A Modified Robust Homotopic Method for the Low-Thrust Fuel-Optimal Orbital Control Problem

Abstract

This study focuses on improving the application of the quadratic penalty smoothing technique for solving the fuel-optimal problem of low-thrust trajectory. Some practical techniques, including the Particle Swarm Optimization algorithm (PSO), the co-state normalization technique, and the single shooting method, are employed. These approaches can enhance convergence to the globally optimal solution. The application of PSO is improved through the introduction of the diversity termination term. Furthermore, a new parameter, the maximum thrust to initial mass ratio (CTm), is introduced and analyzed. The relationships among Lagrange multipliers for different CTm in the energy-optimal auxiliary problem are also derived. These relationships can be used in scenarios with high CTm to reduce the variable search space, leading to a significant decrease in computation time. Nonetheless, few researchers have proposed a well-defined strategy for the homotopic process. We propose a robust iteration strategy, involving the determination of the maximum step size and the distinction of sub-optimal solutions. This iterative strategy could ensure a robust convergence toward the optimal solutions. An interplanetary rendezvous example is provided to demonstrate the effectiveness of the presented techniques and strategy.

Keywords

• low-thrust trajectory optimization
• homotopic method
• fuel-optimal problem
• energy-optimal problem
• homotopic iteration strategy
• optimal control