Predefined-Time Singularity-Free Control With Hybrid Actuator Optimal Allocation for Autonomous Spacecraft Docking

Autonomous rendezvous and docking operations require precise control of coupled translational and rotational dynamics under environmental disturbances and actuator constraints. This paper presents a novel control framework integrating a singularity-free predefined-time sliding mode controller with optimal control allocation for hybrid actuation systems. The proposed approach addresses the challenges of time-critical docking manoeuvres while managing the inherent underactuation of electromagnetic actuators. A comprehensive nonlinear dynamics model is developed to capture the six-degree-of-freedom coupled relative motion in elliptical orbits, explicitly incorporating orbital perturbations and environmental effects. The hybrid actuation architecture comprises electrostatically charged magnetocoulombic plates, magnetic torque coils, and chemical thrusters. A modified terminal sliding surface with time-regulator functions ensures state convergence within a prescribed time bound, independent of initial conditions, while eliminating singularities inherent to conventional terminal sliding mode formulations. The control allocation algorithm optimally distributes control effort among actuators according to their physical constraints and mission objectives, minimizing propellant consumption and electrical energy expenditure. Lyapunov stability analysis rigorously establishes convergence guarantees for both the reaching and sliding phases. Numerical simulations demonstrate successful rendezvous and docking manoeuvres with feasible actuator demands and effective disturbance rejection, validating the robustness of the control framework. These results illustrate the potential of hybrid electromagnetic-propulsive actuation with advanced nonlinear control for future on-orbit servicing and space debris mitigation missions.