Optimal Control and Pursuit Game for Planar Rigid Segments with Inertial Dynamics

Abstract

This paper studies time-optimal control and pursuit differential game problems for planar rigid segments with inertial dynamics, actuated by bounded forces applied perpendicularly at their endpoints. The objective of the control problem is to transfer a segment between prescribed configurations in minimum time. We derive closed-form expressions for the minimal transfer time, together with a complete analytical description of optimal motions. The obtained time-optimal steering results are then used to construct a capture strategy for the pursuit game, which guarantees finite-time capture.