High-Precision Displacement and Force Hybrid Modeling of Pneumatic Artificial Muscle Using 3D PI-NARMAX Model

Abstract

Pneumatic artificial muscle (PAM) is attractive in rehabilitation and biomimetic robots due to its flexibility. However, there exists a strong hysteretic nonlinearity in PAMs and strong coupling between the output displacement and the output force. At present, most commonly used hysteresis models can be treated as two-dimensional models, which only consider the nonlinearity between the input and the output displacement of the PAM without considering the coupling of the output force. As a result, high-precision modeling and estimation of the PAM’s behavior is difficult, especially when the external load of the system varies significantly. In this paper, the influence of the output force on the displacement is experimentally investigated. A three-dimensional model based on the modified Prandtl–Ishlinskii (MPI) model and the Nonlinear AutoRegressive Moving Average with eXogenous inputs (NARMAX) model is proposed to describe the relationship and couplings among the input, the output displacement, and the output force of the PAM. Experiments are conducted to verify the modeling accuracy of the proposed model when the external load of the PAM varies across a wide range. The experimental results show that the proposed model captures well the hysteresis and couplings of the PAM and can precisely predict the PAM’s behavior.

Keywords

• pneumatic artificial muscle
• hysteresis model
• nonlinearity
• NARMAX
• RFNN