Rendezvous Control for Non-Cooperative Tumbling Targets with Stability and Feasibility Guarantees

A novel predictive controller is introduced for rendezvous with non-cooperative tumbling targets in active debris removal applications, based on the model predictive control for tracking (MPCT) framework, which improves the robustness and computational efficiency of conventional MPC by optimizing the system toward artificial equilibrium points rather than fixed references. This paper aims to provide a computationally efficient and theoretically sound control strategy that enables reliable proximity operations around tumbling objects, despite their complex rotational motion. The target’s nonperiodic rotational dynamics and state and control constraints are considered. The approach is based on applying an intermediate coordinate transformation that eliminates the time dependency due to rotations in the constraints. The proposed algorithm leverages feasible trajectories, obtained through the conservation of momentum and energy of rotating bodies, to obtain strong convergence guarantees on arbitrary horizons. A control law is then found as the solution to a quadratic programming problem that provides feasibility and stability guarantees by means of a terminal virtual controller. The main result is an MPCT-based controller for linear time-varying systems induced by rotational dynamics, with provable feasibility and stability guarantees. A near-rendezvous simulation with the Envisat spacecraft confirms the practical relevance and performance of the proposed controller.