Inertial Properties in Robotic Manipulation: An Object-Level Framework

Consideration of dynamics is critical in the analysis, design, and control of robot systems. This article presents an extensive study of the dynamic properties of several important classes of robotic structures and proposes a number of general dynamic strategies for their coordination and control. This work is a synthesis of both previous and new results developed within the task-oriented operational space formulation. Here we in troduce a unifying framework for the analysis and control of robotic systems, beginning with an analysis of inertial prop erties based on two models that independently describe the mass and inertial characteristics associated with linear and angular motions. To visualize these properties, we propose a new geometric representation, termed the belted ellipsoid, that displays the magnitudes of the mass/inertial properties directly rather than their square roots. Our study of serial macro/mini structures is based on two models of redundant mechanisms. The first is a description of the task-level dy namics that results from projecting the system dynamics into operational space. The second is a unique dynamically con sistent relationship between end-effector forces and joint torques. It divides control torques at the joint level into two dynamically decoupled vectors: torques that correspond to forces at the end effector, and torques that affect only internal motions. The analysis of inertial properties of macro-/mini- manipulator systems reveals another important characteristic: that of reduced effective inertia. We show that the effective mass/inertia of a macro-/mini-manipulator is bounded above by the mass/inertia of the mini-manipulator alone. Because mini structures have a limited range of motion, we also pro pose a dextrous dynamic coordination strategy to allow full use of the high mechanical bandwidth of the mini-structures in extended-motion operations. Finally, a study of the dy namics of parallel, multiarm structures reveals an important additive property. The effective mass and inertia of a multi arm system at some operational point are shown to be given by the sum of the effective masses and inertias associated with the object and each arm. Using this property, the mul tiarm system can be treated as a single augmented object and controlled by the total operational forces applied by the arms. Both the augmented object construct and the dynam ically consistent force/torque relationship are extended for the analysis and control of multiarm systems involving redun dancy.