Closed-Form Solution to Controller Design for Human-Robot Interaction

This paper deals with controller design for gentle physical human-robot interaction. Two objectives are set up. The first is to establish an analytical framework in order to justify the good features of state of the art controller, recently designed by numerical search of parameter space. The second is to investigate the possibilities to improve the performance of such controller. Our method ensures “prescribed” admittance behavior of the robot, similar to natural admittance controller design but with both more realistic model of the robot and more realistic target admittance. Joining natural admittance approach with the concept of complementary stability allows reaping the benefits of both. Limited knowledge about the environment via structured uncertainty allows a very simple worst-case analysis using elementary tools such as Routh–Hurwitz stability criterion. Consequent relation within the parameters determines an allowed region in the parameter space, where the contact stability is guaranteed. Not surprisingly, on one border of this region, the system behaves exactly the same as when the state of the art controller is employed. In addition, unexpected stability regions are discovered, suggesting theoretical performance improvements.