On the recursive implementation of adaptive control for robot manipulators

This paper investigates the recursive implementation of adaptive control for robot manipulators. Using the spatial vector tool and exploiting some physical properties of multi-body systems, we propose a general framework on the seeking of the Coriolis and centripetal matrix which satisfies the so-called skew-symmetric requirement. Then two existing choices are analyzed and a new kind of Coriolis and centripetal matrix is proposed. Comparisons between these choices show that the simplest-form Coriolis and centripetal matrix comes from the original recursive Newton-Euler dynamics based on spatial vectors, which implies that skew-symmetric property is an inherent property possessed by spatial-vector based recursive Newton-Euler dynamics formulation. Under the proposed general framework regarding establishment of the Coriolis and centripetal matrix, a class of recursive passivity based adaptive algorithms have been proposed. In the next, we present an algorithm on how to derive the filtered manipulator torque recursively. With this filtered torque, the prediction error of the filtered torque is obtained and injected to the direct adaptation, forming the well-known composite adaptation law. Composite adaptation driven by both the tracking errors and the prediction errors gives more smooth tracking error response and estimated parameter response, and also better tracking accuracy. A six-DOF manipulator is employed as a simulation example to show the performance of the proposed recursive algorithms.