Task space robot control: convergence analysis and gravity compensation via integral feedback

The problem of the task level position and orientation regulation of the end-effector of a generic robot is discussed in this paper. A hierarchical control scheme is proposed, implementing task-level B-type position control loop (outer loop), and P or PI-type one operating at joint velocity level (inner loop). Finally it is proved that a suitable choice of the feedback gains always ensure for P-type inner loop, uniform ultimate boundedness of the errors, while using PI-type inner loop it is possible to prove the local asymptotic convergence to zero of the position and orientation errors