From underactuation to quasi-full actuation: Aiming at a unifying control framework for articulated soft robots

We establish a structure preserving state and input transformation that allows a class of underactuated Euler Lagrange systems to be treated as “quasi-fully” actuated. In this equivalent quasi-fully actuated form, the system is characterized by the same Lagrangian structure as the original one. This facilitates the design of control approaches that take into account the underlying physics of the system and that shape the system dynamics to a minimum extent. Due to smoothness constraints on the new input vector that acts directly on the noncollocated coordinates, we coin the term quasi-fully actuated. The class of Euler–Lagrange systems we consider is the class of articulated soft robots with nonlinear spring characteristics that are modeled with a block diagonal inertia matrix. We illustrate how the quasi-fully actuated form enables the direct transfer of control concepts that have been derived for fully actuated manipulators. We adopt the popular energy-shaping and two passivity-based concepts. The exemplary adoptions of the PD+ and Slotine and Li controllers allow us to solve the task-space tracking problem for highly elastic joint robots with nonlinear spring characteristics. These control schemes allow compliant behavior of the robot's TCP to be specified with respect to a reference trajectory. A key aspect of the presented framework is that it enables the adoption of rigid joint controllers as well as concepts underlying the original stability analysis. We believe that our framework presents an important step toward unifying the control design for rigid and articulated soft robots