(c) shows the moment that before obot 2 reaches ts frst task goal poston obot 1 has reached ts second task start poston. The blue lne n Fgure 5(c) ndcates the orgnal path of obot 1 at ths moment. That s to say, obot 1 should not go around any statc obstacle. Fgure 5(d) shows the 375
2nd Internatonal Conference on Autonomous obots and Agents moment that obot 2 reaches ts frst task s goal poston and obot 1 s on the way to ts goal poston. Fgure 5(e) shows the moment that obot 2 moves ts frst task to ts goal poston and obot 1 replans ts path accordng to state of the statc obstacle. The yellow curve n Fgure 5(e) ndcates the changed path of obot 1. That s to say, obot 1 wll move along the yellow curve to ts goal poston. Fgure 5(f) shows that obot 1 goes around the obstacle. Fgure 5(g) shows the fnal state of the two robots when they fnsh ther tasks. 5 Concluson The smulaton results have shown that the proposed method n ths paper can dynamcally plannng the paths of a team of robots under the condtons of the three cases. Partcularly, when several robots perform dstrbuted prortzed tasks, the method can guarantee collson-free paths for each robot. Ths method wll be further nvestgated and mplemented for smultaneous task allocaton and path plannng problems and appled to a number of robots n a hghly dynamc envronment wth many tasks. Experments wll be conducted. 6 eferences [1] Hu, E., Yang, S.Y., Chou, D., and Smth, W.., eal tme trackng control obstacle wth obstacle of multple moble robots. Proceedngs of IEEE Internatonal Symposum on Intellgent Control, pages 87-92, Vancouver, Canada, 2002 [2] Bennewtz, M., Burgard, W., and Thrum, S., Optmzng schedules for properted path plannng of mult-robot systems, Proceedngs of IEEE Internatonal Conference on obotcs and Automaton, volumn 1, P.271-276, Seoul, South Korea, May 2001. [3] Aronov, B., M. de Berg, F. van der Stappen, Svestka, P., and Vleugels, J., "Moton plannng for multple robots," Dscrete and Computatonal Geometry, 22:505-525 (1999). [4] Perera, Gulherme A. S., Das, Aveek K., Vay Kumar; Campos, Maro F. M., Decentralzed moton plannng for multple robots subect to sensng andcommuncaton constrants, Second Internatonal Workshop on Mult-obot Systems Mar, 2003 Washngton DC,USA, P.267-278. [5] LaValle, S.M.; Hutchnson, S.A, Optmal moton plannng for multple robots havng ndependent goals, IEEE Internatonal Conference on obotcs and Automaton. P.2847-2852, 1996. 376
2nd Internatonal Conference on Autonomous obots and Agents 1 10 6 4 5 2 9 3 8 7 1: obot 1 start poston 2: obot 2 start poston 3: obot 1 frst task start poston 4: obot 2 frst task start poston 5: obot 1 frst task goal poston 6: obot 2 frst task goal poston 7: obot 1 second task start poston 8: obot 2 second task start poston 9: obot 1 second task goal poston 10: obot 2 second task goal poston Fgure 2: The ntal postons of the robots and ther tasks n example one (a) (b) (c) (d) (e) (f) (g) (h) Fgure 3: The state of robot1 and robot2 at dfferent tme example one 377
2nd Internatonal Conference on Autonomous obots and Agents 1: obot 1 start poston 8 10 2: obot 2 start poston 3: obot 1 frst task start poston 7 6 9 4: obot 2 frst task start poston 4 5 3 2 5: obot 1 frst task goal poston 6: obot 2 frst task goal poston 7: obot 1 second task start poston 1 8: obot 2 second task start poston 9: obot 1 second task goal poston 10: obot 2 second task goal poston Fgure 4: The ntal postons of the robots and ther tasks n example two (a) (b) (c) (d) (e) (f) (g) Fgure 5: The state of robot1 and robot2 at dfferent tme n example two 378