Differential Game Approach to Orbital Pursuit-Evasion Problems

Orbital pursuit-evasion problem arises frequently in proximity operations missions. In this scenario, the pursuer spacecraft aims to minimize its relative distance to the evader spacecraft under dynamic constraints. This paper uses an optimal control approach based on differential game theory to solve the orbital pursuit-evasion problem. The relative motion between the pursuer spacecraft and the evader spacecraft is modeled using the Clohessy-Wiltshire (C-W) equations, and a cost function with quadratic performance indices is formulated. A Min-Max Differential Dynamic Programming (DDP) method is then adopted to derive an optimal control strategy for both spacecraft. A forward-backward iterative process is utilized to update the control policy, thereby avoiding the direct solution of high-dimensional equations and reducing computational complexity. Numerical simulations demonstrate that the proposed method can effectively guide the pursuer to intercept the evader under bounded control constraints.