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/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we consider the gathering problem of seven autonomous mobilerobots on triangular grids. The gathering problem requires that, starting fromany connected initial configuration where a subgraph induced by all robot nodes(nodes where a robot exists) constitutes one connected graph, robots reach aconfiguration such that the maximum distance between two robots is minimized.For the case of seven robots, gathering is achieved when one robot has sixadjacent robot nodes (they form a shape like a hexagon). In this paper, we aimto clarify the relationship between the capability of robots and thesolvability of gathering on a triangular grid. In particular, we focus onvisibility range of robots. To discuss the solvability of the problem in termsof the visibility range, we consider strong assumptions except for visibilityrange. Concretely, we assume that robots are fully synchronous and they agreeon the direction and orientation of the x-axis, and chirality in the triangulargrid. In this setting, we first consider the weakest assumption aboutvisibility range, i.e., robots with visibility range 1. In this case, we showthat there exists no collision-free algorithm to solve the gathering problem.Next, we extend the visibility range to 2. In this case, we show that ouralgorithm can solve the problem from any connected initial configuration. Thus,the proposed algorithm is optimal in terms of visibility range.

Gathering of seven autonomous mobile robots on triangular grids