Robot Control as a System Control Problem

Abstract

Abstract Robot arm control is a mechanical system control problem rather than a problem of controlling single actuators of a robot arm. Using principles and techniques of differential geometric system and control theory, a new dynamic system feedback technique is presented referenced to task space commands. In this task-driven dynamic control scheme the nonlinear robot arm system is feedback linearized and simultaneously output decoupled by an appropriate nonlinear feedback and a nonlinear coordinate transformation. The new dynamic control technique actually transforms robot arm control problems from the joint space to the task space and performs robot servoing in terms of task space variables within a linear system frame, allowing also the use of powerful techniques of optimal control of linear systems. On the joint space level, the new dynamic control scheme only commands drive forces or torques or their equivalent quantities addressed to the joint drives. An important property of the new dynamic control technique is that the planned and commanded task space trajectory together with its time derivatives directly drives the robot arm through a linear system model. A method is briefly presented for task space motion planning matching the requirements of the new dynamic control scheme. It requires that the planned motion be presented to the controller as an input in form of a closed function of time. The implications of the new dynamic control technique are discussed for second and third order model robot arms with and without force feedback measurements and for two (or more) dynamically cooperating robot arms using distinguished and indistinguished modeling for multiple cooperating arms. The paper concludes with a brief discussion of a suggested computing architecture for implementing the new dynamic control technique together with the corresponding planning procedures.