Optimal deterministic protocols for mobile robots on a grid

  • Authors:
  • Roberto Grossi;Andrea Pietracaprina;Geppino Pucci

  • Affiliations:
  • Univ. of Pisa, Pisa, Italy;Univ. of Padova, Padua, Italy;Univ. of Padova, Padua, Italy

  • Venue:
  • Information and Computation
  • Year:
  • 2002

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Abstract

This paper studies a system of m robots operating in a set of n work locations connected by aisles in a nxn grid, where m≥n.Form time to the robots need to move along the aisles, in order to visit disjoint sets of locations. The movement of the robots must comply with the following constraints: (1) no two robots can collide at a grid node or traverse a grid edge at the same time; (2) a robot's sensory capability is limited to detecting the presence of another robot at a neighboring node. We present a deterministic protocol that, for any small constant e 0, allows m≤(1-e)n targets and no target is visited by more than one robot. We also prove a lower bound showing that our protocols were known only for m≤ n, while for general m≤ n only a suboptimal randomized protocols were known.