Pseudospectral Convex Programming for Free-Floating Space Manipulator Path Planning

To efficiently plan the point-to-point path for a 7-degrees-of-freedom (7-DOF) free-floating space manipulator system, a path planning method based on Legendre pseudospectral convex programming (LPCP) is proposed. First, the non-convex dynamics are approximated by utilizing the first-order Taylor expansion in the vicinity of the initial guess path, which results in a convex system. Next, the linearized dynamics are discretized at Legendre–Gauss–Lobatto collocation points to transcribe the differential equations to a set of equality constraints. To obtain a reliable initial guess trajectory, the auxiliary path planning problem of the 7-DOF space manipulator with a fixed base is initially resolved. Additionally, the penalty function method is introduced to enhance the convergence performance of the LPCP. Finally, simulation results show that the proposed algorithm in this paper can generate the point-to-point path and has higher computational efficiency than the general sequential convex programming method while ensuring optimality.