is applied to the robot system 300 the angular position signal 303 and its first and second derivatives 305 and 307 are generated by the robot system 300 for use in generating the new torque signal 320 these robot system generated signals are compared in the summing nodes 302 304 and 306 with the desired performance determining signals 308 310 and 312 to generate the error signal 324 and its first and second derivative 326 and 328 that are applied to the adaptive controller 314 in order to generate the new torque signal 320 in the fig3 controller in the absence of gravity the error e t 324 is zero resulting in u03c4 total at 322 u03c4 applied at 318 and u03c4 new at 320 0 as shown from fig3 the relationship between total torque u03c4 total at 322 the applied torque u03c4 applied at 318 and the new torque u03c4 new at 320 is given by when gravity is present the new torque u03c4 new is used to compensate for the nonlinear effect due to gravity when gravity or some other nonlinear effect enters the relationship u03b1 at 303 may not be the same as u03b1d at 308 or possibly u03b1 at 305 may differ from u03b1d at 310 or possibly u03b1 at 307 is different from u03b1d at 312 this occurs because of the appearance of an error signal when the torque u03c4 specified in equation 2 is applied and the u03b1 which results is different from the u03b1d which was expected in the present invention the adaptive controller as.