Effect of disturbances on subtle-guided and streaker-guided swarms of bees

By Apratim Shaw

Hypothesis

� Can robustness to disturbances shed light into the preferred method of informed flocking in honey bees?

Movement of the swarm to new nest

� Homeless bees form a cluster around queen

� Scout bees search for new nesting site

�� Scout bees guide the swarm to new siteScout bees guide the swarm to new site

� Worker bees build a new nest

The influence of queen mandibular pheromones on worker attraction to swarm clusters … Winston et al. 1989

House hunting by honey-bee swarms … Camazine et al. 1999

Guiding mechanisms

� Pheromone guides

� Subtle guides

� Streaker guides

Model

Reactive algorithm based model

Follower bee

� Interaction force based

� Threshold based

Guide bee

� Subtle

� Streaker

Random noise in movements

Limited Range of sensors

Follower bee

� Herding tendency of follower

bees modeled by an interaction force. (limited range)

� Dispersing tendency is modeled by randomness in the velocity

� Damping term is included to slow the bees down in the absence of external stimulus.

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Subtle guide

� Potential gradient drives subtle guides towards the destination.

� Velocity of subtle guides is only marginally higher than the average velocity of follower bees

Streaker guide

� Streaker bees make high speed flights through the swarm in the direction of the new home.

� On reaching the front-end of the swarm, the streakersreturn at low speed towards the rear. Return paths still not known.

� Model does not show the return path of streakers, but uses a short delay to account for return time.

Threshold based followers

� Followers of subtle guides are driven entirely by the interaction forces that arises out of their herding tendency.

� Followers of streaker guides are driven by a threshold based algorithm. This allows them to latch on to the velocity of any nearby bee with a velocity exceeding the threshold value.

Disturbance

� Uniform disturbance

� Unidirectional wind

� Both types equally robust

� Scattering disturbance

� Eddies & turbulences

� Difference in robustness

Experiment

Subtle Guide Streaker Guide

Questions

Thank you.

Threshold Algorithms

I Stephen Heck (Computer Science)

I Ask Questions!

Introduction - Threshold Algorithms

I Threshold based agent models are a simple and elegent way ofmodelling complex phenomena in biological systems.

I Beyond giving insight into biological systems, this modellingtool can be applied in a variety of applications.

Biological Motivation - Corpse Clustering in AntsI Several species of ants are known to cluster corpsesI Messor sancta:

(a) initial state (b) 2 hours (c) 6 hours (d) 26 hours(images from http://www.chemoton.org/ref39.html)

Figure:

Deneubourg’s Basic Clustering Algorithm

I Randomly move

I Compute Perceived item Density Score

I Use a threshold function to determine whether to pick up ordrop an item

I Iterate

What is a Threshold Function?

I Sigmoid Threshold Function:

f (s, θ) =s2

s2 + θ2

Notes:0 ≤ f ≤ 1⇒ f is a probability

the higher f is, the more likely the agent will perform itsfunction

s is the stimulus

θ is the stimulus point where an agent has a 50% chance ofbecomming/staying active

Sigmoid Threshold Function

10−3 10−2 10−1 100 101 1020

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

log of stimulus

prob

of a

ctiv

atio

nSigmoid Function Plot

theta = 0.500000theta = 1.000000theta = 2.000000theta = 4.000000theta = 8.000000theta = 16.000000

Student Version of MATLAB

Figure:

Basic Clustering Algorithm Details

I Probability of picking up an item:

pp =

(kp

kp + f

)2

I Probability of dropping up an item:

pp =

(f

kd + f

)2

Notes:kp and kd are specified constants

f can be thought of as a density score for the item an agent isconsidering picking-up/dropping

Threshold Function Behavior

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

f = Perceived Density Score

prob

of a

ctiv

atio

nPick−up Threshold

k = 0.100000k = 0.200000k = 0.300000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

f = Perceived Density Score

prob

of a

ctiv

atio

n

Drop Threshold

Student Version of MATLAB

Figure:

Defining the Density Score

I The density score can be defined many ways

I Basic Algorithm Density Score is implemented as a short-termmemory: An agent keeps track of the number of itemsencountered (N) during the past T timesteps

f =N

T

Results - Basic AlgorithmI kp = .1 kd = .3 T = 50I Number of Agents = 10I Number of items = 1000I Number of time steps = 106

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Begin State t=0

Student Version of MATLAB

Figure:

Sorting - Lumer-Faieta Algorithm

Now consider clustering n sets of things with any number ofattributes

I Same basic algorithm applies

I Similar in concept to SOMs

Lumer-Faieta Algorithm

I Density Score

f (oi ) =1

neigh(oi )

∑oi∈neigh(oi )

(1−

d(oi , oj)

α

)

Notes: d(oi , oj) is a distance function defined on some set ofattributes

α is the “descriminating factor”, it determines the level at which 2objects become different

Density Score

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

alpha

Den

sity

Sco

re

Density score

Student Version of MATLAB

Figure:

Lumer-Faieta Algorithm - Drop Threshold

I Drop Thresholdpd = 2 ∗ f if f ≤ k2pd = 1 otherwise

Notes: Conceptually this behaves the same way as all thresholdfunctions do.

Drop Threshold

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

f = Perceived Density Score

prob

of a

ctiv

atio

n

Drop Threshold

k = 0.100000k = 0.200000k = 0.400000

Student Version of MATLAB

Figure:

Applications

I Trash collection/organization

I No more raking leaves!

I High-dimensional data exploration

I Any problem where you want to gather items that aredispersed over some physical region.

Caveats

I 106 iterations

I No gaurantee on the number of clusters that will be formed

Improvements

I Different types of agents, fast moving/less descriminativeagents and slower/more discriminative agents

I Directed movement through Pheromones/memory - agentsremember the last m items it picked-up and move towards themost similar location

I Agents that have not performed an action in a while startdestroying clusters - helps avoid locally optimal solutions

SummaryI Threshold algorithms are coolI Questions?

Figure:

A story about plants and putting them in their place(s)

Some approaches to combinatorial optimization

By Rhonda Hoenigman

Multi-robot SystemsFinal Presentation

Problem Statement

Original Question: Given a landscape with light and water conditions available, and plant types (different light and water requirements, and sizes)

How many plants and of what type can the landscape support?

Complexity

Really hard problem Modified question: Find best places for fixed

collection of plants. Problem is exponential (if landscape discretized).

− i.e. We have 5 plants and 60 spots where the plants could go. What are the best spots?

− Problem has complexity of 605 Collection is not fixed, so problem is harder than

exponential.

Algorithms Agent-based model

− Me− Find best locations for fixed collection− Use solution to modify collection and add

more plants Genetic algorithm

− Patrick

Motivation and relevance to robot systems

Harvest Automation Maximize growth and get robots to do the

work

Setting up the problem

• Plant Model – how plants grow• Optimization criteria• Algorithm to optimize• Evaluate the results

Plant Model

Reasonable representation for how plants grow – not too much detail

Limiting model to light and water requirements

3 categories of light requirements− Shade, partial sun, and full sun

2 categories of water requirements− Low and high

Light requirements

Adapted from: Harvey, G.W. Photosynthetic performance of isolated leaf cells from sun and shade plants, Carnegie Inst. Washington Yearbook, (79), 161-164.

Water Requirements

Adapted from: Van Gardingen, P.R. and Grace, J. Plants and Wind, Advances in Botanical Research, (18), 192-254.

Landscape Representation

Conditions effecting plants Discrete cells, 1ft x 1ft Each cell has values for morning light,

afternoon light, and water available.

Plant-landscape Interaction Plant occupies one cell Plants influence their surroundings by

generating shade and using water– Shading reduces light by 30 percent

Influence based on plant size– Interaction if plant is larger than 1ft.

Optimization - Growth Score Objective function Maximize growth score for each plant,

individually Growth score is percent of ideal.

– If plants are at light saturation point, and enough water is available, growth =

– Growth limited by not enough light, or not enough water

70 percent is good enough

Agent-based algorithm• Generate random collection of plants

– Randomly selected light and water requirements, sizes, and x,y locations.

• Find best places on the landscape for that fixed collection

– From starting locations, move plants around until growth score is above 0.70.

– Change initial x,y locations and restart– Limit number of new locations that a plant

can try out before stopping.• Limiting moves ensures algorithm will stop

Searching for plant collection

• Based on agent-based algorithm for fixed collection.

• Discard plants that don't find a suitable location– Growth score below 0.70

• Generate new plant probabilistically based on what survived on previous iteration

• Continue adding plants until average number of plants on landscape is not changing more than some threshold.

Experiment

• Created a 6x10 grid (landscape) with arbitrary light and water conditions.

• 5 plants – selected to match conditions on landscape

– Test that algorithm works– Multiple samples of 5 plants

• 5 plants – selected randomly• Landscape designed to be water-restrictive

– Water available should limit growth for some plants

Results

• 5 plants – one large full sun, low water, and 4 shade, low water of various sizes

– All plants found suitable locations• Random trials

– High water plants survived half the time

Results – fixed collection

• How well did algorithm place the fixed collection

• Present examples of how it did over x trials for y number of plants

• To do: validate against exhaustive search.• Also, no analysis of difficulty for any given

collection

Results – emerging collection

• Start: 5 plants, one large full sun, 4 shade, all low water

• Multiple trials from random starting collection.

– Algorithm did converge– Number of plants did increase from

starting collection of five.

Future Work

Formal analysis of results – compare to exhaustive search for a few examples

No comparison to landscape maximum.

Not sure this worked very well at finding the collection.