SIX APPLICATION TO THE ROBOTIC MANIPULATOR 94 Manipulator Dynamics.............. 94 Actuator Driving Torques 96 Feedback Control System for Tracking and Disturbance Rejection.............. 97 Determining the Dynamics of the Internal Model System... 98 Feedback Gain Calculation 101 Compensation for Flexibilities in the Manipulator's Links 106 SEVEN SIMULATION RESULTS 109 The Simulated System 109 Control about a Stationary Configuration 112 Control over a Time-varying Nominal Trajectory 124 Correcting for Flexibilities 147 EIGHT CONCLUSIONS AND OPEN PROBLEMS 153 REFERENCES 155 BIOGRAPHICAL SKETCH..... 158 IV