  Due to its decentralised, distributed and scalable nature, swarm robotics has
great potential for applications ranging from agriculture to environmental
monitoring and logistics. Various swarm control methods and algorithms are
currently known, such as virtual leader, vector and potential field, and
others. Such methods often show good results in specific conditions and tasks.
The variety of tasks solved by the swarm requires the development of a
universal control algorithm. In this paper, we propose an evolution of a
thermal motion equivalent method (TMEM) inspired by the behavioural similarity
of thermodynamic interactions between molecules. Previous research has shown
the high efficiency of such a method for terrain monitoring tasks. This work
addresses the problem of swarm formation of geometric structures, as required
for logistics and formation movement tasks. It is shown that the formation of
swarm geometric structures using the TMEM is possible with a special nonlinear
interaction function of the agents. A piecewise linear interaction function is
proposed that allows the formation of a stable group of agents. The results of
the paper are validated by numerical modelling of the swarm dynamics. A linear
quadrocopter model is considered as an agent. The fairness of the choice of the
interaction function is shown.
