Exponential Convergence of a Unified CLF Controller for Robotic Systems under Parameter Uncertainty

Abstract — This paper presents a novel method for achieving exponential convergence of a Control Lyapunov Function (CLF) based controller in a n-DOF robotic system in the presence of parameter uncertainty. Utilizing the linearity of parameters in the equations of motion, we construct the regressor and aug-ment the state space of the robot to include a vector of unknown parameters, called base inertial parameters. The augmented state space can be utilized to realize an optimal controller that is exponentially stable while simultaneously estimating the parameters online. To achieve this result, acceleration data for a given torque input is measured and used to compute the regressor. This, in turn, is used to compute the set of base inertial parameters in the form of linear equality constraints. By demonstrating that it is not necessary for the estimated parameters to converge to the actual parameters, but rather convergence is only needed on a specified space, we are able to construct a quadratic program enforcing convergence. The end result is that exponential convergence of a Control Lyapunov Function can be guaranteed, in an optimal fashion, without prior knowledge of the parameters. I