Parameter estimation and adaptive control of Euler–Lagrange systems using the power balance equation parameterisation

Abstract

It is widely recognised that the existing parameter estimators and adaptive controllers for robot manipulators are extremely complicated, stymieing their practical use – in particular, for robots with many degrees of freedom. This is mainly due to the fact that the existing parameterisation includes the complicated signal and parameter relations introduced by the Coriolis and centrifugal forces matrix. In an insightful remark of their seminal paper, Slotine and Li suggested to use the parameterisation of the power balance equation, which avoids these terms – yielding significantly simpler designs. To the best of our knowledge, such an approach was never actually pursued in on-line implementations, because the excitation requirements for the consistent estimation of the parameters are ‘very high’. In this paper, we use a recent technique of generation of ‘exciting’ regressors developed by the authors to overcome this fundamental problem. The result is applied to general Euler–Lagrange systems and the fundamental advantages of the new parameterisation are illustrated with comprehensive simulations of a 2 degrees-of-freedom robot manipulator.

Keywords:

• Parameter estimation
• adaptive control
• Euler–Lagrange systems

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 We refer the interested reader to the long citation list given in the recent book (Zhang & We, 2021) for additional references.

2 See Ortega et al. (2020) and Ortega, Aranovskiy, et al. (2021) for other methods to construct the dynamic extension.

3 Of course, other identification methods (Ljung, 1987; Sastry & Bodson, 1989) could be used, but we select this one because of its simplicity and widespread popularity.

4 To simplify the notation we omit the subindex i in the proposition A.2.