Maximum principle in finding free final-time optimal trajectory of mobile robot for moving target tracking

Abstract

Moving target tracking with free final-time is a special case of optimal control problem where both the final state and the final time are free but dependent on each other. In this paper, the necessary first order conditions for a candidate optimal trajectory and admissible optimal control inputs for a two wheeled differential drive robot have been derived in the light of Pontryagin's Maximum Principle. The boundary value problem has been solved analytically and soundness of the results have been established by simulations.