Flatness-Based Low-Thrust Trajectory Optimization for Spacecraft Proximity Operations

Abstract

This chapter presents a novel computational framework integrating the differential flatness theory and the analytic homotopic technique for the low-thrust trajectory optimization for spacecraft proximity operations. Based on the flatness property of relative motion equations, the trajectory optimization problem is transformed into the flat output space with all the differential constraints eliminated and the number of decision variables reduced. Then the mapped Chebyshev pseudospectral method is applied to parameterizing the profiles of flat outputs, whose high-order derivatives are enhanced by improving the differential matrix’s ill- conditioning. Furthermore, the analytic homotopic technique is introduced to improve the applicability to non-smooth trajectory optimization problems. Numerical simulation results show that the proposed framework scheme is feasible and effective for spacecraft proximity maneuvers.