On the Exact Parameter Estimation for Robot Manipulators Without Persistence of Excitation.

Adaptive control is one of the most employed techniques to achieve trajectory tracking of robot manipulators. Although it is desirable to obtain exact parameter estimation, most adaptive schemes need the persistency of excitation (PE) condition on the regressor to be satisfied. In the recent years, the so-called dynamic regressor extension and mixing (DREM) procedure was developed to provide an alternative in the design of adaptive laws with conditions different from PE. When met, the improvement in parameter estimation is remarkable, but when not, adaptation can simply stop, which might be unacceptable for control purposes. This article proposes for the first time a composite scheme, which combines the standard gradient adaptive law with a DREM-based additional term with the following properties: 1) Trajectory tracking for joint desired positions and velocities is guaranteed; 2) in the absence of PE, if a new condition that can partially be verified online for the additional DREM-based term is matched, then exact parameter estimation takes place in finite time. Simulation results are in good accordance with the developed theory.