Nonlinear Optimal Trajectory Planning for Free-Floating Space Manipulators using a Gauss Pseudospectral Method

In this paper, an optimal trajectory guidance law is developed for a free-floating space manipulator through a combination of a Gaussian pseudospectral collocation scheme with a Non-Linear Problem solver. Specifically, the resulting nonlinear optimal guidance problem with path constraints is defined with the general pseudospectral optimal software and numerically solved by the sparse nonlinear optimizer solver. By utilizing this solver, the pseudospectral method simultaneously solves the entire trajectory over a small number of nodes based on the path constraints, initial conditions, and initial guesses provided by the user. Simulations demonstrate the performance for a two degree-of-freedom space manipulator, and the results suggest an improvement in terms of attitude displacements, compared to previously-published results.