A Fast Trajectory Optimization of Pinpoint Landing by Chebyshev Pseudospectral and SOCP

In this paper, a fast trajectory optimization based on Chebyshev Pseudospectral and SOCP is proposed to solve a pinpoint landing problem with unknown terminal time, nonconvex control constraints and nonlinear dynamics. The rapidness of the solution is improved by reducing the number of decision variables and changing the way of determining the terminal time. The unknown terminal time, namely the time-of-flight, is considered as a control variable and solved directly, rather than determined by the golden section search. Chebyshev Pseudospectral is adopted to discretize the problem into a SOCP for fewer nodes and higher accuracy. Additionally, Lossless Convexification and Successive Linearization are applied to address the nonconvex constraints and nonlinear dynamics. Simulations demonstrate the superiority in efficiency and accuracy of the proposed method.