Abstract:

 A multi-stage trajectory optimization algorithm is proposed by modulating the aerodynamic force and thrust via the convex optimization. In the aero-braking phase, the trim angle is taken as the control variable, and the Legendre-Gauss-Radau pseudospectral method is adopted to discretize the states and control due to its high numerical precision. During the powered descending phase, the thrust vector is taken as the control variable, and the uniform discretization is applied since the thrust may alter discontinuously. Then, taking the constraints and the start and cut-off time of the engine into account, a multi-stage optimization problem is built up. The lossless convexification is used to relax the lift and thrust constraints, and the successive convexification is used to eliminate the non-convexities, introduced by the aerodynamic, free-time-variables and mass. The problem is finally described as a second-order cone programming problem (SOCP), which can be solved by the sequence iteration. The numerical simulations show that the convergence is obtained after a few successive iterations. As well, the larger landing range and less fuel consumption can be achieved.

Key words: Vertical landing, Convex optimization, Second-order cone programming, Pseudospectrum discretization, Multi-stage trajectory optimization