Computer Science

Convexly stratified deformation spaces and efficient path planning for planar closed chains with revolute joints

Document Type

Conference Paper

Abstract

Systems involving loops have been especially challenging in the study of robotics, partly because of the requirement to maintain loop closure constraints, conventionally formulated as highly nonlinear equations in joint parameters. In this paper, we present our novel triangle-tree-based approach and parameters for planar closed chains with revolute joints. For such a loop, the loop closure constraints are exactly, not approximately, a set of linear inequalities in our new parameters. Further, our new parameters provide explicit parametrization of the system deformation space (configuration space modulo the group of rigid motions of the system's ambient space respecting system specifications) and endow it with a nice geometry. More precisely, the deformation space of a generic planar loop with n revolute joints consists of 2n-2 copies of one and the same convex polytope (which, when all of the link lengths are fixed, is bounded and of dimension n - 3), glued together into either one connected component or two (ignoring collision-free constraints), via proper boundary identification. Such a completely solved, stratified space of convex strata will have profound implications for these systems and lead to great simplifications in many kinematics related issues. For example, in essence, our approach makes path planning for planar loops with revolute joints no more difficult than for open chains. We also briefly point out the connection and extension of the work presented here to other systems such as spatial loops with spherical joints and systems involving multiple loops. © 2008 SAGE Publications.

Publication Title

International Journal of Robotics Research

Publication Date

2008

Volume

27

Issue

11-12

First Page

1189

Last Page

1212

ISSN

0278-3649

DOI

10.1177/0278364908097211

Keywords

configuration spaces, construction trees of triangles, convex stratification, deformation spaces, Kinematics, loop closure constraints, motion planning, triangle-based parameters

APA Citation

Han, L., Rudolph, L., Blumenthal, J., & Valodzin, I. (2008). Convexly stratified deformation spaces and efficient path planning for planar closed chains with revolute joints. The International Journal of Robotics Research, 27(11-12), 1189-1212.

Link to Full Text

Share

COinS