Inverse Dynamics and Kinematics of Multi- Link Elastic Robots: An Iterative Frequency Domain Approach

A technique is presented and experimentally validated for solving the inverse dynamics and kinematics of multi-link flexible robots. The proposed method finds the joint torques necessary to produce a specified end-effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Further more the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solu tion scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested, first through simulation analysis, and second through experimental validation using feed-forward control. Results show the potential use of this method not only for open-loop control, but also for incorporation in feedback control strate gies. 1. This section contains a revised and corrected formulation of open-chain case. A previous method reported by the first author in: Computed Torque for the Fosition Control of Open-Chain Flexible Robots. Proc. 1988 IEEE International Conference in Robotics and Automation contained an error.