Adaptive controller designs for robot manipulator systems yielding reduced Cartesian error

A set of nonlinear coupled differential equations that represents a 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 note. It is shown that by proper compensation of the input torque, the norm of the state error becomes less than that which resulted from the conventional design. A Jacobian relation is introduced and is used in the design methodology of the Lyapunov direct method to reduce the Cartesian error.