Research Article
HJB approach for motion planning and reachabilty analysis
@INPROCEEDINGS{10.4108/icst.valuetools.2011.245820, author={Hasnaa Zidani and Olivier Bokanowski and Anna D\^{e}silles}, title={HJB approach for motion planning and reachabilty analysis}, proceedings={5th International ICST Conference on Performance Evaluation Methodologies and Tools}, publisher={ICST}, proceedings_a={VALUETOOLS}, year={2012}, month={6}, keywords={minimal time problem moving targets time-dependant state constraints motion planning obstacle avoidance hamilton- jacobi equations level set method reachablity analysis}, doi={10.4108/icst.valuetools.2011.245820} }- Hasnaa Zidani
Olivier Bokanowski
Anna Désilles
Year: 2012
HJB approach for motion planning and reachabilty analysis
VALUETOOLS
ICST
DOI: 10.4108/icst.valuetools.2011.245820
Abstract
Because of their importance in many applications, questions of path planning and reachability analysis for nonlinear dynamical systems have been studied extensively in the control theory. Here we focus on the cases when the controlled systems are constrained to evolve in a certain known set (e.g avoidance of obstacles). We study general framework based on an optimal control approach and on solving Hamilton-Jacobi (HJ) equations. This approach provides a very efficient tool for treating many cases encountered in real applications and can be extended to general situations including moving targets and/or obstacles problems, dynamical systems under uncertainties, or differential games. The relevance of the method will be shown on some numerical examples (motion planning with obstacle avoidance).