Maximum Kinetic Energy Paths for A Decaying-Speed Dubins Vehicle With Application to Gliding Flight

Abstract

This paper considers the optimal control problem of steering a Dubins vehicle with a decaying speed that depends linearly on the turn-rate to a terminal point and heading with maximum kinetic energy. Pontryagin’s minimum principle is applied and the extremals are identified as sequences of straight segments and spiral-shaped turns described by involutes of a circle. A method is proposed to exactly transcribe the optimal control problem into a series of finite dimensional optimizations. Each of these optimizations determines a locally optimal candidate path that reaches the terminal state. The lowest cost path among the candidate paths is then identified. The approach is demonstrated through several numerical examples.