Task Space Tracking of Soft Manipulators: Inner-Outer Loop Control Based on Cosserat-Rod Models

The control problem of soft robots has been considered a challenging subject because they are of infinite degrees of freedom and highly under-actuated. Existing studies have mainly relied on approximated finite-dimensional models. In this work, we exploit infinite-dimensional feedback control for soft robots. We adopt the Cosserat-rod theory and employ nonlinear partial differential equations (PDEs) to model the kinematics and dynamics of soft manipulators, including their translational motions (for shear and elongation) and rotational motions (for bending and torsion). The objective is to achieve position tracking of the entire manipulator in a planar task space by controlling the moments (generated by actuators). The design is inspired by the energy decay property of damped wave equations and has an inner-outer loop structure. In the outer loop, we design desired rotational motions that rotate the translational component into a direction that asymptotically dissipates the energy associated with position tracking errors. In the inner loop, we design inputs for the rotational components to track their desired motions, again by dissipating the rotational energy. We prove that the closed-loop system is exponentially stable and evaluate its performance through simulations.