Attitude Trajectory Planning for Spacecraft with Time-Varying Mass Using Sequential Conic Optimization

This article presents an attitude trajectory planning algorithm for spacecraft with time-varying mass and nonconvex state constraints. As a stepping stone, the problem of constrained attitude trajectory planning is posed as a finite-horizon optimal control problem (OCP). Then, the relaxation/convexification for control constraints is introduced that is proven to be lossless; i.e., the relaxed OCP is equivalent to the original one. By discretization and successive linearization, the relaxed OCP is then transformed as a sequence of second-order cone programming (SOCP) subproblems. Accordingly, the nonconvex motion constraints are converted into conic constraints. In particular, the so-called integration-correction technique is utilized to cancel the error resulting from the successive linearization, by which the recursive feasibility of the sequential SOCP is guaranteed. Moreover, the convergence to local optimality of the proposed algorithm is proved. Benefiting from the properties of the artificial potential function-based method, an initial solution can be rapidly generated to start the algorithm. Finally, the effectiveness of the trajectory planning algorithm is demonstrated by numerical examples.