One active debris removal control system design and error analysis

• APN is effective in autonomous rendezvous with uncooperative targets.
• Constant deceleration performs best using the general formulation of 3D APN.
• System Efficiency is verified by analyzing error propagation of LOS rate.
• Covariance analysis is fast and reliable to evaluate control system performance.

The increasing expansion of debris presents a significant challenge to space safety and sustainability. To address it, active debris removal, usually involving a chaser performing autonomous rendezvous with targeted debris to be removed is a feasible solution. In this paper, we explore a mid-range autonomous rendezvous control system based on augmented proportional navigation (APN), establishing a three-dimensional kinematic equation set constructed in a rotating coordinate system. In APN, feedback control is applied in the direction of line of sight (LOS), thus analytical solutions of LOS rate and relative motion are expectedly obtained.To evaluate the effectiveness of the control system, we adopt Zero-Effort-Miss (ZEM) in this research as the index, the uncertainty of which is directly determined by that of LOS rate. Accordingly, we apply covariance analysis (CA) method to analyze the propagation of LOS rate uncertainty.Consequently, we find that the accuracy of the control system can be verified even with uncertainty and the CA method is drastically more computationally efficient compared with nonlinear Monte-Carlo method. Additionally, to justify the superiority of the system, we further discuss more simulation cases to show the robustness and feasibility of APN proposed in the paper.