Free Final-Time Low Thrust Trajectory Optimization Using Homotopy Approach

Abstract

This paper discusses the application of the homotopy approach to optimizing the free-flight-time low-thrust trajectory considering the performance characteristics. The trajectory optimization problem is formulated as an optimal control problem (two-point boundary value problem). The developed homotopy algorithm to solve the optimal control problem comprises three steps-orbital energy/acceleration matching, flight-time matching, and orbital reshaping. A comprehensive case study demonstrates the effectiveness of the proposed homotopy-based optimization algorithm for an optimal design of a low-thrust trajectory involving long mission time.