PDE modeling and control of a cylindrical soft manipulator with bounded cable tension

In this paper, we establish a planar dynamic model of a soft manipulator and propose a boundary control algorithm to regulate the end of the manipulator to a given bending angle. The soft manipulator is driven by cables and has uniformly spatial parameters. As opposed to common approaches, the dynamic model is dominated by two sets of partial differential equations, which remain more concise and exacter expression. Then, we propose a bounded control law where the value of the controller is limited by the hyperbolic tangent function to deal with the control problem of soft manipulators. Specially, this paper presents a Lyapunov-based stability analysis, which is rare in the control synthesis of soft robots. Finally, some numerical examples are utilized to assess the established model and control.