Improved Robustness Measures for the Exact Linearization Control of Robots

Abstract

New and improved bounds are obtained for the stability robustness of robots controlled by exact linearization technique. Uncertainties in the equivalent link masses, Coulomb and viscous friction coefficients and unknown external disturbances are shown to be accommodated to a certain degree by controllers of this type. Uncertainties are both modelled as deterministic and stochastic perturbations. In the deterministic case, uniform ultimate boundedness using both Lyapunov theorems and Gronwall-Bellman inequality and in the stochastic case sample path boundedness using Martingale results can be secured if the bounds given in this paper are not exceeded. We demonstrate the improvement in bounds over the previous ones by analytical means for a general n degree-of-freedom manipulator. Finally, the results are illustrated by using a 2 degree-of-freedom numerical example.