Movement Forms: A Graph-Dynamic Perspective

Abstract

The focus of this article is on characterizing the physical movement forms (e.g., walking, crawling, rolling) that are used to actualize abstract, functionally-specified behavioral goals (e.g., locomotion). Emphasis is placed on distinguishing such forms by their topological patterns of physical contact between agent and environment (i.e., the forms' physical graphs) and the transitions among these patterns displayed during skilled performance (i.e., the forms' physical graph dynamics). Crucial in this regard are the creation and dissolution of loops in these graphs, which can be related to the distinction between open and closed kinematic chains. Formal similarities are described within a task-dynamics framework between the physically-closed kinematic chains (physical loops) created during skilled actions and the functionally-closed kinematic chains (functional loops) associated with task-space control of end-effectors; we argue that both types of loop must be flexibly incorporated into the coordinative structures governing skilled action. Finally, implications of the graph-dynamic perspective are discussed for understanding patterns of inter-agent coordination and the perceptual guidance of action using informational links between agents and spatially remote (nonsentient) environmental objects.

ACKNOWLEDGMENT

This article is dedicated with deep affection and respect to the memory of Herbert Pick, Jr., whose fascination with the role of nested coordinate system geometries in the control and coordination of skilled action led, somehow, to the writing of this article.

FUNDING

The authors gratefully acknowledge the support of National Institutes of Health grants 2-P01-HD-001994 and 1-R01-GM-105045.

Notes

¹ In graph theoretic terms (e.g., Bulca, 1998; Harary, 1969), the open chain in Figure 1a is described as a tree in which only a single path exists between any two nodes (body segments and environmental objects) through the set of nodes and edges (joints) in the chain; due to the loop inherent in the closed chain of Figure 1b, however, a cycle is present and there are two paths available, one clockwise and one counterclockwise, between any two segments. Because we are dealing with systems in which nodes (body segments and environmental objects) are physically defined and joints (edges) are physically enforced, we refer to the graphs of such systems as physical graphs.