Adaptive Control for Nonlinearly Parameterized Uncertainties in Robot Manipulators

In this brief, a new adaptive control framework to compensate for uncertain nonlinear parameters in robot manipulators is developed. The designed adaptive controllers possess a linear parameter structure, guarantee global boundedness of the closed-loop system as well as tracking of a given trajectory within any prescribed accuracy. Our design approach takes advantage of a Lipschitzian property with respect to the plant nonlinear parameters. The outcome is that a very broad class of nonlinearly parameterized adaptive control problems for robot manipulators can be solved using this technique. Another feature of the proposed method is the design of low-dimensional estimator, even 1-D if desired, independently of the unknown parameter vector dimension. Simulations and experiments in friction compensation task for low-velocity tracking of a 2 degree-of-freedom planar robot demonstrate the viability of the technique and emphasize its advantages relatively to more classical approaches.