Maximum Kinetic Energy Paths for a Dubins Vehicle with Decaying Speed

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. A method is proposed to exactly transcribe the continuous optimization into a series of finite dimensional optimizations; each of which solves for locally optimal extremal that satisfies the terminal condition. Next, an application of this path planning approach to gliding flight is examined. A technique is established to map the planar paths to three-dimensional trajectories for an aerodynamic glider model with angle-of-attack and bank-angle controls. The maximum kinetic energy obtained using the mapping is compared to a baseline glider guidance technique through numerical simulations.