In terms of Rudyak's generalization of Farber's topological complexity of the path motion planning problem in robotics, we give a complete description of the topological instabilities in any sequential motion planning algorithm for a system consisting of non-colliding autonomous entities performing tasks in space whilst avoiding collisions with several moving obstacles. The Isotopy Extension Theorem from manifold topology implies, somewhat surprisingly, that the complexity of this problem coincides with the complexity of the corresponding problem in which the obstacles are stationary.
Bibliographical note10 pages; Final version, to appear in Proc. Amer. Math. Soc
- 55R80, 55S40 (Primary), 55M30, 68T40 (Secondary)
- robot motion planning
- higher topological complexity
- sectional category
- configuration spaces
- moving obstacles