Figure 26: Learning in Scene 3. Figure 27: Learning in Scene 4. about 100 Nodes per Second in Scene 1. 7 Conclusions and Related Work

A motion planner for car-like robots based on a global/local approach. REFERENCES 26 Acknowledgments We would like to thank Geert-Jan Giezeman for the implementation of many cruciaìgeometric' routines (some of which are contained in the Plageo library, see Gie93]), Erik Vermeer, who has written most of the code for articulated robots, Jules Vleugels, Erik van Wessel, and Otfried Schwarzkopf for Ipe, with which all gures in this paper where either created or edited. References BL90] J. Barraquand and J.-C. Latombe. A monte-carlo algorithm for path planning with many degrees of freedom. A local approach for path planning of manipulators with a high number of degrees of freedom. A practical approach to motion planning for manipulators with many degrees of freedom. In Proc. 5th Intern. Kon91] K. Kondo. Motion planning with six degrees of freedom by multistrategic bidirectional heuristic free-space enumeration. In this paper we have presented a probabilistic technique for the learning motion planning problem. This technique, which is conceptually is simple, proves to be very fast for simple robots (e.g., free ying planar robots, easy articulated robots), and powerful enough to deal reasonably well with non-holonomicaly constrained robots (car-like robots) and robots with high degrees of freedom. A nice property furthermore is the great exibility of the method. In order to apply the method to some particular robot type, all that is needed is a local method which computes feasible paths for this robot type, and some (induced) metric. Experimental results (see Mas92], Sve93]) indicate that very primitive local methods achieve the best results. Hence, it should normally be no problem to nd a good local method for some given robot type. Currently we are working on the application of the method to tractor-trailer robots, and furthermore we are planning extensions of the method in various directions, aimed at solving more diicult motion planning problems, such as motion planning in scenes with multiple robots, moving obstacles, or perhaps some amount of uncertainty. Also we are planning to apply our method to 3-dimensional workspaces. Finally, we are also considering some possibilities to do the node adding in a non-random manner, which guarantees completeness in the query phase. 24 Figure 22: A 4DOF articulated robot in scene 3. Figure 23: A 9DOF articulated robot in scene 4.