Navigating in unfamiliar geometric terrain

Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rather, it finds out about obstacles as it encounters them. We compare the distance walked by the robot in going from .s to t to the length of the shortest path between s and t in the scene. We describe and analyze robot strategies that minimize this ratio for different kinds of scenes. In particular, we consider the cases of rectangular obstacles aligned with the axes, rectangular obstacles in more general orientations, and wider classes of convex bodies both in two and three dimensions. We study scenes with non-convex obstacles, which are related to the study of maze-traversal. We also show scenes where randomized algorithms are provably better than deterministic algorithms. 1. Motivation and Results Practical work on robot motion planning falls into two categories: motion planning through a known scene, in which the robot has a complete map of the environment, and motion planning through an unknown scene in which an autonomous robot must find its way through a new environment (see, for example, [6, 8, 9, 13, 15] and references therein). Virtually all previous theoretical work ([23] and ref“Laboratory for Computer Science, MIT, Cambridge, MA 02139. Supported in part by an NSF graduate fellowship. Part of the work was done while this author was visiting IBM T. J. Watson Research Center. avrim’dtheory. lcs. mit. edu tIBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10598. {pragh, sbar]@ibm. com Permission to copy without fee all or part of ths material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and ifs date appear, and notice is given that copying is by perrmsslon of the Asoclation for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. @ 1991 ACM 089791-397-3/91/0004/0494 $1.50 erences therein) has focused on the former problem. Papadimitriou and Yannakakis [17] studied the latter problem, which is also the subject of this paper: the design and evaluation of strategies for navigation in an unknown environment. The unfamiliar environment may be either a warehouse or a factory floor whose contents are frequently moved, or a remote terrain such as Mars [21]. The design and evaluation of algorithms for such navigation is a natural algorithmic problem that deserves more theoretical study.

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