Port-Hamiltonian approach to deployment on a line

In this talk we present a port-Hamiltonian approach to the
deployment on a line of a robotic sensor network (see e.g.
[3] for related work). Using the port-Hamiltonian modelling
framework has some clear benefits. Including physical interpretation
of the model, insight in the system’s energy and
structure, scalability, and use of the Hamiltonian for stability
analysis. A concise overview of port-Hamiltonian systems
theory can be found in [2].
Deployment on a line fits within the broader context of using
robotic sensors networks for (autonomous) inspection of
dikes. The aim of the autonomous dike inspection is to make
a group (swarm) of robotic sensor move along the surface of
the dike, while monitoring it with e.g. ground penetration
radars (GPR).
The ideas in this talk are inspired by [1], who uses a passivity
based-approach for coordination. It is well known that
there is a strong link between port-Hamiltonian systems and
passivity, which can be used in the stability analysis of the
network.
In this talk we’ll look at a network of N robots, which are
modelled as fully actuated point masses. The interaction
among the robots is represented by a graph G. The robots
correspond to the vertices of the graph. The M edges of the
graph correspond to virtual couplings [4], which are virtual
springs and dampers. The dynamics of the interconnected
system [4] are given by
q˙
vc = −B
T ∂H
∂ p
p˙ = B
∂H
∂q
vc −

D
r +BDvcB
T

∂H
∂ p
,
(1)
where q
vc
, p, B, H, D
r
, and D
vc denote respectively the
relative distances, momenta, incidence matrix of graph
G, Hamiltonian, robots dissipation matrix, and the virtual
dampers dissipation matrix.