Autonomous trajectory planning for space vehicles with a Newton–Kantorovich/convex programming approach

Space maneuverings of the space vehicle require the capability of onboard trajectory planning. Convex programming based optimization strategy gets much attention in the design of trajectory planning methods with deterministic convergence properties. Due to the nonlinear dynamics, space-trajectory planning problems are always non-convex and difficult to be solved by the convex programming approach directly. This paper presents a Newton–Kantorovich/convex programming (N–K/CP) approach, based on the combination of the convex programming and the Newton–Kantorovich (N–K) method, to solve the nonlinear and non-convex space-trajectory planning problem. This trajectory planning problem is formulated as a nonlinear optimal control problem. By linearization and relaxation techniques, the nonlinear optimal control problem is convexified as a convex programming problem, which can be solved efficiently with convex programming solvers. For the linearized convex optimization problem, N–K method is introduced to design an iterative solving algorithm, the solution of which approximates the original trajectory planning problem with high accuracy. The convergence of the proposed N–K/CP approach is proved, and the effectiveness is demonstrated by numerical experiments and comparisons with other state-of-the-art methods.