Abstract
In this paper, a novel adaptive robust approach to modeling and control of a class of flexible-arm robots subject to actuators unmodeled dynamics is proposed. It is shown how real-time signals measured from a dynamical system can be utilized to improve the accuracy of the mathematical model of flexible robots. Given the elasticity of the robot’s arms, flexible manipulators have both passive and active degrees of freedom. A nonlinear robust controller is designed for the active degrees of freedom to enable the robot to follow desired trajectories in the presence of actuators unmodeled dynamics. Furthermore, it is shown that under some feasible conditions, another nonlinear robust controller is designed for the passive degrees of freedom. Moreover, to use the system response for model extraction, two auxiliary signals are proposed to provide sufficient information for improving the accuracy of the dynamics of the system numerically. Additionally, two adaptive laws are proposed in each case to update the two introduced auxiliary signals. As a result, the controller controls the passive degrees of freedom after the active degrees of freedom converge to their desired trajectories. Simultaneously, the information collected from the system to update the auxiliary signals enhances the model accuracy. In the end, simulation results are presented to verify the performance of the proposed controller.
Highlights
The area of flexible-arm robots has attracted much attention during the last few decades [1] [2]
A nonlinear robust controller is designed for the active degrees of freedom to enable the robot to follow desired trajectories in the presence of actuators unmodeled dynamics
It is shown that under some feasible conditions, another nonlinear robust controller is designed for the passive degrees of freedom
Summary
The area of flexible-arm robots has attracted much attention during the last few decades [1] [2]. As one of the requirements of their approach, the non-integrable acceleration relations are required to be satisfied [19] As another example, Zhang and Tarn designed a hybrid switching control strategy for nonlinear and underactuated mechanical systems [20]. The entire system can be either linearized with respect to the active degrees of freedom (collocated problem) or with respect to the passive degrees of freedom (non-collocated problem) Be that as it may, such a control strategy fails to handle uncertainties as control inputs to feedback-linearized systems depend on the governing equations. Adaptive laws are proposed to estimate the system uncertainties as well as approximating actuators uncertain dynamics Another adaptive robust controller is designed to control the passive degrees of freedom where the stabilities of the overall closed-loop system, in both cases, in the presence of uncertainties are established. Two adaptive signals are introduced and synthesized such that the cumbersome analytical part of the model extraction can be done numerically
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