On how swarm robotics can be used to describe particle system's deformation

In previous works, we have described time evolution of a two-dimensional particle lattice, subject to deformation, without the use of Newton's law. According to our experience, in control of robotic swarm, the new position of a particle is determined by the spatial position of its neighbours; therefore, we have used an interaction law based on the spatial position of the particles themselves. The tool that we have realized reproduced some behaviour of deformable bodies both according to the standard Cauchy model and the second gradient theory. In this paper, we try to stress what is still under investigation, like the relationship describing the interaction rule and its physical meaning; moreover, we shall describe as some solutions do not agree with the behaviour of the classical solution coming out from differential equations.