Linear and Competitive Strategies for Continuous Robot Formation Problems

摘要: We study a scenario in which n mobile robots with limited viewing range are distributed the Euclidean plane and have to solve formation problem. The problems we consider Gathering problem Chain-Formation In problem, gather one (not predefined) point, while they form connected communication chain of minimal length between two stationary base stations. Each robot may its decisions where move only on current relative positions neighboring (that within range); that is, besides having range, oblivious (they do not use information from past), none or very identities, common sense direction. Variants these (especially for problem) been studied extensively different discrete time models. contrast, our work focuses continuous model; continuously other their adapt speed direction according some simple, local rules. Hereby, assume maximum movement one. show this idealized idea sensing allows us mentioned linear O(n) (which, given one, immediately yields traveled distance O(n)). Note more classical models, best known strategies need at least Θ(n2) even Θ(n2logn) timesteps problems. For analysis solves left open by Gordon et al. [2004], authors could prove gathering model is possible finite time, but were able give runtime bounds. Apart bounds, also provide bounds both relate an optimal, global algorithm. Specifically, strategy log OPT-competitive log n-competitive. Here, c-competitive, mean (local) asymptotically most factor c slower than strategy.