We address the problem of dispersing a large number of autonomous mobile
robots, for building wireless ad hoc sensor networks performing environmental monitoring
and control. For this purpose, we propose the adaptive triangular mesh generation
algorithm that enables robots to generate triangular meshes of various sizes, adapting to
changing environmental conditions. A locally interacting, geometric technique allows each
robot to generate a triangular mesh with its two neighbor robots. Specifically, we have assumed
that robots are not allowed to have any identifiers, any pre-determined leaders or
common coordinate systems, or any explicit communication. Under such minimal conditions,
the positions of the robots were shown to converge to the desired distribution. This
convergence was mathematically proven and also verified through extensive simulations.
Our results indicate that the proposed algorithm can be applied to problems regarding the
coverage of an area of interest by a swarm of mobile sensors.
