Rules governing swarm robot in continuum mechanics

Abstract

To determine material body’s deformation is usual to solve Newton’s equation, under assigned boundary conditions; but this is not the only possibility to obtain a plausible description of the phenomenon. In recent years, position-based dynamic (PBD) concept has consolidated its success. The idea has its roots in computer graphic graphics aimed at saving processing time in computing object’s deformation and breakage in video games applications; PBD tries to give a plausible description of the deformation taking into account only the relative point’s positions to describe the action of internal forces. The aim is to obtain an algebraical equation capable of calculating the position of a point using as input the position of some other points. This kinematic approach has the advantage to work with simple algebraical equations; the complexity of the system increases linearly, rather than quadratically, with increasing the point’s number. Working on swarm robotics we have addressed the problem concerning flocking rules, to determine the behaviour of a single element to achieve an assigned configuration of the group. One possibility to perform this task, for each single robot, is to see what some of its neighbours are doing. We then use these rules to reproduce some behaviour of bi-dimensional deformable bodies both consistent with the standard Cauchy model and according to the second-gradient theory. All constitutive properties of the material are hidden within the rules, determining the displacements of the particles each relative to the others. The tool has an advantage in terms of computational cost and is very flexible to be adapted to objects of complex geometry and problems of different nature. The results are encouraging and fracture can be easily managed. However, a connection between the parameters of the tool and the constitutive parameters of the materials is not yet provided and our efforts are addressed in this direction, to validate the tool by a solid classical theory.