Crossing-changeable braids from chromatic configuration spaces

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. ...

Chromatic Derivatives, Chromatic Expansions and Associated Spaces

This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential operators which correspond to certain families of orthogonal polynomials. Chromatic expansions are series of the corresponding special functions, which possess th...

Hex, Braids, the Crossing Rule, and XH-Search

We present XH-search, a Hex connection finding algorithm. XH-search extends Anshelevich’s H-search by incorporating a new crossing rule to find braids, connections built from overlapping subconnections.

Configuration Spaces

0 7 4 0 7 4 5 9 / 0 4 / $ 2 0 . 0 0 © 2 0 0 4 I E E E distributed systems is most often specified in terms of quality-of-service (QoS) requirements, which help define the acceptable levels of dependability with which capabilities such as processing capacity, data throughput, or service availability reach users. For longer-term properties such as scalability, maintainability, adaptability, and s...

Crossing Matrices and Thurston's Canonical Form for Braids