STABILITY OF ROBOTIC MANIPULATORS DURING TRANSITION TO AND FROM COMPLIANT MOTION

The stability and control of robotic manipulators during tasks in which the manipulator end-effector makes intentional contact with objects in its work environment represents a problem of much practical interest. This paper addresses the specific problem of stability of a general class of nonlinear control laws applied to rigid link manipulators during the transition to and from point contact with compliant objects in the work environment. The work environment is modeled as a general lumped parameter linear mechanical impedance characterized by inertia, damping and stiffness terms. The manipulator dynamic structure is ideally suited to the establishment of the stability results of this paper. The manipulator is treated as a set of interconnected subsystems, permitting the application of an existing stability theory to this problem. To establish the stability of the manipulator during the transition to and from contact, the manner in which the controls are to be applied during this transition are first characterized. Under the implicit assumption that two separate controls, one for noncontact motion and one for contact motion, are to be applied to the manipulator, it is clear that due to timing and other errors, an incorrect control law may be applied to the manipulator for a brief period of time during the transition to and from contact. Hence, the stability results for this transition to and from contact are equivalent to the establishment of system stability for a variety of incorrect control laws applied to the manipulator. The conditions that lead to these stability results are then combined to form a single set of conditions for transitional stability. It is noted that during the transition from free to contact motion, a collision occurs, requiring the introduction of additional conditions to ensure stability. The collision is assumed to be plastic. Hence, conditions are established such that a single control law when applied to a robotic manipulator, is shown to exhibit locally stable behaviour during the transition to and from contact motion. It is shown that the common engineering practice of the use of high gain local feedback to control robotic manipulators readily leads to establishment of the transitional stability results. A detailed numerical example is introduced to illustrate the nature of the results obtained. © 1990.