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.

Optimal control of rapid cooperative spacecraft rendezvous with multiple specific-direction thrusts

Focusing on the long-distance rapid cooperative rendezvous of two spacecraft under finite continuous thrust, this paper proposes a practical strategy for space operation using multiple specific-direction thrusts. Based on the orbital dynamic theory and Pontryagin’s maximum principle, the dynamic equations and optimal control equations for radial, circumferential, and normal thrust are determined. The optimization method is a hybrid algorithm. The initial costate variables for the fuel-optimal rapid cooperative rendezvous problem are obtained using quantum particle swarm optimization and subsequently set as the initial values in the sequence quadratic programming to search for the exact convergent solution. The elliptical and near-circular mission orbital rendezvous for spacecraft with multiple specific-direction thrusts are simulated and optimized. Numerical examples verifying the proposed method are provided. The results facilitate easier realization of rapid spacecraft maneuvering under continuous thrust conditions.

Optimization for far-distance and fuel-limited cooperative rendezvous between two coplanar spacecraft based on Lambert method

Concentrating on far-distance and fuel cooperative rendezvous between two coplanar spacecraft under impulse thrust, this paper presents fuel-optimal results obtained by optimization algorithms numerically. Former research works have formulated optimization models of multiple-impulse orbit transfer and cooperative rendezvous under continuous thrust. In this paper, optimization models of cooperative rendezvous under impulse thrust are formulated based on these former researches. The process of cooperative rendezvous is simplified by introducing a hypothetical spacecraft. The degradation from cooperative rendezvous to active–passive rendezvous is prevented by revising objective functions. Quantum-behaved particle swarm optimization and sequential quadratic programming are combined to solve a practical problem, which is used to illustrate advantages of cooperative rendezvous when fuel consumption of one spacecraft is limited.