A SEMIGLOBALLY STABLE OUTPUT-FEEDBACK (PID)-D-2 REGULATOR FOR ROBOT MANIPULATORS

In this technical note, we provide an answer to the longstanding question of designing asymptotically stable proportional plus integral regulators with only position feedback for robots with uncertain payload. It has recently been shown in [1] and [2] that globally asymptotically stable set-point regulators for robot manipulators without velocity measurement can be obtained replacing the velocity feedback of a proportional plus derivative controller by a filtered position feedback, In these schemes, the only robot prior information required is the evaluation of the gravity forces at the reference (constant) position. This prior knowledge is used to shape the robot potential energy to have a unique minimum at the desired position. A mismatch in the estimation of the gravity forces leads to a position steady-state error. Our main contribution is to obviate the need of this prior information via the inclusion of two integral terms, around the position error and the filtered position, respectively. Semiglobal stability of the resulting control law is established.