This paper proposes a detailed nonlinear mathematical model of an antagonistic pneumatic artificial muscle (PAM) actuator system for estimating the joint angle and torque using an unscented Kalman filter (UKF). The proposed model is described in a hybrid state-space representation. It includes the contraction force of the PAM, joint dynamics, fluid dynamics of compressed air, mass flows of a valve, and friction models. A part of the friction models is modified to obtain a novel form of Coulomb friction depending on the inner pressure of the PAM. For model validation, offline and online UKF estimations and sensor-less tracking control of the joint angle and torque are conducted to evaluate the estimation accuracy and tracking control performance. The estimation error is less than 7.91 %, and the steady-state tracking control performance is more than 94.75 %. These results confirm that the proposed model is detailed and could be used as the state estimator of an antagonistic PAM system.

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This paper proposes a simultaneous control method for the angle and stiffness of the joint in an antagonistic pneumatic artificial muscle (PAM) actuator system using only pressure measurements, and clarifies the allowable references for the PAM actuator system. To achieve a sensor-less control, the proposed method estimates the joint angle and contraction forces using an unscented Kalman filter that employs a detailed model of the actuator system. Unlike previous control methods, the proposed method does not require any encoder and force sensor to achieve angle and stiffness control of the PAM actuator system. Experimental validations using three control scenarios confirm that the proposed method can control the joint angle and stiffness simultaneously and independently. Moreover, it is shown that a reference admissible set can be used as an indicator to establish reference values by demonstrating that the reference set covers the experimentally obtained trajectories of the angle and stiffness.