Trajectory tracking control of a pneumatically actuated continuum manipulator in the presence of obstacles by using terminal sliding mode control

This paper proposes an efficient trajectory planning and dynamic tracking controller scheme for a pneumatic continuum manipulator under the effect of material hysteresis. First of all, generalized governing nonlinear dynamic equations in the form of partial differential equations for pneumatic continuum manipulator dynamics are developed by using discrete Cosserat-rod theory, where the manipulator material hysteresis is modeled by using a fractional order Bouc-Wen model. Then, the trajectory planning for the end-effector of a continuum manipulator is proposed, which accounts for the static obstacles in the workspace and the Jacobian singularity. Subsequently, an adaptive terminal sliding mode controller for the joint space control combined with a simple PI controller for task space control is proposed. The proposed controller guarantees exponential convergence of the manipulator tip positional error in finite time, even in the existence of external disturbances and model uncertainties, without any need for prior knowledge of their upper bounds. Finally, the proposed controller is applied to a two-segment continuum manipulator, the trunk of Robotino-XT, through numerical simulations and the performance gain over two controllers proposed in the literature for similar pneumatic continuum manipulators is demonstrated.