Explicit Spacecraft Thruster Control Allocation With Minimum Impulse Bit

Thruster control allocation (TCA) is a key functionality for many spacecraft, with a significant impact on control performance, propellant consumption, and fault tolerance. Propellant-optimal solutions are desirable and are either based on onboard numerical optimization, or explicit optimization via the use of offline-generated look-up tables (LUTs). This article proposes a TCA and modulation method of the latter type by using multiparametric programming and presents a novel fast LUT evaluation algorithm. Fault tolerance and the handling of non-attainable control commands with full controllability exploitation are also addressed. Furthermore, the solution is extended to include the non-convex minimum impulse bit (MIB) constraint, where the proposed solution can find the global optimum. The use of this constraint is demonstrated in a close-range orbital rendezvous scenario, yielding significant improvements to the performance of boosts, forced motions, and station-keeping maneuvers, at the cost of greater propellant consumption and computation time. Results in consumer hardware for a12-thruster configuration show a worst case onboard computation time of $7~\mu $ s and 0.5 ms for the cases without and with the MIB constraint, which are up to two orders of magnitude lower than those for numerical optimization with a state-of-the-art optimizer. The proposed onboard algorithms are simple, non-iterative, and have worst case computational effort guarantees.