Dynamic analysis of a hyper-redundant space manipulator with a complex rope network

Abstract

This paper studies the dynamics of a space manipulator. The space manipulator is designed for precise on-orbit servicing missions in a highly constrained environment. The concerned manipulator has hyper-redundant degrees of freedom and moves with a piecewise constant curvature, which enhances the flexibility and controllability. Such manipulator consists of a large number of links and a complex rope network. When the manipulator is driven, the interacting forces between the links and ropes introduce complexity into the dynamic behavior. In terms of dynamic modeling, the manipulator is a very complex system. This paper proposes a dynamic model of the manipulator based on methods of multibody dynamics. The ropes are assumed to be massless and linear elastic. The equations of motion are derived using space operator algebra. The vibration of the manipulator is investigated. The governing equations of the vibration are derived by applying the perturbation method to the proposed dynamic model. The values of the natural frequencies are investigated for the elasticities of the ropes. The proposed dynamic model is also applied in numerical simulation. The explicit fourth-order Runge-Kutta method is utilized to solve the equations of motion numerically. In numerical simulation, an upper bound of the time step is encountered. The value of upper bound is found to be related to the elasticities of the ropes. Such phenomena are studied by analyzing the stability region of the Runge-Kutta methods. Besides, the computational efficiency of the numerical simulation is also limited by the value of upper bound. Two modifications of the dynamic model are introduced to relax the upper bound of the time step. The effects of the modifications are demonstrated by numerical results.