Cascade Control for Robust Tracking of Continuum Soft Robots With Finite-Time Convergence of Pneumatic System

Pneumatic soft robots have become the premier soft robot type among the plethora of soft robot testbeds under research, being the continuum pneumatic soft robot (cPSR) the most compliant, yet challenging due to its hyperelastic behavior of its constitutive elastomer material. In this type of cPSR, embedded pneumatic chambers materialize the pneumatic controller from within, thus, there arises two highly intertwined dynamical systems: the kinetic one due to the cPSR inertia and to the pneumatic system itself. Unfortunately, the embedded pneumatic control for the cPSR has been outlined using pneumatics developed for rigid bodies. In this letter, we study the resultant Lagrangian dynamics of the highly coupled nonlinear cPSR system equipped with 3 embedded pneumatic chambers (thus the system is fully actuated and controllable). Then, a robust feedback cascade tracking controller is proposed so that the cPSR control torque yields the desired pressure for the pneumatic dynamics. Chatterless integral sliding modes are proposed to render semi-global finite-time convergence of pressure tracking errors. Finally, simulations are presented, and concluding remarks are discussed.