The Modeling and Nonlinear Dynamic Analysis of Volume-Controlled Hydraulic Artificial Muscles

Hydraulic artificial muscles (HAM) offer higher stiffness and faster response. Unlike pneumatic artificial muscles (PAM), which rely on pressure control, hydraulic artificial muscles are more suitable for volume control. This study focuses on the modeling and nonlinear dynamic analysis of volume-controlled McKibben hydraulic artificial muscles. To address the limitations of existing models, a hierarchical semi-empirical modeling method is adopted to construct a static model with constant volume, which integrates a geometric model and a static force model. This model supports not only pressure control, but also volume control, and considers the end effects, the effective bulk modulus, and the nonlinear dependence of artificial muscles on Young's modulus. Furthermore, a dynamic model encompassing four state parameters is established by combining the static model with fluid continuity equations, enabling the characterization of dynamic responses under volume control. Experimental methods were employed to determine the parameters in the formulas, significantly improving the accuracy of calculating the required injected volume for the given contraction ratio and load force. Nonlinear dynamics analysis reveals that HAM exhibit significant nonlinear damping, and the initial volume of connecting pipes significantly affects static pressure and working performance. Experimental validation shows that the static model achieves a maximum relative error of 2.05% in contraction ratio, while the dynamic model accurately captures the second-order oscillatory characteristics of force and pressure responses. This research provides a comprehensive modeling framework for volume-controlled HAM and deepens the understanding of their nonlinear dynamic behavior, facilitating engineering applications in robotics and rehabilitation devices.