Modeling of a 3-D Light-Weight Space Manipulator

Abstract

This report addresses the problem of modeling a 3-D flexible robot. First, the flexibility of each link is modeled by a lumped system assuming the bending deflection is not too large compared to the length of the link. Then the kinematics of a serial-chain flexible mechanism is obtained by using transform of rigid coordinates and flexible coordinates. The flexible coordinates frame is defined to represent deflections of each link. Based on the kinematics, overall dynamics is derived by Lagrangian method. To obtain transfer functions from the joint torque to the tip displacements, the inertial matrix must be invertible. We defined a set of new variables by which the inertial matrix is invertible. This provides a general approach for modeling a large class of multi-joint flexible robot, and the resultant model is simple to be implemented in real-time model-based control. Vibration experiments have been performed on the laboratory 3-D flexible model, and the experimental results have been compared to the analytical results.