Computationally efficient dynamic modeling of robot manipulators with multiple flexible-links using acceleration-based discrete time transfer matrix method

- This work has presented a computationally efficient dynamic modeling method: acceleration-based discrete time transfer matrix method for flexible-link robot manipulators. In DT-TMM, the robot manipulator system is decomposed into components: links, actuated joints. Each link is further broken down into the connections to joints, link beam elements, and connections between two adjacent link beam elements. The transfer matrix of each component/element is established based on the linearization of kinematic and dynamic equations of each component. The transfer matrices of components/elements are used to concatenate the state vectors from the base to the end-effector of a robot manipulator. Finally, the system equations of the robot manipulator are established and used to analyze the dynamics. With DT-TMM, the dimension of the resultant global system transferring equations does not the increase either the DOF of the robot manipulator or the number of link elements decomposed from each flexible link. This leads to significant reduction of computation. To illustrate the proposed method, the numerical simulations have been conducted with a single flexible link robot manipulator and a robot manipulator with three flexible links. Preliminary experiments have been performed with an in-house developed testing system of a single flexible link robot manipulator. The experimental results agree well with the simulation results based on the DT-TMM. Our ongoing work will extend the proposed method to parallel robot manipulators, and 3-dimensional serial robot manipulator systems.

This paper presents a novel and computationally efficient modeling method for the dynamics of flexible-link robot manipulators. In this method, a robot manipulator is decomposed into components/elements. The component/element dynamics is established using Newton-Euler equations, and then is linearized based on the acceleration-based state vector. The transfer matrices for each type of components/elements are developed, and used to establish the system equations of a flexible robot manipulator by concatenating the state vector from the base to the end-effector. With this strategy, the size of the final system dynamic equations does not increase with the number of joints or the number of link beam elements that each link is decomposed. The developed method intends to avoid the traditional computation of the global system dynamic equations that usually have large size for flexible robot manipulators, and only involves calculating and transferring component/element dynamic equations that have small size. The numerical simulations and experimental testing of flexible-link manipulators are conducted to validate the proposed methodologies.