Abstract
This article treats the design and implementation of a multi-input multi-output fractional-order controller for a nonlinear system composed of a tendon-driven continuum mechanism. As the continuum can be deformed along all Cartesian directions, it is suitable for the application as a flexible neck of a humanoid robot. In this work, a model-based control approach is proposed to control the position of the head, that is, the rigid body attached to the top of the continuum mechanism. Herein, the system is modeled as a rigid body on top of a nonlinear Cartesian spring, with an experimentally obtained deflection characteristic which provides a simple and real-time capable model. By nonlinear feedback, the output dynamics are linearized and decoupled, which enables the design of single-input single-output fractional-order controllers for the regulation of each output independently. The design of a fractional-order [Formula: see text] controller is discussed to incorporate robustness and a fast transient response. The proposed control approach is tested in several experiments on the real system.
Highlights
Continuum mechanisms provide a passive compliance as the continuum structure reacts to any kind of disturbance with a deformation
The mechanism can collide with the environment without being damaged, which is termed “mechanical robustness.”. Mechanisms of this kind are used as finger joints in robotic[1] or prosthetic[2] hands, quadrupedal spines,[3] humanoid necks or spines,[4] or whole robotic arms made of serially attached mechanisms.[5]
This article has dealt with the design and implementation of an multi-input multi-output (MIMO) FO controller for a nonlinear system composed of a continuum mechanism currently used as a neck of a humanoid robot
Summary
Continuum mechanisms provide a passive compliance as the continuum structure reacts to any kind of disturbance with a deformation. The model-based approach developed in this work is a dynamic controller in the task space of the continuum mechanism. This work proposes to model and identify second-order linear transfer functions for the remaining output dynamics and apply an extensively robust control approach to handle the remaining coupling and nonlinearities. In this respect, the concept of fractional-order (FO) control is investigated, which extends a general linear proportional derivative (PD) controller with an additional coefficient to account for robustness and a fast transient as assessed by Deutschmann et al.[18]. To implement the FO controllers in the real setup, the transfer functions in equations (23) to (26) have been approximated to those of an integer-order
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