Stability criteria for robot compliant maneuvers

Abstract

Abstr8ctThe work prossnted hem i s a nonlinear approach for the stability analysis of robot manipulators in constrained maneuvers. Stability 4 the environment and the manipulator taken as a whole has been investigated, and a bound for staMc manipulation has bcm derived. We &ow that for stability a# the robot, there must be some initial compliancy either in the robot or in the environment. The general stability condition hos &en extended to the particular mse where thc environment is wry rigid in comparison with the robot stiffness. 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 Lagrangian approoeh. It allows us to incorporaie the dynamic behavior of dl tha elements of a robor manipulator (i.e. actuators, 8cnwra and the structural compliance of the links) in addition to the rigid body dynamics. Nomenclature m b r l of the extcrnal force on the robot endpoint inplt trajectory vector environment dynamics vector of the contact foree, [ff, f2, ...., fniT the limiting value of the contact force and robot porition for rigid environment robot dynamics with positioning controller compensator operating on the contact force, f identity metrix environment impedance in the linear domain input-command vector degrees of the freedom of the robot n < 6 robot manipulator sensitivity (l/stifhess) positive scalar the forward loop mapping from e to f in Figure 5. vector of the environment deflection Mctor of the robot endpoint position vector of the environment position before contact vector of the joint angles of the robot positive scalars frequency range of operation (bandwidth) positive scalars IntroductionMost assembly operations and manufacturing tasks require mechanical interactions with the environment or with the object being manipulated, along with "fast" motion in free and unconstrained space. In constrained maneuvers, the interaction force2 must be accommodated rather than resisted.

Control of Robotic Manipulators During General Task Execution: A Discontinuous Control Approach

“…Results reported in Mills (1990b) prove the local asymptotic stability of a closed-loop manipulator with a continuous control law applied during transition to and from contact motion under very restrictive conditions. Work presented in Kazerooni and Tsay (1988) and implicitly examines the control of manipulators during such transitions. Through experimental evidence presented in these papers, it can be deduced that the manipulator system has undergone a stable transition to and from contact motion with a continuous control law applied.…”

Intelligent compliant motion control

“…Consider 1083-4419/98$10.00 © 1998 IEEE a position-controlled robot. Many other researchers [15]- [17], have used a set of linear decoupled equations to model the dynamics of the system. It should be noted that the modeling is not for a bare robot but the robot and its controller.…”

Trajectory planning for two manipulators to deform flexible materials using compliant motion

“…The model of the robot positioning system is very important in the stability analysis. Most of the researchers used second order linear control systems to model the position of the end-effector as a function of the command [12] [13] [14].…”