Exact Task Execution in Highly Under-Actuated Soft Limbs: An Operational Space Based Approach

Recently, the development of soft robots is imposing a change of prospective in several aspects of design and control, moving the robotic field closer to the natural world. Soft robots, like many animals, are often built of continuously deformable elements, and are consequently characterized by a highly under-actuated input space. In this letter we prove that given a generic nonlinear task to be accomplished by a soft robot - as e.g., the positioning of its end effector in space - a linear actuation space with the size of the task itself is already sufficient to achieve the goal. We then introduce the dynamically consistent projector into synergistic space, which can be used to convert controllers designed in operational space, to work in the under-actuated case. This enables a direct translation of control strategies from classic to soft robotics. Leveraging on this result, we present the first dynamic feedback controller for trunk-like soft robots taking in account nonconstant deformations of the soft body. We present simulations showing that using this controller it is possible to track a prescribed dynamic evolution of the robot's tip with zero error at steady state, both in planar and 3-D case with gravity.