Bio-Inspired Computing and Networking

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Bio-Inspired Computing and Networking

We collect all the robot states in r =



r

T

1

, ..., r

T

N



T

∈ R

2N

and the robot controls

in u =



u

T

1

, ..., u

T

N



T

∈ R

2N

. We denote by Q the set of all swarm configurations,

which equals

R

2N

if no obstacles and environment limits are imposed.

To construct a continuous abstraction with a product structure of group and

shape, we build a smooth surjective map

h : Q → A, h(r) = a, (9.2)

where

h is called the (continuous) abstraction,oraggregation,orquotient map

a is denoted as the abstract state of the swarm

We require A to have a product structure of a group G and a shape S, i.e.,

A = G × S, a = (g, s), a ∈ A, g ∈ G, s ∈ S. (9.3)

g ∈G and s ∈S are the group and the shape part of a ∈A, respectively. Theinvariance

to robot identifications ...