Adaptive controls for nonlinearly parameterized uncertainties in robot manipulators

A framework of adaptive controls to compensate for uncertain nonlinear parameters in robot manipulators is developed. The proposed adaptive controllers with a linear parameter-like structure guarantee global boundedness of the overall system and tracking of a given trajectory within any prescribed accuracy. Our design approach takes advantage of a Lipschitzian condition with respect to the nonlinear parameters of the plant dynamics. This allows our approach to solve a very broad class of nonlinearly parameterized adaptive control problems for robot manipulators. Another feature of the proposed method is the design of low-dimensional observers, even one-dimensional, whose dimension is independent of the dimension of unknown parameters. Comparative simulations and experiments confirm the advantages of the proposed adaptive controls for a friction compensation task in low-velocity tracking of a 2 DOF planar robot.