With the rapid development of space exploration technology, the frequency and complexity of on-orbit activities have significantly increased, accompanied by a growing number of non-functional spacecraft and space debris. These non-cooperative targets may perform uncontrolled maneuvers and be subject to complex external disturbances, leading to high uncertainty in their trajectories. Such uncertainty challenges traditional proximity operation methods, making it difficult to ensure both safety and robust during orbital approach processes.
  To address this problem, this study proposes a proximity operation method for non-cooperative spacecraft based on the Model Predictive Path Integral (MPPI) algorithm, combined with short-term reachable set prediction. Instead of assuming a deterministic trajectory, the target spacecraft is modeled as a dynamical system subject to bounded external disturbances and limited maneuvering capability. Based on this assumption, a multi-step short-term reachable set extrapolation model is constructed to characterize the potential state distribution of the target over a finite horizon with the effect of uncertainty and disturbances.
  Within the predicted reachable set, the tracking spacecraft employs MPPI to perform stochastic sampling of control sequences and receding-horizon optimization. For each control step, the relative motion between the tracking and target spacecraft is propagated forward while accounting for the worst-case motion of the target within the reachable set and the cost of orbital maneuvering for tracker. A cost function is designed to jointly penalize collision risk, violation of safety constraints, terminal tracking error, and excessive control input. By aggregating the weighted costs of sampled trajectories, MPPI generates an optimal control policy that minimizes expected cost under uncertainty, without requiring explicit convex reformulation of the dynamics.
  The integration of reachable set prediction and MPPI optimization effectively balances safety, mission constraints, and maneuver efficiency. The reachable set provides a structured description of target uncertainty while MPPI offers a flexible and computationally efficient mechanism for handling complex constraints. The proposed framework allows the tracking spacecraft to dynamically adapt its approaching strategy in response to target behavior.
  Numerical simulations verify the effectiveness of the proposed method under complex disturbances and uncontrolled target maneuvers. The results indicate that this approach provides a reliable theoretical method for intervention, collision avoidance, and active approach missions involving non-cooperative or failed spacecraft and space debris.

 

Download file