Application of Logarithmic-based Parameter and Upper Bounding Estimation Rules to Adaptive-Robust Control of Robot Manipulators

This paper presents a new adaptive-robust control law for robot manipulators with parametric uncertainty. The control law for n-link robot manipulators using the Lyapunov-based theory of guaranteed stability of uncertain system is derived by means of analytical approach. The proposed adaptive-robust control law includes an adaptive dynamic compensation, robust feedforward compensators with an adaptive upper bounding function and a PD feedforward part, and both system parameters and robust feedforward compensator are updated in time. As distinct from similar studies, the manipulator parameters are updated with a logarithmic function depending on manipulator kinematics, inertia parameters and tracking error and on the other hand, robust compensator is updated as a function of uncertainty bound, robot kinematics and tracking error. The developed approach has the advantages of both adaptive and robust control laws, and besides it eliminates disadvantages of them.