A Formalism for the Analysis and Design of Modular Kinematic Structures

Abstract

The exploitation of robotic systems with more complex kinematic structures than those of conventional serial chains is widely perceived as one of the main avenues of development for robotics. The concept encompasses systems of different scales and characteristics, such as hybrid manipulators, multifingered hands, cooperative robotic arms, walking machines, and so on. The underlying kinematic structure of these systems is the same in the sense that they can be regarded as combinations of modules. In this paper, we aim to provide a framework for systematically identifying, classifying, and combining different modules of such manipulators. Hence, we introduce a formalism that comprises a set of definitions, a symbolic representation of modules, and a set of operations based on the kinematic structure, degree of actuation, and mobility of the modules. The proposed formalism allows us to efficiently analyze and synthesize modular manipulators according to their constituent kinematic modules. Moreover, the foregoing operations can be easily performed in symbolic form, using commercial software, which makes their implementation generic and more useful. The information that is obtained from these operations provides a data base for either designing an inventory of modules or interchanging modules when an inventory of modules is available to the system. The application of the proposed formalism is demonstrated through a few examples, one of which pertains to a 7-DOF hybrid manipulator with parallel subchains, whose architecture is introduced here for the first time.

Operating High-DoF Articulated Robots Using Virtual Links and Joints

“…Davis [7] explored spatial geometric abstraction at a conceptual level, including an interesting but brief mention of a "kinematic device as black box." Zanganeh and Angeles [44] give a more detailed and formal development of the idea of separating topologically large kinematic structures into sub-mechanisms, but their approach does not specifically separate interface from implementation-it just demarcates sub-mechanisms. Our structure abstraction includes this capability, but also allows interface mechanisms that stand-in for underlying implementations.…”

Graph theoretic foundations of multibody dynamics

“…They have been used for the systematic formulation of the equations of motion [24, 31, 36], as well as for kinematical analysis [37]. …”

“…Some of the extensions have led to computer techniques for organizing and automatically generating symbolic representations of the equations of motion [31]. Graph theory techniques have also been used for the kinematic analysis of mechanisms [37]. …”

Multibody graph transformations and analysis

“…Graph techniques have been developed for the systematic formulation of the equations of motion [20,24, 28, 30]. The sparsity structure of the equations of motion have been exploited to develop efficient dynamics computational algorithms [3, 7, 8, 23, 25].…”