Robot Motion Planning with Uncertainty in Control and Sensing

One of the key topics in robot reasoning is motion planning. Most of the research in this domain has focused on the topological and geometrical problem of finding a collision-free path connecting two configurations of the robot among obstacles, by assuming complete and accurate prior knowledge of the robot workspace and perfect control of the robot. But there exists a variety of robot operations which cannot be achieved reliably by simply executing preplanned paths. These operations require several kinds of uncertainty to be taken into account at the planning stage in order to generate motion strategies, which typically combine motion and sensing commands. In this paper, we consider the problem of planning motion strategies in the presence of uncertainty in both control and sensing for simple robots described in a two-dimensional configuration space. We consider the preimage backchaining approach to this problem, which was first proposed by Lozano-Perez, Mason and Taylor (1984). A preimage of a goal is a region such that if the robot is in this region prior to the execution of a motion command, it is guaranteed that the robot will be in the goal after the execution of the command. Backchaining consists of recursively treating each computed preimage as an intermediate goal, until a computed preimage contains the region in which the initial configuration of the robot is known to be. Although attractive, the approach raises several difficult computational issues. One of them, which is directly addressed in this paper, is preimage computation. We describe two practical methods for computing preimages, which we call backprojection from sticking edges and backprojection from goal kernel. Both methods proceed by separating two basic issues in preimage computation: goal reachability and goal recognizability. They both make use of the notion of backprojection, a concept developed by Erdmann (1984). The second method presents significant advantages over the first, but the two methods can be combined in order to draw the best of each. The combined method is probably the most effective method proposed so far for computing preimages. A motion planner embedding this method has been implemented. In the last sections of the paper, we discuss non-implemented improvements of this planner and present additional results. Acknowledgements: This research was funded by DARPA contract DAAA21-89-C0002 (Army), and SIMA (Stanford Institute of Manufacturing and Automation). The authors also thank Randy Wilson for useful suggestions. PROTECTED UNDER INTERNATIONAL COPYRIGHT ALL RIGHTS RESERVED. NATIONAL TECHNICAL INFORMATION SERVICE U.S. DEPARTMENT OF COMMERCE