Stiffness Bounds for Resilient and Stable Physical Interaction of Articulated Soft Robots

It is widely recognized that impedance modulation is a key aspect in applications in which robots significantly interact with the environment or humans. Either active impedance controllers or actuators with passive variable impedance can be exploited to modulate the impedance. However, methods capable of determining the right (constant or time-varying) impedance profile in order to guarantee task performance as well as resilience and stability are required. In this letter, we discuss how task-related aspects, such as uncertainties, contact surface shapes, and interaction forces, set bounds on the admissible Cartesian stiffness. We recall that, an upper bound on the stiffness is required to prevent high forces exchanged during the interaction to guarantee adaptability and safety. Despite this, however, there is also a lower bound to be considered in order to preserve stability during the interaction. To this purpose, we study the interaction of a robot, with controllable Cartesian impedance, with a curved surface. Thus, we provide an analytic lower bound for the Cartesian stiffness that guarantees stability of such interaction task, and we prove that this bound directly depends on task parameters, namely contact force and surface curvature. Theoretical results are experimentally validated on robots powered by variable stiffness actuators and compliance controlled industrial robots.