Optimal trajectory planning of space flexible-link manipulator based on singular perturbation theory

Abstract

In this paper, a computationally efficient joint trajectory planning method for a space flexible-link manipulator is proposed based on the Singular Perturbation (SP) theory. The dynamic coupling of the space flexible-link manipulator is decomposed into the coupling between the rigid motions of the base and link, and the coupling between the rigid motion and the flexible vibration according to the SP theory. The dynamic coupling between the base and the link is used to adjust the position and attitude of the base and the link vibration is reduced based on the coupling between the rigid motion and flexible vibration. According to SP theory, the rigid motion of the base is approximated by its quasi-steady state value. A low frequency vibration around quasi-steady state value of link vibration is obtained and used to approximate the dynamic behavior of link vibration within fast time scale. On this basis, two novel objective functions of minimizing vibration during motion and residual vibration are constructed. Since the calculation of high-frequency vibration is avoided, the efficiency of the trajectory optimization method is greatly improved. Particle Swarm Optimization (PSO) algorithm is adopted to realize multi-objective optimization. Numerical simulations are performed to verify the vibration reduction effect and ability of achieving multi-objective optimization of the proposed method. Moreover, experiments are conducted to further validate the vibration reduction effect of the proposed method.