Dual quaternion based autonomous rendezvous and docking via model predictive control

This paper presents a Guidance and Control (G&C) strategy to address 6-Degrees-Of-Freedom (6-DOF) spacecraft attitude and position control for future Rendezvous and Docking (RVD) missions. Future RVD missions, specifically when the target is uncooperative, are challenging as geometric constraints and parameter uncertainties are both present. In addition, due to close proximity and potential angular motion of the target satellite, the point mass approach is no longer sufficient to represent the relative motion dynamics. Hence, throughout this paper, the coupling between translational and rotational motion of spacecraft relative motion is addressed via Dual Quaternions and Piece-wise Model Predictive Control (MPC) framework. The algorithm is developed such that the relative position of interest is no longer Centre-Of-Mass (COM) position of the target satellite but can be the docking port or a predefined grasping feature. In addition, physical constraints are explicitly formulated and respected by formulating a constrained optimization problem. The proposed framework is real-time implementable because the control problem is formulated as a convex optimization problem. This is demonstrated by Hardware-In-The-Loop experiments to control a 5-DOF motion of spacecraft. The spacecraft simulator has 16 thrusters; therefore, convex optimization based allocation strategy to map the force and torque control signals to the 16 thrusters is also proposed