HJB Approach for Motion Planning and Reachabilty Analysis
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, the authors focus on the cases when the controlled systems are constrained to evolve in a certain known set (e.g., avoidance of obstacles). They 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.