Multi-input multi-output fractional-order control of an underactuated continuum mechanism

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 P D α controller is discussed to incorporate robustness and a fast transient response. The proposed control approach is tested in several experiments on the real system.