English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We propose a new camera-based method of robot identification, tracking andorientation estimation. The system utilises coloured lights mounted in a circlearound each robot to create unique colour sequences that are observed by acamera. The number of robots that can be uniquely identified is limited by thenumber of colours available, $q$, the number of lights on each robot, $k$, andthe number of consecutive lights the camera can see, $\ell$. For a given set ofparameters, we would like to maximise the number of robots that we can use. Wemodel this as a combinatorial problem and show that it is equivalent to findingthe maximum number of disjoint $k$-cycles in the de Bruijn graph$\text{dB}(q,\ell)$.  We provide several existence results that give the maximum number of cyclesin $\text{dB}(q,\ell)$ in various cases. For example, we give an optimalsolution when $k=q^{\ell-1}$. Another construction yields many cycles in largerde Bruijn graphs using cycles from smaller de Bruijn graphs: if$\text{dB}(q,\ell)$ can be partitioned into $k$-cycles, then$\text{dB}(q,\ell)$ can be partitioned into $tk$-cycles for any divisor $t$ of$k$. The methods used are based on finite field algebra and the combinatoricsof words.

Partitioning de Bruijn Graphs into Fixed-Length Cycles for Robot Identification and Tracking