Chapter 14
Flocking Rules Governing Swarm Robot
as Tool to Describe Continuum
Deformation
Ramiro dell’Erba
Abstract In robotic swarm, the position of an element is often determined by the
behaviour of its neighbours. Following this concept, we have realized a tool able
to give a visually plausible simulation of continuum deformation. Without solving
Newton’s equation, we reproduced some behaviour of bidimensional deformable
bodies both according to the standard Cauchy model and second gradient theory.
Fracture can be easily managed. The tool has computational cost advantage, and it
is very flexible to adapt for complex geometry samples.
Keywords Swarm robotics · Discrete mechanical systems
14.1 Introduction
The aim of this paper is not to compute physical processes but to generate visually
plausible simulation results with low computational cost, sacrificing some accuracy,
with respect to the solution of heavy differential equations, solved by finite element
methods (FEM). The dynamic simulation of mechanics has its roots in computer
graphics for videogames; classical methods are based on discretization (Lagrangian
or Eulerian) of Newton’s second law and formulate forces for each mechanical effect.
Owing to the power of GPU, some new methods have become popular. The tool we
propose is based on position-based dynamics (PBD), Bender et al. 2015) widely
used it in computer animation due to its efficiency, robustness and simplicity. Like
the robot swarm behaviour dell’Erba 2015; dell’Erba and Moriconi 2014), it does not
determine forces or solve differential equations, but uses a position-based approach,
where the new position of a particle is determined by its neighbour’s positions, that
approach being easily used to describe complex objects. So far, by using the flocking
rules employed in underwater robotic swarms to compute the displacement of the
elements in order to achieve an assigned swarm configuration (dell’Erba and Moriconi 2015; dell’Erba 2012; Moriconi and dell’Erba 2012), we adapted the swarm
R. dell’Erba (B)
Robotics Laboratory, ENEA Technical Unit technologies for energy and industry, Rome, Italy
e-mail: ramiro.dellerba@enea.it
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_14
223
Flocking Rules Governing Swarm Robot
as Tool to Describe Continuum
Deformation
Ramiro dell’Erba
Abstract In robotic swarm, the position of an element is often determined by the
behaviour of its neighbours. Following this concept, we have realized a tool able
to give a visually plausible simulation of continuum deformation. Without solving
Newton’s equation, we reproduced some behaviour of bidimensional deformable
bodies both according to the standard Cauchy model and second gradient theory.
Fracture can be easily managed. The tool has computational cost advantage, and it
is very flexible to adapt for complex geometry samples.
Keywords Swarm robotics · Discrete mechanical systems
14.1 Introduction
The aim of this paper is not to compute physical processes but to generate visually
plausible simulation results with low computational cost, sacrificing some accuracy,
with respect to the solution of heavy differential equations, solved by finite element
methods (FEM). The dynamic simulation of mechanics has its roots in computer
graphics for videogames; classical methods are based on discretization (Lagrangian
or Eulerian) of Newton’s second law and formulate forces for each mechanical effect.
Owing to the power of GPU, some new methods have become popular. The tool we
propose is based on position-based dynamics (PBD), Bender et al. 2015) widely
used it in computer animation due to its efficiency, robustness and simplicity. Like
the robot swarm behaviour dell’Erba 2015; dell’Erba and Moriconi 2014), it does not
determine forces or solve differential equations, but uses a position-based approach,
where the new position of a particle is determined by its neighbour’s positions, that
approach being easily used to describe complex objects. So far, by using the flocking
rules employed in underwater robotic swarms to compute the displacement of the
elements in order to achieve an assigned swarm configuration (dell’Erba and Moriconi 2015; dell’Erba 2012; Moriconi and dell’Erba 2012), we adapted the swarm
R. dell’Erba (B)
Robotics Laboratory, ENEA Technical Unit technologies for energy and industry, Rome, Italy
e-mail: ramiro.dellerba@enea.it
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_14
223