, Volume 2, Issue 1, pp 403–430

Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape

  • Vladimir J. Lumelsky
  • Alexander A. Stepanov

DOI: 10.1007/BF01840369

Cite this article as:
Lumelsky, V.J. & Stepanov, A.A. Algorithmica (1987) 2: 403. doi:10.1007/BF01840369


The problem of path planning for an automaton moving in a two-dimensional scene filled with unknown obstacles is considered. The automaton is presented as a point; obstacles can be of an arbitrary shape, with continuous boundaries and of finite size; no restriction on the size of the scene is imposed. The information available to the automaton is limited to its own current coordinates and those of the target position. Also, when the automaton hits an obstacle, this fact is detected by the automaton's “tactile sensor.” This information is shown to be sufficient for reaching the target or concluding in finite time that the target cannot be reached. A worst-case lower bound on the length of paths generated by any algorithm operating within the framework of the accepted model is developed; the bound is expressed in terms of the perimeters of the obstacles met by the automaton in the scene. Algorithms that guarantee reaching the target (if the target is reachable), and tests for target reachability are presented. The efficiency of the algorithms is studied, and worst-case upper bounds on the length of generated paths are produced.

Key words

RoboticsRobot motion planningCollision avoidance algorithmsPlanning with uncertaintyProvable algorithms

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Vladimir J. Lumelsky
    • 1
  • Alexander A. Stepanov
    • 2
  1. 1.Yale UniversityNew HavenUSA
  2. 2.Polytechnic UniversityBrooklynUSA