Modeling and Compensation of Stiffness-Dependent Hysteresis Coupling Behavior for Parallel Pneumatic Artificial Muscle-Driven Soft Manipulator

The parallel driving soft manipulator with multiple extensors and contractile pneumatic artificial muscles (PAMs) is able to operate continuously and has varying stiffness, achieving smooth movements and a fundamental trade-off between flexibility and stiffness. Owing to the hysteresis of PAMs and actuator couplings, the manipulator outputs display coupled hysteresis behaviors with stiffness dependence, causing significant positioning errors. For precise positioning control, this paper takes the lead in proposing a comprehensive model aimed at accurately predicting the coupled hysteresis behavior with the stiffness dependence of the soft manipulator. The model consists of an inherent hysteresis submodule, an actuator coupling submodule, and a stiffness-dependent submodule in series. The asymmetrical hysteresis nonlinearity of the PAM is established by the generalized Prandtl–Ishlinskii model in the inherent hysteresis submodule. The serial actuator coupling submodule is dedicated to modeling the actuator couplings, and the stiffness-dependent submodule is implemented with a fuzzy neural network to characterize the stiffness dependence and other system nonlinearities. In addition, an inverse compensator on the basis of the proposed model is conducted. Experiments demonstrate that this model possesses high accuracy and good generalization, and its compensator is effective in decoupling and mitigating hysteresis coupling of the manipulator. The proposed model and control methods significantly improve the positioning accuracy of the pneumatic soft manipulator.