A Positive-Real Modification of a Class of Nonlinear Controllers for Robot Manipulators

In this paper the new class of "PD+" control laws for rigid-link manipulators, whose members are PD joint controllers plus dynamic compensation, is extended. We show that the PD joint control can be generalized to a positive-real (PR) controller without altering the exponential stability of these control algorithms. This positive-real modification allows a robot control system designer to do joint-by-joint loop shaping of the joint servos to improve stiffness and stability margin. Moreover, the use of the passive positive-real joint controllers guarantees that stiction and friction will not induce limit cycling. This PR modification is applicable to adaptive control laws as well.