Application of the Lennard-Jones Potential in Modelling Robot Motion

Abstract

The article proposes a method of controlling the movement of a group of robots with a model used to describe the interatomic interactions. Molecular dynamics simulations were carried out in a system consisting of a moving groups of robots and fixed obstacles. Both the obstacles and the group of robots consisted of uniform spherical objects. Interactions between the objects are described using the Lennard-Jones potential. During the simulation, an ordered group of robots was released at a constant initial velocity towards the obstacles. The objects’ mutual behaviour was modelled only by changing the value of the interaction strength of the potential. The computer simulations showed that it is possible to find the optimal value of the potential impact parameters that enable the implementation of the assumed robotic behaviour scenarios. Three possible variants of behaviour were obtained: stopping, dispersing and avoiding an obstacle by a group of robots.

Three‐dimensional lattice ground states for Riesz and Lennard‐Jones–type energies

“…39–41). It also appears to be a good model for social aggregation 42 and has many other applications, like in robotics 43 . In dimension $$d=2$$, numerical investigations suggest that the ground state of the classical Lennard‐Jones energy (i.e., $$(n,m)=(12,6)$$) is a triangular lattice, 44 whereas the hexagonal close‐packing (HCP) structure is expected to be the one in dimension $$d=3$$ 45 .…”

Three-dimensional lattice ground states for Riesz and Lennard-Jones type energies

“…[35,42,69]). It also appears to be a good model for social aggregation [49] and has many other applications, like in Robotics [68]. In dimension d = 2, numerical investigations suggest that the ground state of the classical Lennard-Jones energy (i.e.…”