Landing Trajectory Generation using Gauss Pseudo-spectral Method

The soft landing of the Mars lander is one of the key problems of Mars exploration. The lander’s dynamic equation is nonlinear and is restricted by various constraints. Analytical solution is hard to be obtained. This paper focuses on planning the Mars landing trajectory by the Gauss pseudo-spectral method. The motion equations during the landing stage is firstly established. The trajectory optimization problem is then established with consideration to dynamic constraints, terminal state constraints, and landing site constraints. The control variables and state variables are discretized using Gauss pseudo-spectral method. Thereby a large-scale sparse nonlinear programming problem is formulated. The problem is then solved by SNOPT solver based on sequential quadratic programming algorithm. Simulation results show the efficiency of the proposed method.