Trajectory planning for satellite swarms with nonlinear terminal constraints using penalty concave relaxation

Convex programming (CP) is widely used in trajectory planning for space missions due to its high efficiency. Existing CP methods may not handle well with trajectory planning problem for satellite swarms involving multiple nonlinear terminal constraints, leading to solution chattering and initial infeasibility. To overcome this issue, this paper introduces a penalty concave relaxation (PCR) treatment to the conventional CP methods. First, the nonconvex terms in multiple nonlinear terminal constraints are equivalently concentrated into a unique equality constraint to reduce the number of relaxation variables. This equality constraint is then relaxed along the concave direction to guarantee the initial feasibility of the subsequent iterative solution process. Meanwhile, only one penalty coefficient is added on the objective. Finally, the relaxed concave constraint is linearized so that chattering can be avoided in an iterative strategy to solve the original swarm trajectory planning problem. Numerical examples are set up for two swarm trajectory planning missions with nonlinear terminal constraints. The performance of avoiding chattering and ensuring initial feasibility is verified.