Trajectory Design via Convex Optimization for Six-Degree-of-Freedom Asteroid Powered Landing

Abstract

This paper presents a convex programming algorithm based on modified Rodrigues parameters for a six-degree-of-freedom asteroid powered landing trajectory design problem. The trajectory design problem is formulated as a nonconvex fuel-optimal control problem with nonlinear coupled translational and rotational dynamics, nonconvex state and control constraints. In order to tackle the fuel-optimal control problem in the convexification framework, the original nonconvex continuous-time optimization problem is converted into a convex discrete-time optimization subproblem by linearizing and discretizing the dynamics and constraints. The effect of the coupling of translational and rotational dynamics on the convexification of nonconvex control constraints is discussed. The successive convexification method of solving a sequence of constrained convex subproblem is used to generate the optimal trajectory. The validity of the proposed algorithm for generating fuel-optimal trajectories and the effect of asteroid gravity on generated trajectories are examined through simulations of landing on different irregular asteroids. The Monte Carlo simulation is performed to examine the calculation performance of the proposed algorithm comparing to the Radau pseudospectral method algorithm and the proposed algorithm with the rotational motion parameterized by quaternions.