Fractional Order KDHD Impedance Control of the Stewart Platform

Abstract

In classical impedance control, KD, the steady-state end-effector forces are imposed to be proportional to the end-effector position errors through the stiffness matrix, K, and a proper damping term is added, proportional to the first-order derivatives of the end-effector position errors according to the damping matrix, D. This paper presents a fractional-order impedance control scheme, named KDHD, in which an additional damping is added, proportional to the half-order derivatives of the end-effector position errors according to the half-derivative damping matrix, HD. Since the finite-order digital filters which implement in real-time the half-order derivatives modify the steady-state stiffness of the end-effector—which should be defined exclusively by the stiffness matrix—a compensation method is proposed (KDHDc). The effectiveness of this approach is validated by multibody simulation on a Stewart platform. The proposed impedance controller represents the extension to multi-input multi-output robotic systems of the PDD1/2 controller for single-input single-output systems, which overperforms the PD scheme in the transient behavior.

Keywords

• impedance control
• fractional calculus
• half-order derivative
• parallel kinematics machine
• KDHD
• Stewart platform