Abstract: For a close-proximity inspection mission of a tumbling space target with a complex geometry, considering collision avoidance under actuator saturation and coupled position–attitude dynamics, an approximately optimal safety-critical control strategy is proposed based on the control barrier function (CBF) methodology. First, an integrated pose tracking-error dynamics model is formulated on the Lie group SE(3), and a value function incorporating control-input saturation constraints is constructed; an integrated pose-level approximately optimal nominal control policy is then obtained within an adaptive dynamic programming (ADP) framework. Next, to address the issues that target tumbling induces strong pose coupling, making safety constraints time-varying with attitude evolution, and that complex geometry amplifies near-field collision risk, an algebraic safety index function is designed based on relative pose and geometric features to yield collision-avoidance constraints. Furthermore, a repulsion-guidance strategy is developed as a candidate nominal control policy to mitigate reachability degradation near complex obstacle boundaries, thereby reducing the conservatism of the original nominal controller. Finally, a safety-critical control framework combining a backup control barrier function and quadratic programming is established to modify the nominal control input, achieving safe tracking control under motion constraints and input saturation. Numerical simulations validate the effectiveness of the proposed method.

Key words: On-orbit maintenance, Adaptive dynamic programming, Collision avoidance, Control barrier function, Lie group SE(3)