Design and implementation of a nonlinear controller for a robotic arm with flexible joints and rigid links

Abstract

The robotic systems are becoming more and more complex and the traditional control law theories lose robustness, increasing the difficulty with which the robot can be controlled to interact with the environment around it. The objective of this research work is the study of complex nonlinear systems with the particularity of having flexible joints and rigid links. Such flexibility causes an interesting behavior in the robotic systems because duplicates the number of variables involved in the control task. Several studies have been carried out in the research of flexible robots, however most of them use the classical Euler-Lagrange framework to describe the mechanical systems. This work has been focused on the implementation of nonlinear controllers within the port-Hamiltonian framework, and the singular perturbation multi-scale systems theory. In this sense, the mathematical description of two different control laws proposed by Jardón-Kojakhmetov et al. (2017) and Reyes-Báez et al. (2016) are presented and adapted to the physical plant of the two degrees of freedom Quanser robotic arm. Moreover, the equations of the proposed port-Hamiltonian controllers have been implemented into a simulation to test the validity of the control laws for the rigid and the flexible configuration of the robot. Finally, the controllers have been implemented into the physical plant of the robotic arm to validate experimentally the proposed mathematical control theory. The experimental implementation of the proposed port-Hamiltonian controllers showed an improvement in the control of the position error for the rigid and the flexible configuration in comparison with a benchmark controller proposed by the manufacturer of the robotic arm, with an error rate for the RMS value of the signal lower than 1.2% of the RMS value of the desired trajectory. Further studies and experimental tests should be aimed to the implementation of port-Hamiltonian controllers to achieve an even lower error rate.