Configuration Spaces and Braid Groups on Graphs in Robotics
نویسنده
چکیده
Configuration spaces of distinct labeled points on the plane are of practical relevance in designing safe control schemes for Automated Guided Vehicles (robots) in industrial settings. In this announcement, we consider the problem of the construction and classification of configuration spaces for graphs. Topological data associated to these spaces (e.g., dimension, braid groups) provide an effective measure of the complexity of the control problem. The spaces are themselves topologically interesting objects. We show that they are K(π1, 1) spaces whose homological dimension is bounded by the number of essential vertices. Hence, the braid groups are torsion-free. AMS classification: 57M15,57Q05,93C25,93C85. 1 Configuration Spaces in Manufacturing
منابع مشابه
Configuration Spaces, Braids, and Robotics
Braids are intimately related to configuration spaces of points. These configuration spaces give a useful model of autonomous agents (or robots) in an environment. Problems of relevance to autonomous engineering systems (e.g., motion planning, coordination, cooperation, assembly) are directly related to topological and geometric properties of configuration spaces, including their braid groups. ...
متن کاملConnectivity at Infinity for Braid Groups on Complete Graphs
We show that the connectivity at infinity for configuration spaces on complete graphs is determined by the connectivity of chessboard complexes.
متن کاملThe conjugacy problem in right - angled Artin groups and their subgroups
We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups (i.e. fundamental groups of configuration spaces of points in graphs), many hyperbolic groups, and it coincides with the class of fundamental groups of “specia...
متن کاملConfiguration Spaces and Braid Groups
The main thrust of these notes is 3-fold: (1) An analysis of certain K(π, 1)’s that arise from the connections between configuration spaces, braid groups, and mapping class groups, (2) a function space interpretation of these results, and (3) a homological analysis of the cohomology of some of these groups for genus zero, one, and two surfaces possibly with marked points, as well as the cohomol...
متن کاملSemi-algebraic Geometry of Braid Groups
The braid group of n-strings is the group of homotopy types of movements of n distinct points in the 2-plane R. It was introduced by E. Artin [1] in 1926 in order to study knots in R. He gave a presentation of the braid group by generators and relations, which are, nowadays, called the Artin braid relations. Since then, not only in the study of knots, the braid groups appear in several contexts...
متن کامل