Prescribing Cartesian Stiffness of Soft Robots by Co-Optimization of Shape and Segment-Level Stiffness

Soft robots aim to revolutionize how robotic systems interact with the environment thanks to their inherent compliance. Some of these systems are even able to modulate their physical softness. However, simply equipping a robot with softness will not generate intelligent behaviors. Indeed, most interaction tasks require careful specification of the compliance at the interaction point; some directions must be soft and others firm (e.g., while drawing, entering a hole, tracing a surface, assembling components). On the contrary, without careful planning, the preferential directions of deformation of a soft robot are not aligned with the task. With this work, we propose a strategy to prescribe variations of the physical stiffness and the robot's posture so to implement a desired Cartesian stiffness and location of the contact point. We validate the algorithm in simulation and with experiments. To perform the latter, we also present a new tendon-driven soft manipulator, equipped with variable-stiffness segments and proprioceptive sensing and capable to move in three dimensional. We show that, combining the intelligent hardware with the proposed algorithm, we can obtain the desired stiffness at the end-effector over the workspace.