Trajectory Planning Method of Spacecraft Cluster Based on Geodesic

One of the critical problems the cluster faces is the functional extremum problem of multi-constraint trajectory planning. This paper proposes a trajectory planning method based on geodesics, which abstracts the planning problem to the differential manifold. The motion constraints, collision avoidance constraints, and configuration constraints of the cluster are integrated into the manifold metric. Further, the functional local extremum problem is transformed into a partial differential equation by using the homotopy parameter. Finally, the cluster trajectory is obtained by solving PDE. The simulation results show that the multi-constraints are integrated with the measurement without increasing the system dimension. Moreover, the method does not rely on initial guess and consumes less fuel than the model predictive control-sequential convex programming algorithm.