Planning Smooth Paths for Mobile Robots

Abstract

A mobile robot with a wheeled based is subject to non-holonomic constraints on its motion. We present a planner for finding obstacle-avoiding paths subject to the constraints. We define a set of canonical trajectories which satisfy the constraints. A configuration space can be constructed for these trajectories in which there is a simple characterization of the boundaries of the obstacles generated by the workspace obstacles.

We describe a graph search algorithm which divides the configuration space into sample trajectories. The characterization of the boundaries enables us to calculate an approximate path in time $O\left( {\frac{{{{n}^{3}}}}{\delta }\log n + A\log \left( {\frac{n}{\delta }} \right)} \right)$, where n is the number of obstacle vertices, A is the number of free trajectories, and δ is a robustness measure. Using a plane sweep technique and quadtrees we can generate robust paths in time $O\left( {{{n}^{4}}\log n + \frac{{{{n}^{2}}}}{{{{\delta }^{2}}}}} \right)$.

Research supported by the Defense Advanced Research Projects Agency (DoD), monitored by Space and Naval Warfare Systems Command under Contract N00039-88-C-0292.

Supported by a David and Lucile Packard Foundation Fellowship and by NSF Presidential Young Investigator Grant IRI-8958577