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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
 ...
Guiding mechanisms
 Pheromone guides
 Subtle guides
 Streaker guides
Model
Reactive algorithm based model

Follower bee
      Interaction force based
      Threshold based
Guide bee
      Sub...
Follower bee
 Herding tendency of follower
 bees modeled by an
 interaction force. (limited
 range)

 Dispersing tendency ...
Subtle guide
 Potential gradient drives
 subtle guides towards the
 destination.

 Velocity of subtle guides is
 only marg...
Streaker guide
 Streaker bees make high
 speed flights through the
 swarm in the direction of the
 new home.
 On reaching ...
Threshold based followers
 Followers of subtle guides are driven entirely by the interaction forces
 that arises out of th...
Disturbance
 Uniform disturbance
    Unidirectional wind
    Both types equally robust


 Scattering disturbance
    Eddie...
Experiment
   Subtle Guide   Streaker Guide
Questions



            Thank you.
Threshold Algorithms




      Stephen Heck (Computer Science)
      Ask Questions!
Introduction - Threshold Algorithms




      Threshold based agent models are a simple and elegent way of
      modelling...
Biological Motivation - Corpse Clustering in Ants
       Several species of ants are known to cluster corpses
       Messo...
Deneubourg’s Basic Clustering Algorithm




      Randomly move
      Compute Perceived item Density Score
      Use a thr...
What is a Threshold Function?

      Sigmoid Threshold Function:

                                               s2
      ...
Sigmoid Threshold Function
                                                 Sigmoid Function Plot
                        ...
Basic Clustering Algorithm Details

       Probability of picking up an item:
                                            ...
Threshold Function Behavior
                                                         Pick−up Threshold
                   ...
Defining the Density Score




      The density score can be defined many ways
      Basic Algorithm Density Score is imple...
Results - Basic Algorithm
      kp = .1 kd = .3 T = 50
      Number of Agents = 10
      Number of items = 1000
      Numb...
Sorting - Lumer-Faieta Algorithm




   Now consider clustering n sets of things with any number of
   attributes
       S...
Lumer-Faieta Algorithm



       Density Score

                                1                              d(oi , oj )...
Density Score
                                                        Density score
                      1.5




        ...
Lumer-Faieta Algorithm - Drop Threshold




       Drop Threshold
       pd = 2 ∗ f if f ≤ k2
       pd = 1 otherwise
   N...
Drop Threshold
                                                            Drop Threshold
                           1.5
 ...
Applications




       Trash collection/organization
       No more raking leaves!
       High-dimensional data explorati...
Caveats




      106 iterations
      No gaurantee on the number of clusters that will be formed
Improvements




      Different types of agents, fast moving/less descriminative
      agents and slower/more discriminati...
Summary
     Threshold algorithms are cool
     Questions?
A story about plants and putting
     them in their place(s)
Some approaches to combinatorial optimization



         By ...
Problem Statement

    Original Question: Given a landscape with
    light and water conditions available, and
    plant ...
Complexity

    Really hard problem

    Modified question: Find best places for fixed
    collection of plants.

    P...
Algorithms

    Agent-based model
       −   Me
       −   Find best locations for fixed collection
       −   Use soluti...
Motivation and relevance to robot
            systems

    Harvest Automation

    Maximize growth and get robots to do ...
Setting up the problem
•   Plant Model – how plants grow
•   Optimization criteria
•   Algorithm to optimize
•   Evaluate ...
Plant Model

    Reasonable representation for how plants
    grow – not too much detail

    Limiting model to light an...
Light requirements




Adapted from: Harvey, G.W. Photosynthetic performance of isolated leaf cells from sun and shade pla...
Water Requirements




Adapted from: Van Gardingen, P.R. and Grace, J. Plants and Wind, Advances in Botanical Research, (1...
Landscape Representation

    Conditions effecting plants

    Discrete cells, 1ft x 1ft

    Each cell has values for ...
Plant-landscape Interaction

    Plant occupies one cell

    Plants influence their surroundings by
    generating shad...
Optimization - Growth Score

    Objective function

    Maximize growth score for each plant,
    individually

    Gr...
Agent-based algorithm
•   Generate random collection of plants
     –   Randomly selected light and water
         require...
Searching for plant collection
•   Based on agent-based algorithm for fixed
    collection.
•   Discard plants that don't ...
Experiment
•   Created a 6x10 grid (landscape) with arbitrary
    light and water conditions.
•   5 plants – selected to m...
Results
•   5 plants – one large full sun, low water,
    and 4 shade, low water of various sizes
     –   All plants foun...
Results – fixed collection
•   How well did algorithm place the fixed
    collection
•   Present examples of how it did ov...
Results – emerging collection
•   Start: 5 plants, one large full sun, 4
    shade, all low water
•   Multiple trials from...
Future Work
Formal analysis of results – compare to
 exhaustive search for a few examples


No comparison to landscape max...
December 7, Projects
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Transcript of "December 7, Projects"

  1. 1. Effect of disturbances on subtle-guided and streaker-guided swarms of bees By Apratim Shaw
  2. 2. Hypothesis Can robustness to disturbances shed light into the preferred method of informed flocking in honey bees?
  3. 3. 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 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
  4. 4. Guiding mechanisms Pheromone guides Subtle guides Streaker guides
  5. 5. Model Reactive algorithm based model Follower bee Interaction force based Threshold based Guide bee Subtle Streaker Random noise in movements Limited Range of sensors
  6. 6. Follower bee Herding tendency of follower bees modeled by an interaction force. (limited range) Dispersing tendency is modeled by randomness in the velocity j ≠i ( Fi = ∑ 1 − 2e j − 0.5 rij 2 )rˆ , ij rij ≤R Damping term is included to Fi = 0 , rij > R slow the bees down in the absence of external stimulus.
  7. 7. 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
  8. 8. 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 streakers return 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.
  9. 9. 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.
  10. 10. Disturbance Uniform disturbance Unidirectional wind Both types equally robust Scattering disturbance Eddies & turbulences Difference in robustness
  11. 11. Experiment Subtle Guide Streaker Guide
  12. 12. Questions Thank you.
  13. 13. Threshold Algorithms Stephen Heck (Computer Science) Ask Questions!
  14. 14. Introduction - Threshold Algorithms Threshold based agent models are a simple and elegent way of modelling complex phenomena in biological systems. Beyond giving insight into biological systems, this modelling tool can be applied in a variety of applications.
  15. 15. Biological Motivation - Corpse Clustering in Ants Several species of ants are known to cluster corpses Messor sancta: (a) initial state (b) 2 hours (c) 6 hours (d) 26 hours (images from http://www.chemoton.org/ref39.html)
  16. 16. Deneubourg’s Basic Clustering Algorithm Randomly move Compute Perceived item Density Score Use a threshold function to determine whether to pick up or drop an item Iterate
  17. 17. What is a Threshold Function? Sigmoid Threshold Function: s2 f (s, θ) = s2 + θ2 Notes: 0 ≤ f ≤ 1 ⇒ f is a probability the higher f is, the more likely the agent will perform its function s is the stimulus θ is the stimulus point where an agent has a 50% chance of becomming/staying active
  18. 18. Sigmoid Threshold Function Sigmoid Function Plot 1 theta = 0.500000 0.9 theta = 1.000000 theta = 2.000000 0.8 theta = 4.000000 theta = 8.000000 0.7 theta = 16.000000 prob of activation 0.6 0.5 0.4 0.3 0.2 0.1 0 −3 −2 −1 0 1 2 10 10 10 10 10 10 log of stimulus
  19. 19. Basic Clustering Algorithm Details Probability of picking up an item: 2 kp pp = kp + f Probability of dropping up an item: 2 f pp = kd + f Notes: kp and kd are specified constants f can be thought of as a density score for the item an agent is considering picking-up/dropping
  20. 20. Threshold Function Behavior Pick−up Threshold 1 k = 0.100000 0.8 k = 0.200000 k = 0.300000 prob of activation 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f = Perceived Density Score Drop Threshold 1 0.8 prob of activation 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 f = Perceived Density Score
  21. 21. Defining the Density Score The density score can be defined many ways Basic Algorithm Density Score is implemented as a short-term memory: An agent keeps track of the number of items encountered (N) during the past T timesteps N f = T
  22. 22. Results - Basic Algorithm kp = .1 kd = .3 T = 50 Number of Agents = 10 Number of items = 1000 Number of time steps = 106 Begin State t=0 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
  23. 23. Sorting - Lumer-Faieta Algorithm Now consider clustering n sets of things with any number of attributes Same basic algorithm applies Similar in concept to SOMs
  24. 24. Lumer-Faieta Algorithm Density Score 1 d(oi , oj ) f (oi ) = 1− neigh(oi ) α oi ∈neigh(oi ) Notes: d(oi , oj ) is a distance function defined on some set of attributes α is the “descriminating factor”, it determines the level at which 2 objects become different
  25. 25. Density Score Density score 1.5 1 Density Score 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 alpha
  26. 26. Lumer-Faieta Algorithm - Drop Threshold Drop Threshold pd = 2 ∗ f if f ≤ k2 pd = 1 otherwise Notes: Conceptually this behaves the same way as all threshold functions do.
  27. 27. Drop Threshold Drop Threshold 1.5 k = 0.100000 k = 0.200000 k = 0.400000 1 prob of activation 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f = Perceived Density Score
  28. 28. Applications Trash collection/organization No more raking leaves! High-dimensional data exploration Any problem where you want to gather items that are dispersed over some physical region.
  29. 29. Caveats 106 iterations No gaurantee on the number of clusters that will be formed
  30. 30. Improvements Different types of agents, fast moving/less descriminative agents and slower/more discriminative agents Directed movement through Pheromones/memory - agents remember the last m items it picked-up and move towards the most similar location Agents that have not performed an action in a while start destroying clusters - helps avoid locally optimal solutions
  31. 31. Summary Threshold algorithms are cool Questions?
  32. 32. A story about plants and putting them in their place(s) Some approaches to combinatorial optimization By Rhonda Hoenigman Multi-robot Systems Final Presentation
  33. 33. 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?
  34. 34. 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.
  35. 35. Algorithms  Agent-based model − Me − Find best locations for fixed collection − Use solution to modify collection and add more plants  Genetic algorithm − Patrick
  36. 36. Motivation and relevance to robot systems  Harvest Automation  Maximize growth and get robots to do the work
  37. 37. Setting up the problem • Plant Model – how plants grow • Optimization criteria • Algorithm to optimize • Evaluate the results
  38. 38. 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
  39. 39. 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.
  40. 40. Water Requirements Adapted from: Van Gardingen, P.R. and Grace, J. Plants and Wind, Advances in Botanical Research, (18), 192-254.
  41. 41. Landscape Representation  Conditions effecting plants  Discrete cells, 1ft x 1ft  Each cell has values for morning light, afternoon light, and water available.
  42. 42. 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.
  43. 43. 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
  44. 44. 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
  45. 45. 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.
  46. 46. 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
  47. 47. 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
  48. 48. 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
  49. 49. 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.
  50. 50. 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.
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