Lagrangian dynamics and nonlinear control of a continuum manipulator

This paper presents a study on dynamics and nonlinear control strategies of a type of continuum manipulators that possess both bending and contractile capabilities. First, based on curve geometry under the Frenet frame, kinematics of the continuum manipulator is established. Then, both the kinetics and potential energies are considered for dynamic control. By applying the Euler-Lagrangian equation of motion, the system dynamics equation is obtained. According to this dynamic model, two control methods are developed, which are the inverse dynamics control and the sliding mode control, respectively. In the end, the MATLAB simulations are conducted to demonstrate the feasibility and effectiveness of these two control strategies.