Spacecraft close-range trajectory planning via convex optimization and multi-resolution technique

Discretization of the state and control is indispensable for solving a trajectory planning problem numerically via convex optimization, and uniform-grid discretization is the most common strategy in recent studies. However, when a higher-precision solution is desired, this kind of discretization will greatly increase the scale of optimization variables and then reduce the optimization efficiency. To remedy this weakness, a novel trajectory planning strategy for spacecraft relative motion is proposed in this paper by combining convex optimization and multi-resolution technique (MRT). In this optimization strategy, convex optimization works as an inner-layer algorithm for trajectory optimization, and the MRT works as an outer-layer algorithm for mesh refinement. Moreover, the no-fly zone constraints are considered in the trajectory optimization, and the affine approximations of the spherical and ellipsoidal no-fly zones are derived by the analytical formula of the tangent plane. Numerical simulations demonstrate the effectiveness of the proposed methods. Results show that the combined optimization method can adaptively adjust the local grid density according to the designed resolution level and performs better in computing efficiency than the traditional uniform discretization.