Dynamic modeling and modal analysis of multiple degrees of freedom robot manipulators with flexible joints

Abstract

Thanks to of their production flexibility and safety in human interactions, robots with rigid links and flexible (elastic) joints have recently received the attention from researchers and application engineers. In the past, the elasticity of the joints was often neglected due to the complexity of the robot dynamic models. In addition, the limitations in the ability to measure and calculate the dynamics led to the robot model with rigid joints being often used for simulation and control purposes. However, this approach can lead to the robot instability during its functioning. The first objective of this research is to develop relevant mathematical models for flexible joint robots in order to simulate and predict their dynamic behavior. In addition to experimental methods such as modal analysis, we established an analytical model to compute the natural frequencies and damping ratios for arbitrary robot configurations. We showed that the proposed model could consider the effect of gravity and the parameters of the robot’s controller. The second objective is to contribute an optimization procedure to identify the stiffness and damping parameters of joints in which the incomplete modal information is assumed to be measured in several robot configurations. For flexible joint robots, these parameters are essential to understanding their dynamic behavior. We showed that the proposed procedure could identify unknown parameters, even when the damping ratios are estimated with deviations. The last objective is to propose an efficient algorithm to solve the inverse dynamics problem in real-time applications. The output of this algorithm, including a list of mathematical expressions written in optimized C/Matlab code, can be used in the design of advanced model-based control laws. We demonstrated that our algorithm can be used to control flexible joint robots with the feedforward control laws.

Date	13 Dec 2021
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	Zhaoheng Liu (Supervisor) & Viet Hung Vu (Co-supervisor)