Adaptive control based on speed gradient algorithm for robot manipulators

In this short note, we present three types of adaptive parameter update law for the rigid body robot manipulator based on the speed gradient algorithm which is introduced by Fradkov (1979). In the derivation of the new adaptive parameter update laws, we refer the dynamics of rigid body robot manipulators and it´s error dynamics which were derived by Slotine and Li (1987, 1988). It is shown that the parameter update law which was derived by Slotine belongs to one of three types of adaptive parameter update law proposed in this paper. The three types of adaptive parameter update laws proposed in this paper can ensure the global stability under some conditions such as attainability and convexity in the error dynamics. Computer simulation shows that proposed control algorithm can be used for the tracking problem of rigid body robot manipulators