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Two-stage path planning approach for designing multiple spacecraft reconfiguration maneuvers and application to SPHERES onboard ISS

The paper presents a two-stage approach for designing optimal reconfiguration maneuvers for multiple spacecraft. These maneuvers involve well-coordinated and highlycoupled motions of the entire fleet of spacecraft while satisfying an arbitrary number of constraints. This problem is particularly difficult because of the nonlinearity of the attitude dynamics, the non-convexity of some of the constraints, and the coupling between the positions and attitudes of all spacecraft. As a result, the trajectory design must be solved as a single 6N DOF problem instead of N separate 6 DOF problems. The first stage of the solution approach quickly provides a feasible initial solution by solving a simplified version without differential constraints using a bi-directional Rapidly-exploring Random Tree (RRT) planner. A transition algorithm then augments this guess with feasible dynamics that are propagated from the beginning to the end of the trajectory. The resulting output is a feasible initial guess to the complete optimal control problem that is discretized in the second stage using a Gauss pseudospectral method (GPM) and solved using an off-theshelf nonlinear solver. This paper also places emphasis on the importance of the initialization step in pseudospectral methods in order to decrease their computation times and enable the solution of a more complex class of problems. Several examples are presented and discussed.