Dynamic analysis of mobility and graspability of general manipulation systems

We present a geometric approach to the dynamic analysis of manipulation systems of a rather general class, including some important types of manipulators as, e.g., cooperating, super-articulated, and whole-arm manipulators. The focus is in particular on simple industry-oriented devices, for which a minimalistic design approach requires a clear understanding of mobility and graspability properties in the presence of kinematic defectivity. The paper discusses the dynamics of these systems, and considers how their structural properties (in the classical system-theoretic sense, i.e., stability, controllability, observability, etc.) are related to frequently used concepts in robotics such as "redundancy", "graspability", "mobility", and "indeterminacy". Less common or novel concepts, such as those of "defectivity," "hyperstaticity," and "dynamic graspability", are elicited and/or enlightened by this study. Some important practical consequences of the limited control possibilities of defective systems are thus put into evidence. Finally, a standard form of the dynamics of general manipulation systems is provided as a compact and readable synopsis of the dynamic structure. The form is a valuable tool for synthesizing dynamic controllers for such systems, especially suited to geometric control design methods.