Trajectory control of a manipulator constrained by the contact of the end-effector with the environment represents an important class of control problems. A method is proposed whereby both contact force exerted by the manipulator, and the position of the end-effector while in contact with the surface are controlled. The controller parameters are derived based on a linearized dynamic model of the manipulator during constrained motion. Hence the method is valid only in a neighborhood about the point of linearization. Additionally, a perfect kinematic model of the contact surface is assumed. The proposed method utilizes the fundamental structure of the dynamic formulation of the manipulator's constrained motion. With this formulation, the trajectory control problem is naturally expressed in terms of the state vector variables of the model of the constrained dynamic system. A detailed numerical example illustrates the proposed method.
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