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A trajectory planning scheme based on Particle Swarm Optimization (PSO) is presented for Free Floating Space Robot (FFSR) to minimize the spacecraft disturbance due to the motion of manipulator. Firstly, by analyzing the momentum conservation law and angular momentum conservation law, an optimal control algorithm is developed for FFSR trajectory planning, in which the spacecraft disturbance is considered as the objective function. High order polynomial is used to approximate the trajectories of manipulator joints, and the coefficients of the polynomial are set as optimization parameters. To guarantee the convergence of the algorithm, the PSO with constriction factor is used such that an optimal trajectory can always be achieved in limited evolution generations. Numerical simulation results show the validity of the proposed methodology.