Exact Linearization of Nonlinear Manipulator Models using Adaptive Control

Abstract

Exact linearization of robot dynamics using nonlinear feedback requires an accurate knowledge of the robot parameters and payload. These parameters are often not known `a priori.' A Model Reference Adaptive Control system is developed for tracking the unknown or imprecisely known parameters. The values of these parameters are updated in the nonlinear feedback loop, using adaptive control, to achieve exact linearization. The adaptation algorithm is synthesized using Lyapunov stability criterion. Numerical simulation studies are conducted for a prototype three degree-of-freedom manipulator with five unknown parameters. A study of parameter convergence shows the importance of weighting factors in the adaptation law to control interaction between parameters. When multiple parameters are adapted simultaneously, the rate of adaptation of one parameter affects the values of other parameters. This results in mutual parameter compensation to reduce errors between the robot and the reference model. Parameter interaction can be reduced by using high speeds of adaptation within the bounds of stability.