A Reduced-Order Regressor and Its Application to Adaptive Robotic Control

Manipulator regressors are n x l matrix functions in the dynamic expressions τ = Y(q, q, q)ζ_r or (1/D + σ)τ = W(q, q)ζ_r, which linearize the robot dynamics with respect to a properly defined inertia parameter vector ζ _r ∈ R^l. Many modern adaptive controllers require on-line computation of a regressor to estimate the unknown inertia parameters and ensure robustness of the closed-loop system.

Although the computation of Y(q, q, q) has been studied by Atkeson et al. (1985), Khosla and Kanade (1985), and Khosla (1989), the computation of W(q, q) for a general n-link robot has not been reported in the literature. This article presents an algorithm to compute W(q, q) for a general n-link robotic manipulator The variables used to construct the regressor matrix are directly available from the outward iteration of a Newton-Euler algorithm; some additional arithmetic operations and first-order, low-pass filtering are needed. The identification of unknown inertia parameters is also discussed.