Collision prediction and avoidance for satellite ultra-close relative motion with zonotope-based reachable sets

Collision prediction and avoidance are critical for satellite proximity operations, and the key is the treatment of satellites' motion uncertainties and shapes, especially for ultra-close autonomous systems. In this paper, the zonotope-based reachable sets are utilized to propagate the uncertainties. For satellites with slender structures (such as solar panels), their shapes are simplified as cuboids which is a special class of zonotopes, instead of the classical sphere approach. The domains in position subspace influenced by the uncertainties and shapes are determined, and the relative distance is estimated to assess the safety of satellites. Moreover, with the approximation of the domains, the worst-case uncertainties for path constraints are determined, and a robust model predictive control method is proposed to deal with the line of sight and obstacle avoidance constraints. With zonotope representations of satellites, the proposed robust model predictive control is capable of handling the shapes of the satellite and obstacle simultaneously. Numerical simulations demonstrate the effectiveness of the proposed methods with an elliptic reference orbit. 1