LAUSR

This paper presents an approach to develop a variable impedance controller with considerations of the optimality and stability. Firstly, an original optimal variable law is designed via demonstration learning, through which the Gaussian mixture model/Gaussian mixture regression (GMM/GMR) algorithm is employed to transfer the human impedance functions to the robot. By using the formulation of the GMR result, the regression task can be completed without using the ground-truth information of the human impedance parameters. To ensure the stability, a minimal complementary input is designed for the learned second-order impedance system. We transform the design problem to a constrained convex optimization problem, of which the constraints are related to a Lyapunov function. A criterion for choosing the Lyapunov functions is presented to ensure the feasibility of the problem, and an analytical solution is computed. The proposed approach is verified by the robotic assisted rehabilitation and trajectory reproduction experiments conducted on a 7-DOF Franka Panda robot.