Mobility Aspects in WSN - Application and Multidisciplinary Aspects of Wireless Sensor Networks - page 117

• Vector-based approaches

• Voroni-based approaches

• Quorum-based approaches

• Grid structure approaches

Representative models for each of the enumerated groups are further described.

6.3.1.1 Vector-Based Approaches

Vector-based approaches are extensively used for sensor self-deployment and
coverage improvement. The literature presents many variations of the basic tech-
nique introduced in [ 18 ], where the sensor nodes are treated as virtual particles
subject to virtual forces. This approach is originally proposed for mobile autono-
mous robots and is based on potential fields, which are assumed to exist in the
sensor field.
Similar technique is used in [ 19 ], where a feature for providing constrained
coverage in the sensor field (at least k -coverage) is added. The so-called Potential
Field Algorithm (PFA) works by abstracting the sensor node to be a particle in the
potential field, which will be influenced by the forces on the nearby nodes. The
force which acts on the sensors is a gradient of the scalar potential field U , and is
presented with FU

=−∇ . The forces between the nodes are obtainable by attractive
and repulsive patterns -

att F and

re F , and the resultant force between any two

nodes i and j is given by:

ij FFF

= + , where

, attr rep

ij , ij ,

  

xx − 

− K

i j

F = 

attr

(6.1)

  

attr 2

∆  x ∆ x

ij ,

  

ij

ij



− Kxx  − 

rep
2

i j



 

F = ∆ x ∆ x , if critical connec tion (6.2)



 

rep ij

ij ij ,




0

and x i is the position of the i -th node,

∆ is the Euclidean distance between
nodes i and j and K attr and K rep are the force constraints. The attractive and repul-
sive forces follow inverse square law depending on the distance between the
sensors. The attractive forces - attr F tend to infinity when the distance between
the nodes is zero thus avoiding collisions, while the repulsive forces - rep F tend
to infinity when the distance between the neighboring sensors is equal to the
communication radius, thus preventing the nodes to lose connectivity. The force
that will act on the i -th node is

ij

= ∑ and the node will move according F F

i ij ,

neighbors, ji ≠

to x F xm , where ν is a chosen dumping factor and m is the virtual mass

of the node (assumed to be one).

 = ( − ν  ) /

i i i