Closed-Loop Time-Optimal Attitude Maneuvering of Magnetically Actuated Spacecraft

Abstract

This paper examines the performance of the pseudospectral optimal control scheme for closed-loop time-optimal attitude maneuvering of the NPSAT1 spacecraft, a magnetically actuated spacecraft designed and built at the Naval Postgraduate School. The closed-loop control is devised and implemented using the notion of Caratheodory-π solutions: repeated computation and update of the complete open-loop control solution in real-time. The performance of the pseudospectral feedback-control scheme is compared to a standard state feedback-control technique. It is shown that the use of standard state feedback control leads to significantly slower convergence time and may lead to substantially lower performance metrics. The substantial performance gains when using closed-loop optimal control are attributed to the optimal scheme’s ability to exploit the full maneuverability envelope of the spacecraft by applying bang-bang controls in all three directions. In contrast, traditional gain-based feedback control laws substantially limit the performance of the vehicle to well below its physical capabilities. The feasibility of each open-loop optimal control solution is verified by numerical propagation while Pontryagin’s necessary conditions for optimality are used to verify the solution’s optimality.