Switching time-optimal control of spacecraft equipped with reaction wheels and gas jet thrusters

This paper studies the time-optimal control problem of a rigid spacecraft equipped with both reaction wheels and gas jet thrusters, in which the reaction wheels are the main actuators and the gas jet thrusters act only after saturation or to prevent future saturation of the reaction wheels. It is assumed that the control torques are generated about the principal axes of the spacecraft. The presence of both reaction wheels and thrusters gives rise to two operating modes for each axis. Since this system can change dynamics, it can be regarded as a switched dynamical system. The time-optimal control problem for this system is solved using the embedding approach. With this technique the switched system is embedded into a larger set of systems and the optimal control problem is formulated in the latter. The main advantages of this technique are that assumptions about the number of switches are not necessary, integer or binary variables do not have to be introduced to model switching decisions between modes, and the optimal values of the switching times between modes are obtained without introducing them as unknowns of the optimal control problem. As a consequence, the resulting problem is a classical optimal control problem. Feasibility of the obtained solution is validated through propagation of the initial state. Optimality of the obtained solutions is verified by checking the compliance with Pontryagin's Maximum Principle.