Fractional-order Bouc-wen hysteresis model for pneumatically actuated continuum manipulator

Continuum manipulators with pneumatic actuators are designed for large-scale movements with high dexterity. However, during applications, such manipulators suffer control inaccuracies due to material nonlinearities. Thus, this paper proposes a generalized forward kinematic and forward dynamic model based on Cosserat-rod theory for a pneumatically actuated multi-segment conic manipulator. The model includes the effect of material nonlinearities and reduces the steady-state absolute error. Moreover, the model also considers the self-weight and external loadings to determine the manipulator backbone shape. Explicit fractional-order Bouc-Wen model is used in the constitutive laws to model the effect of material hysteresis in the developed partial differential equations for the manipulator. The developed mathematical model is solved numerically for possible backbone shapes. The results of the model are validated experimentally on the trunk of the Robotino-XT, which is a two-segment pneumatically actuated conic manipulator. The validation results show that the absolute pose error between the experimental and the proposed model for the manipulator tip at steady-state is very small, which is a far superior result to the other existing models for the same system.