Optimal Trajectories for a Mobile Robot with Bounded Accelerations in the Presence of a Wall or a Bounded Obstacle

Abstract

The time-optimal path planning problem in the plane for a point mass mobile robot navigating in an obstacle-presence environment is studied. The robot is subjected to maximal acceleration limits. The paper extends previous results which solved this problem in an obstacle-free environment. The problem is characterized as an optimal control problem with state-dependent obstacle constraints. Two equivalent ways of analysis are employed to obtain the necessary conditions for optimality under these constraints. The optimality conditions yield eight path primitives that form the time-optimal trajectories in the presence of obstacles. Representative examples are studied in order to demonstrate the method.