Pose Tracking Control for Spacecraft Proximity Operations Using the Udwadia-Kalaba Framework

This paper develops an analytical dynamics-based approach for simultaneous position and orientation tracking control of a chaser spacecraft with respect to an uncontrolled target. The control requirements are formulated as holonomic or nonholonomic constraints, which are expressed as linear and angular acceleration constraints. The complete six-degree-of-freedom formulation of the Udwadia-Kalaba-based pose tracking controller generating exact real-time control forces and torques is presented. For design purposes, the method assumes a precise knowledge of the system parameters and states, along with perfect control action by the actuators. The exponential convergence of the constraint dynamics is proven using the Lyapunov stability theory. Simulation results demonstrate exponentially stable position and orientation tracking for close-proximity operations in perturbed low Earth orbits. Finally, the controller is experimentally validated using the Spacecraft Proximity Operations Testbed at Carleton University.