Stochastic Real-time Optimal Control: A Pseudospectral Approach for Bearing-Only Trajectory Optimization

Abstract

A method is presented to couple and solve the optimal control and the optimal estimation problems simultaneously, allowing systems with bearing-only sensors to maneuver to obtain observability for relative navigation without unnecessarily detracting from a primary mission. A fundamentally new approach to trajectory optimization and the dual control problem is developed, constraining polynomial approximations of the Fisher Information Matrix to provide an information gradient and allow prescription of the level of future estimation certainty required for mission accomplishment. Disturbances, modeling deficiencies, and corrupted measurements are addressed with recursive updating of the target estimate with an Unscented Kalman Filter and the optimal path with Radau pseudospectral collocation methods and sequential quadratic programming. The basic real-time optimal control (RTOC) structure is investigated, specifically addressing limitations of current techniques in this area that lose error integration. The resulting guidance method can be applied to any bearing-only system, such as submarines using passive sonar, anti-radiation missiles, or small UAVs seeking to land on power lines for energy harvesting. Methods and tools required for implementation are developed, including variable calculation timing and tip-tail blending for potential discontinuities. Validation is accomplished with simulation and flight test, autonomously landing a quadrotor helicopter on a wire