A Pseudospectral Method for Trajectory Optimization of Free-Floating Space Manipulator

An improved Gauss pseudospectral method with linear final state constraints is proposed to solve the trajectory optimization problem of free-floating space manipulator (FFSM) system. In this paper, the problem is transformed into a nonlinear programming problem (NLP) by states approximation at the Legendre-Gauss (LG) points and the boundary times. The differential of these states can be expressed as linear combinations of values at the discrete points approximately. Therefore, the FFSM dynamic equations and the cost function can be expressed as algebraic equations. The sequential quadratic programming (SQP) method is implemented to achieve the optimal trajectory. The planned joint angle trajectories are continuous, and the angular velocities at the initial and final time equal to zero. Numerical simulation results demonstrate that the proposed method is effective and available for solving the FFSM trajectory optimization problem.