Modelling of Bound Estimation Laws and Robust Controllers for Robustness to Parametric Uncertainty for Control of Robot Manipulators

In this paper, first, a new approach is proposed for derivation of bound estimation laws for robust control of robot manipulators. In this approach, functions depending on robot kinematics and control parameters and integration techniques can be used for derivation of the bound estimation laws based on the Lyapunov theory, thus, stability of the uncertain system is guaranteed. Five new bound estimation laws are proposed, and in this derivations, five novel functions depending on robot kinematics and control parameters and proper integration techniques, such as substitution method, integration by part and integration by partial fractions are used. Then, four new robust control inputs are proposed based on each derived bound estimation law. Lyapunov theory based on Corless and Leitmann (IEEE Trans Automat Contr 26:1139-1144, 1981) approach is used for designing the robust control input achieving uniform boundedness error convergence. This study also allows derivation of other bound estimation laws for robust controllers provided that appropriate novel functions and proper integration techniques are chosen.