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The authors present a nonlinear stability analysis for constrained robotic motion, a maneuver where the manipulator contacts the environment. The external disturbances, sensor noises, parameter uncertainties, and the dynamics of the total system composed of the robot and the environment have been modeled. The control of the manipulator is divided into two components: a computed torque trajectory controller that regulates the robot position and a compliance controller that modulates contact forces. Three sufficient conditions for stability have been derived. The first condition guarantees the stability of the system of robot and finite stiff environment when no force sensor and, consequently, no force feedback is considered for the system. The second condition guarantees stability of the robot and environment when a compliance compensator (operating on the contact force) supplements the trajectory controller. The third stability criterion shows that, for a robot contacting a very stiff environment, the gain of the compliance compensator must vary in inverse proportion to the gain of the trajectory compensator.>
Waibel et al. (Tue,) studied this question.