General formulation of an analytic, Lipschitz continuous control allocation for thrust-vectored controlled rigid-bodies

Abstract

This paper presents a general framework for solving the control allocation problem (CAP) in thrust-vector controlled rigid-bodies with an arbitrary number of thrusters. Two novel solutions are proposed: a closed-form, Lipschitz continuous mapping that ensures smooth actuator orientation references, and a convex optimization formulation capable of handling practical actuator constraints such as thrust saturation and angular rate limits. Both methods leverage the nullspace structure of the allocation mapping to perform singularity avoidance while generating sub-optimal yet practical solutions. The effectiveness and generality of the proposed framework are demonstrated through numerical examples on a marine vessel and an aerial quadcopter.