Construction of cellular automata over hexagonal and triangular tessellations for path planning of multi-robots

Exploring unknown terrains demand for the sophisticated algorithms for path planning in case of multi-robot systems. Robots searching for common goals are complicated as they need to avoid collisions. We need to provide paths for all robots which should be collision free and should take less amount of time. Usually these algorithms use square tessellations in this type of investigations, which leads to the lack of variation and enlargement of neighborhood. In this paper we present the construction of a cellular automaton over triangular and hexagonal tessellations and show the complexity for the same. After going through various literatures on robot path planning most don't consider many objectives, like finding shortest path with least time taken and much less waiting time. This paper is unique in a way that apart from hexagonal tessellation we have given a triangular tessellation as well which adds to the efficiency of this paper.