This document discusses algorithms for aggregation and swarm taxis behaviors in robotics. It describes how simple local rules can allow robots to remain connected as a group (aggregation), and how adding a beacon sensor allows the swarm to move collectively toward an attractor (taxis). The basic algorithm causes over-reactivity. The α-algorithm adds a threshold to prevent this, but some network topologies still cause issues. The β-algorithm uses additional connectivity information to avoid these cases, but had accuracy problems in real robots. Overall, these behaviors are challenging to implement reliably in hardware.

2. Aggregation and Swarm Taxis
Edgar Buchanan
edgar.buchanan@york.ac.uk
https://edgarbuchanan.wordpress.com/
Department of Electronic Engineering

3. Aggregation α and β
algorithms
Swarm Taxis

4. Aggregation

5. Aggregation in biology…

7. Why aggregation is important in robotics?

8. Description
• Swarm’s ability to stay together in a group
• Useful behaviour observed in nature (often the basis
of more complex behaviours)
• Easily solved with centralised control
• Non-trivial with decentralised control
• Robots must behave autonomously and use only local
communication to maintain coherence

9. Description
• Use only local information about the existence of
communication connections between robots
• Each robot is equipped with a limited-range
omnidirectional radio communication device
• Constantly monitors whether or not it is receiving a
signal from another robot

10. Description
• No directional
information about
origin of the signal
• When a connection is
lost, there is no
indication of which way
to turn to rejoin the
swarm

11. The recipe…
1. Move forwards until lose connection to
neighbours.
2. Turn 180o degrees and move forwards.
3. Go to step 1.

12. !!

13. A F

14. A E
C F B
D

15. Advantages
• Simple set of behaviours allows robots to remain
connected, as if by an elastic band
• Swarm aggregation can be maintained without the use
of absolute or relative positional information
• Direct consequence of only local interactions
• Spatial information required for coherence is encoded in
the presence or absence of messages

16. Problems
• When extended to multiple robots, this basic algorithm
results in an over-reactive swarm
• Each robot reacts to every lost connection
• Attempts to form a complete graph of connections,
causing robots to clump together

17. α and β algorithms

18. α-algorithm

19. Description
• Each robot broadcasts its ID
• Receiving robots may discriminate between messages
• Can count the number of unique IDs received
• Tells us how many robots are in range
• Referred to as the connection degree

20. Description
• Robots check for when number of connections has
fallen below a predefined threshold α
• Only then will they react and turn 180 degrees
• Prevents characteristic ‘clumping’ behaviour of the basic
algorithm, because robots no longer react to every lost
connection

21. Description
• α parameter controls area coverage of the swarm
• Higher values result in a denser swarm, approaching a
complete graph
• Stable aggregation for a swarm of N robots is possible
for α thresholds of N/2 or above
• Lower values cause the swarm to disaggregate

22. The recipe…
1. Move forwards until the number of
neighbours is below α.
2. Turn 180o degrees and move forwards.
3. Go to step 1.

23. AC
E
F
D
3
B
3
α = 2 2
1
2354
32
2

24. Problems
• Certain network topologies present problems
• May result in disconnection of the swarm
• Robot (or group of robots) only connected to the rest of
the swarm via a single communication link
• May not react to a loss of essential connection if
there are still α or more connections

25. β -algorithm

26. Description
• Each robot receives an adjacency list from those it is
connected to
• Represents connections to other neighbours
• Allows each robot to check which of its neighbours
are shared neighbours of others

27. Description
• Upon loss of connection
• Check how many remaining neighbours still have the
lost neighbour in their own neighbourhoods
• Turn 180 degrees if this number falls below a predefined
threshold β

28. The recipe…
1. Move forwards until the number of
neighbours losing connections with
robot is greater than β.
2. Turn 180o degrees and move forwards.
3. Go to step 1.

29. AF
DB
β = 2

30. AF
DB
β = 2

32. Advantages
• Use of second-order information allows the swarm to
avoid critical network topologies
• Also avoids over-connectivity problems of basic
aggregation algorithm
• β-algorithm is able to maintain aggregation with greater
stability than the α-algorithm
• At the cost of extra processing and higher bandwidth
utilisation

33. Problems
• Performance observed in simulation did not carry over
to real robot experiments
• Computation of connectivity presents a serious
conceptual problem
• Real robots are asynchronous finite state machines
• No global ‘tick’ for sampling the network topology
• Weakens accuracy of connectivity measure, resulting in
significantly worse performance

34. Swarm taxis

35. Swarm Taxis
• A taxis (plural taxes) is an innate behavioural
response by an organism to a directional stimulus
or gradient of stimulus intensity
• e.g. {photo, chemo, phono, thermo}taxis
• Useful if swarm of robots could move towards an
environmental attractor whilst aggregated

36. Symmetry Breaking
• Aggregation is a symmetrical process
• Some random movement, but no real direction
• Symmetry breaking mechanism is required for
taxis to emerge at the collective level.

37. Beacon sensor
• Deliberately minimal, omnidirectional sensor
• Cannot sense the direction or distance to the
beacon, only whether a robot is illuminated or not
• Placed on the robots such that other robots may
occlude the illumination
• Only robots on the leading edge of the swarm will
be illuminated (the rest are in shadow)

39. A E
C
F
B
D

42. Taxis- β -algorithm
• Illuminated robots set β threshold value to ∞
• React immediately to any lost connection
• If connection to an illuminated neighbour is lost
• React (by turning 180 degrees), ignoring the
value of the β parameter
• These simple mechanisms are enough to produce
emergent swarm taxis

43. The recipe…
1. Follow beacon until losing connection.
2. Turn 180o degrees and move forwards.
3. Go to step 1.

45. Taxis problems
• Both the α and β-algorithm rely strongly upon
precisely limited-range wireless communication,
with a well-defined boundary
• Proven difficult to implement in hardware

46. Summary
• Aggregation and taxis are useful behaviours
• Easy to implement in simulation, but hard to
implement on real robots
• Examples in 2D on ground-based robot platforms
• Principles extend to 3D (e.g. air / underwater)

49. Reading
[1] Minimalist Coherent Swarming of Wireless Networked
Autonomous Mobile Robots [Article]
[2] Emergent Swarm Morphology Control of Wireless
Networked Mobile Robots [Article]

50. Extra reading
[1] Staying alive the amazing survival strategies of marine
creatures [blog post]

51. Cool video (s)
[1] Lens of Time: Secrets of Schooling [link]
[2] How do schools of fish swm in harmony? [link]

52. Note to self:
Seriously need to
stop making gifs