Composite Adaptive Control of Robot Manipulators with Friction as Additive Disturbance

In this paper, an adaptive control scheme composed of an estimated feed-forward compensation and a PD control law with three mutually independent estimators is proposed for the tracking of desired trajectories in joint space for a robotic arm. One of the estimators is used to identify inertial and geometrical parameters, while the others determine the two principal components of the friction phenomenon: the part whose magnitude is position-dependent but velocity-independent and the part whose magnitude is proportional to velocity. Next, the persistently exciting condition is satisfied for each regression matrix of the estimators in a way that is easier to prove than the classical structure. Then, uniform global asymptotic stability can be concluded for the tracking error, regardless of parametric convergence, by applying the direct Lyapunov theorem. This scheme has been applied experimentally for a robotic arm to verify the theoretical results. The experimental results yielded a better performance in both estimating the parameters and tracking, with a much simpler overall analysis than the alternatives consulted.