A hybrid numerical method for solving the inverse kinematics of a class of spatial flexible manipulators

This paper proposes a hybrid numerical method (HNM) to solve the inverse kinematics of a class of spatial flexible manipulators modeled by mass/spring (mass-lumped stations and massless-spring fields) modeling method. The HNM includes two parts: one is an implicit recursive numerical method (IRNM) which is used to find a better approximate solution to the inverse problem, the other is a global iterative learning compensator that can further reduce the end-effector's position errors. The stability of IRNM is also analyzed and a sufficient condition of convergence is obtained. Using this HNM numerical simulation is conducted on a spatial flexible manipulator which possesses two flexible links and three rigid joints. Results are presented to show the effectiveness of the method.