Investigation of human-robot interaction stability using Lyapunov theory

For human-robot cooperation in the context of human-augmentation tasks, the stability of the control model is of great concern due to the risk for the human safety represented by a powerful robot. This paper investigates stability conditions for impedance control in this cooperative context and where touch is used as the sense of interaction. The proposed analysis takes into account human arm and robot physical characteristics, which are first investigated. Then, a global system model including noise filtering and impedance control is defined in a state-space representation. From this representation, a Lyapunov function candidate has been successfully discovered. In addition to providing conclusions on the global asymptotic stability of the system, the relative simplicity of the resulting equation allows the derivation of general expressions for the critical values of impedance parameters. Such knowledge is of great interest in the context of design of new adaptive control laws or simply to serve as design guidelines for conventional impedance control. The accuracy of these results were verified in a user study involving 7 human subjects and a 3-dof parallel robot. In this experiment, the real effective stability frontier was defined for each subject and compared with values predicted using the Lyapunov function.