Inverse modeling of nonlinear artificial muscle using polynomial parameterization and particle swarm optimization

The properties of pneumatic artificial muscle (PAM) with excellent power-to-weight ratio and natural compliance made it useful for healthcare engineering applications. However, it has undesirable hysteresis effect in controlling a robotic manipulator. This behavior is quasistatic and quasirate dependent which changed with excitation frequency and external force. Apart from this, it also inherits frictional presliding behavior with nonlocal memory effect. These nonlinearities need to be compensated to achieve optimal performance of the control system. Even though an inverse modeling of PAM has limited application, it is important on certain control system implementation that requires the solution to the inverse problem. In this paper, the inverse modeling of PAM in the form of activation pressure was proposed. This activation pressure model was derived according to static pressure and extracted hysteresis components from pressure/length hysteresis. The derivation of the static pressure model follows the phenomenological-based model of third-order polynomial. It is capable of characterizing the nonlinear region of PAM at low and high pressure. The derivation of extracted hysteresis model follows the mechanism of dynamic friction. In this principle, the activation pressure model was dependent on regression coefficient of the static pressure model and dynamic friction coefficients of the extracted hysteresis model. The regression constants of these coefficients were characterized from the hysteresis dataset by using model parameter identification and the particle swarm optimization (PSO) method. The result from model simulation shows the root mean square error (RMSE) value of less than 10% error was evaluated at various excitation frequencies and external forces. This inverse modeling of PAM implemented a simple approach, but it should be useful in control design applications such as rehabilitation robotics, biomedical system, and humanoid robots