18 A Plausible Description of Continuum …
333
2008; Placidi et al. 2010; Andreaus et al. 2015; Chang and Misra 1990; Masiani et al.
1995; Cecchi and Rizzi 2001; Goda et al. 2014; Placidi et al. 2004; Scerrato et al.
2015; Dos Reis and Ganghoffer 2011; Placidi and Hutter 2006; Giorgio et al. 2015;
Enakoutsa et al. 2016) for interesting applications (Altenbach et al. 2010; Eremeyev
et al. 2006; Goda et al. 2012; Eremeyev et al. 2007; Pietraszkiewicz and Eremeyev
2009; Berezovski et al. 2016) for recent theoretical results and (Dell’Isola et al. 2015)
for a recent review. The main reason of the interest in these theoretical models can
be explained because they have been useful in mathematical description of objects
whose richness at the microscale cannot be captured by classical continuum models,
that is, metamaterials (see, e.g., (Dell’Isola et al. 2015; Del Vescovo and Giorgio
2014) for reviews of recent results and (Seppecher et al. 2011; Dell’Isola et al. 2016;
d’Agostino et al. 2015; Eremeyev et al. 2010; Madeo et al. 2014; Steigmann and
Pipkin 1991; Steigmann 2008 for interesting examples). The development of new
techniques, such as three-dimensional (3D) printing or electro-spinning, gives the
possibility to obtain increasingly complex and exotic microstructures, which can
provide a reasonably experimental basis. On the other hand, the amount of new
experimental data opens several deep and complex theoretical problems. It is clear
that, in this context, numerical tools are essential in order to have a suitable mediation between theoretical and experimental results. In particular, in our opinion, a
numerical investigation should be a good compromise between computational cost
and accuracy of the results, as is required in rapid prototyping processes typical of
modern technological research.
18.2 The Origin of the Problem
Systems control of a robotic swarm is often derived from Nature teaching, like fish
school behavior; in our laboratory, we are working on underwater robotic swarm,
and on topics close to this, since many years (see Fig. 18.1). In (dell’Erba 2015;
Moriconi and dell’Erba 2012), the author was investigating the calculation of the
geometric configuration of submarine swarm robots by the single elements; this is
very important because the swarm, like school fish, adapt its configuration depending
on the mission assigned. The concept of robot swarms has been a study theme, for
the scientific community, for several years. Swarm research has been inspired by
biological behaviors, like those of bees (Karaboga 2005; Passino et al. 2007; Janson
et al. 2005) for a long time to take advantage by social activities concepts (Khatib
et al. 2008) labor division, task cooperation and information sharing. A single-robot
approach is affected by failures that may prevent the success of the whole task.
On the contrary, a multi-robot approach can benefit from the parallelism of the
operation and by the redundancy given by the usage of multiple agents. Moreover,
the operator has the possibility to have multiple views simultaneously and to follow
pattern by gradient techniques. In a swarm, the members operate with a common
objective, sharing the job workload; the lack of one member can be easily managed
by redistributing the job among the others. This feature is especially useful if we
333
2008; Placidi et al. 2010; Andreaus et al. 2015; Chang and Misra 1990; Masiani et al.
1995; Cecchi and Rizzi 2001; Goda et al. 2014; Placidi et al. 2004; Scerrato et al.
2015; Dos Reis and Ganghoffer 2011; Placidi and Hutter 2006; Giorgio et al. 2015;
Enakoutsa et al. 2016) for interesting applications (Altenbach et al. 2010; Eremeyev
et al. 2006; Goda et al. 2012; Eremeyev et al. 2007; Pietraszkiewicz and Eremeyev
2009; Berezovski et al. 2016) for recent theoretical results and (Dell’Isola et al. 2015)
for a recent review. The main reason of the interest in these theoretical models can
be explained because they have been useful in mathematical description of objects
whose richness at the microscale cannot be captured by classical continuum models,
that is, metamaterials (see, e.g., (Dell’Isola et al. 2015; Del Vescovo and Giorgio
2014) for reviews of recent results and (Seppecher et al. 2011; Dell’Isola et al. 2016;
d’Agostino et al. 2015; Eremeyev et al. 2010; Madeo et al. 2014; Steigmann and
Pipkin 1991; Steigmann 2008 for interesting examples). The development of new
techniques, such as three-dimensional (3D) printing or electro-spinning, gives the
possibility to obtain increasingly complex and exotic microstructures, which can
provide a reasonably experimental basis. On the other hand, the amount of new
experimental data opens several deep and complex theoretical problems. It is clear
that, in this context, numerical tools are essential in order to have a suitable mediation between theoretical and experimental results. In particular, in our opinion, a
numerical investigation should be a good compromise between computational cost
and accuracy of the results, as is required in rapid prototyping processes typical of
modern technological research.
18.2 The Origin of the Problem
Systems control of a robotic swarm is often derived from Nature teaching, like fish
school behavior; in our laboratory, we are working on underwater robotic swarm,
and on topics close to this, since many years (see Fig. 18.1). In (dell’Erba 2015;
Moriconi and dell’Erba 2012), the author was investigating the calculation of the
geometric configuration of submarine swarm robots by the single elements; this is
very important because the swarm, like school fish, adapt its configuration depending
on the mission assigned. The concept of robot swarms has been a study theme, for
the scientific community, for several years. Swarm research has been inspired by
biological behaviors, like those of bees (Karaboga 2005; Passino et al. 2007; Janson
et al. 2005) for a long time to take advantage by social activities concepts (Khatib
et al. 2008) labor division, task cooperation and information sharing. A single-robot
approach is affected by failures that may prevent the success of the whole task.
On the contrary, a multi-robot approach can benefit from the parallelism of the
operation and by the redundancy given by the usage of multiple agents. Moreover,
the operator has the possibility to have multiple views simultaneously and to follow
pattern by gradient techniques. In a swarm, the members operate with a common
objective, sharing the job workload; the lack of one member can be easily managed
by redistributing the job among the others. This feature is especially useful if we