Constrained manipulator dynamic models and hybrid control

Dynamic models which correctly describe the constrained motion of robotic manipulators during contact with rigid work environments are given. The existing hybrid control law is rewritten in terms of the state of these constrained dynamic models. The hybrid control law is shown to be a linear feedback of the deviation from the nominal state of the constrained manipulator dynamic equations of motion. This result is illustrated through reformulation of the generalized force due to contact in terms of the Lagrange multipliers, which properly account for the constraints imposed on the manipulator through contact with a rigid work environment. Thus, while it appears that the hybrid control scheme utilizes feedback of the generalized contact force, this feedback is shown to be more compactly written in terms of the Lagrange multipliers, leading to a reformulation of the hybrid feedback control law