Bio-Inspired Computing and Networking

Abstractions for Planning and Control of Robotic Swarms

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constructed from high-level temporal and logical specifications over the continuous

abstraction a. For example, assume that a = (μ, s) ∈

R

3

,whereμ ∈ R

2

gives the

centroid of a swarm and s ∈

R is its size (e.g., area). If it is desired that the swarm

converges to a configuration in which its centroid belongs to a polygon P

d

and

with a size smaller than s

d

, this can be written more formally as “eventually always

(μ ∈ P

d

and s < s

d

),” with the obvious interpretation that it will eventually happen

that μ ∈ P

d

and s < s

d

and this will remain true for all future times. If during the

convergence to the final desired configuration it is necessary that the swarm visits

a position ¯μ withasize¯s, then the specification ...