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The work presented here is a nonlinear approach for the stability analysis of robot manipulators in compliant maneuvers. Stability of the environment and the manipulator taken as a whole has been investigated, and a bound for stable manipulation has been derived. The stability analysis has been investigated using unstructured models for the dynamic behavior of the robot manipulator and the environment. This unified approach of modeling robot dynamics is expressed in terms of sensitivity functions as opposed to the rigid body dynamics derived by Lagrangian approach. It allows us to incorporate the dynamic behavior of all the elements of a robot manipulator (i.e., actuators, sensors and the structural compliance of the links) in addition to the rigid body dynamics. We show that for stability of the robot, there must be some initial compliancy either in the robot or in the environment. According to this stability condition, smaller sensitivity either in the robot or in the environment leads to a narrower stability range. In the limit, when both robot and environment have zero sensitivity, stability cannot be guaranteed. The general stability condition has been extended to the particular case where the environment is very rigid in comparison with the robot stiffness. This condition has been verified via simulation and experiment on the Minnesota direct drive robot.
Kazerooni et al. (Sat,) studied this question.