Dense Discrete Structures in Nonlinear Control Systems
Dept of Computer Science, University of Illinois-Urbana Cham
Last modified: June 3, 2006
Motion planning for nonlinear control systems is a fundamental problem which has been addressed in various contexts. Using a computational approach to the problem, reachability graphs of discretized nonlinear control systems are used to give resolution complete motion planners. In this paper, we present a new finite set of motion primitives for mobile robots such that the resulting reachability graph is dense in the configuration space of the robot without obstacles. We show the denseness using Ergodic theory. The problem of motion planning for the robot becomes a combinatorial search problem on the graph. Moreover, the size of such set of primitives is minimum.