Distributed Impulsive Multi-Spacecraft Approach Trajectory Optimization Based on Cooperative Game Negotiation

A cooperative game negotiation strategy considering multiple constraints is proposed for distributed impulsive multi-spacecraft approach missions in the presence of defending spacecraft. It is a dual-stage decision-making method that includes offline trajectory planning and online distributed negotiation. In the trajectory planning stage, a relative orbital dynamics model is first established based on the Clohessy–Wiltshire (CW) equations, and the state transition equations for impulsive maneuvers are derived. Subsequently, a multi-objective optimization model is formulated based on the NSGA-II algorithm, utilizing a constraint dominance principle (CDP) to address various constraints and generate Pareto front solutions for each spacecraft. In the distributed negotiation stage, the negotiation strategy among spacecraft is modeled as a cooperative game. A potential function is constructed to further analyze the existence and global convergence of Nash equilibrium. Additionally, a simulated annealing negotiation strategy is developed to iteratively select the optimal comprehensive approach strategy from the Pareto fronts. Simulation results demonstrate that the proposed method effectively optimizes approach trajectories for multi-spacecraft under complex constraints. By leveraging inter-satellite iterative negotiation, the method converges to a Nash equilibrium. Additionally, the simulated annealing negotiation strategy enhances global search performance, avoiding entrapment in local optima. Finally, the effectiveness and robustness of the dual-stage decision-making method were further demonstrated through Monte Carlo simulations.