Motion Planning of Nonholonomic Systems - Nondeterministic Endogenous Configuration Space Approach

This paper presents a new nondeterministic motion planning algorithm for nonholonomic systems. Such systems are represented by a driftless control system with outputs. The presented approach combines two different methods: the endogenous configuration space approach and the Particle Filters. The former, fully deterministic, was originally dedicated to the motion planning problem for mobile manipulators. The latter, of stochastic approach, was designed for solving optimal estimation problems in non-linear non-Gaussian systems. A mixture of these methods results in a nondeterministic endogenous configuration space approach that outperforms the traditional one in regions where the classical inverse Jacobian algorithm loses convergence. In accordance with the Particle Filters approach the new algorithm consists of three major steps: prediction, update, and resampling. In contrast to its original version, the presented algorithm contains an additional step of dividing the particles into different subsets. Each subset is processed in a different way during the prediction phase. The performance of the new algorithm is illustrated by solving the motion planning problem for a rolling ball.