Abstract: To generate the Mars atmospheric entry trajectory with maximum terminal altitude, the Legendre pseudospectral convex programming (LPCP) algorithm is proposed. Firstly, the Mars entry dynamics is reformulated by taking the downrange angle as the independent variable so as to convert the free final time problem into the fixed final downrange angle one, thereby avoiding the optimization of final time; and compared with the energy based formulation, there is no need to know the terminal altitude and velocity in advance, hence the maximum terminal altitude problem can be included. Then, the reformulated dynamics is discretized into a series of algebraic equalities at Legendre Gauss Lobatto (LGL) points, and the path constraints are convexified via the first order Taylor series approximation. Finally, the transcribed convex problem is addressed via successive convex optimization and virtual control techniques. The numerical simulation results show that the algorithm in this paper has higher computational efficiency while ensuring the optimality than the adaptive pseudospectral method and the general sequential convex programming method.

Key words: Mars entry and landing, Legendre pseudospectral method, Convex programming, Maximum terminal altitude, Trajectory planning