Optimization for Far-distance Cooperative Rendezvous with Multiple Direction-fixed Thrusts

The continuous-thrust far-distance cooperative rendezvous problem between two spacecraft is investigated. The indirect optimization method, based on Pontryagin's maximum principle (PMP), is applied to optimize fuel consumption. To overcome the difficulty in nonsmooth integration caused by the bang-bang control, the homotopy method is adopted to solve the fuel-optimal problem from a related energy-optimal problem. The quantum-behaved particle swarm optimization (QPSO) algorithm is used to obtain the energy-optimal solutions. The energy-optimal solutions are used as the initial values for the homotopic procedure to obtain the fuel-optimal solutions and optimal bang-bang control law. A hybrid algorithm combined homotopy method and sequential quadratic programming (SQP) algorithm is proposed. This hybrid algorithm can effectively obtain feasible optimal solutions even though the indirect optimization method exhibits a narrow convergence domain. Simulations of high-thrust and low-thrust rendezvous problems are provided and the proposed hybrid algorithm is verified. Moreover, the necessity of radial thrust is investigated.