Improvement of adaptive controller designs for robot manipulator systems yielding reduced Cartesian error

A set of nonlinear coupled differential equations that represents mathematical model of a robot manipulator whose coefficients are unknown due to the effects of payload, friction and/or backlash, etc., is considered in this paper. It is shown that by proper compensation of the input torque the norm of the state error becomes less than that which is resulted from the conventional design. A Jacobian relation is introduced and being used in the design methodologies of the Lyapunov direct method and the hyperstability method to reduce the Cartesian error. These results are applied to a three-joint revolute manipulator to demonstrate performance improvement.