Trajectory Design for 6-DoF Asteroid Powered Landing via Convex Optimization

Abstract

In this paper, a trajectory design algorithm via convex optimization has been proposed for the 6-DoF asteroid powered landing problem. The main contribution is that the algorithm combines the time-optimal and the fuel-optimal trajectory optimization to give a fuel-optimal trajectory in the optimal flight time. First, two constrained nonconvex optimal control problems of the time-optimal and the fuel-optimal are proposed, then the original nonconvex continuous-time infinite dimensional problems are turned to convex discrete-time finite dimensional optimization problems through linearization and discretization of the nonlinear dynamics and the nonconvex state, control constraints. By developing the successive convexification, the final trajectory is achieved by solving a sequence of convex fuel-optimal sub-problems using the optimal flight time and the time-optimal trajectory given by solving the time-optimal optimization problem in successive manner. The validity of proposed algorithm of generating the fuel-optimal trajectory in the optimal flight time is verified through numerical simulations for landing on an irregular asteroid.