Summary. Introduction to swarm. Modeling Bee Colonies

Transcription

1 Summary Introduction to swarm Definitions by Beni, Bonabeau Examples Essential characteristics repeated Differences compared to symbolic AI Modeling Bee Colonies

2 Speculations Rate of egg laying and pollen collection may be selfregulated Preferential removal of honey and pollen as function of nearby brood suggests positive feedback Amount of brood on comb increases, rate of honey removal and pollen removal nearby increases Provides more cells for queen Eventually, egg laying rate will maximize at some point Will regulate the size of the pollen storage area Simulation at

3 Cellular Automaton (CA) Model Empty Cells Can receive egg, pollen or honey (or be empty) If threshold # of neighboring cells contain brood, then cell will get an egg with probability, P b. P b = f(egg laying rate and empty cell discovery rate) If cell does not receive an egg, probabilities of receiving honey and pollen are P h and P p (or empty P e ) Probabilities are a function of foraging rate, nothing else

4 CA Model Honey and Pollen Cells Contents of honey and pollen cells are incremented in units of a single load corresponding to the amount of honey or pollen a bee brings in from field. Capacity is 20 loads. Honey or pollen can be added to an empty cell or a cell partly full of the same substance, or added to randomly chosen cells without reference to the contents of nearby cells. The relative amounts of honey and pollen added to cells is determined by the foraging rates for these substances. (Varies by season)

5 CA Model Honey and Pollen Cells Honey is removed from a cell with a probability determined by the number of neighboring brood cells and by a baseline rate of removal that is independent of cell usage. For honey, background removal is small (60% consumed during foraging) Probability of pollen removal depends upon number of neighboring brood cells and a baseline rate. Baseline rate is high, (95% consumed during foraging)

6 CA Model Brood Cells With each time increment the age of a brood cell is increased by one day. When the age of the cell is 21, the cell is emptied. Simulation at: Starlogo simulation also. Run demo

7 Other models are possible Get ready for some mathematics

8 Camazine s Model Maximum Rate of honey input

9 Camazine s Model Concentrations of honey

10 Camazine s Model Concentrations of pollen

11 Camazine s Model Concentrations of brood

12 Camazine s Model Honey removal term: Background rate of consumption by adults

13 Camazine s Model Honey removal term: Additional consumption by nearby brood

14 Camazine s Model Functions H, P and B are decreasing functions, which exhibit threshold-like behavior k 1 << 1 H/(k 1 + H) ensures that if honey in cell bees remove it at a uniform rate

15 Camazine s Model Maximum Rate of pollen input

16 Camazine s Model Concentrations of pollen

17 Camazine s Model Concentrations of honey

18 Camazine s Model Concentrations of brood

19 Camazine s Model Pollen removal term: Background rate of consumption by adults

20 Camazine s Model Pollen removal term: Additional consumption by nearby brood

21 Camazine s Model P/(k 1 + P) ensures that if pollen in cell bees remove it at a uniform rate

22 Camazine s Model Maximum rate of egg-laying, and inhibition factors for pollen and honey

23 Camazine s Model Fraction of cells in neighborhood without eggs

24 Camazine s Model Probability queen is a specific distance from centre as a function of time

25 Camazine s Model Movement of the Queen, a biased random walk

26 Summary Concentric Patterns form when: Eggs are deposited near previously laid eggs Preferential removal factor > 0 Ratios of pollen and honey deposition to consumption correspond to those found in nature How did the system evolve

27 Simulation Figure 1.12 Six steps in formation of concentric rings Ass. 1 and 5 ensure growth of comb Honey and pollen initially randomly mixed (Ass 2) while Ass 3 and 4 imply that pollen cells more likely to be emptied than honey. From Swarm Intelligence, Bonabeau et al.

28 From Swarm Intelligence Bonabeau et al.

29 SO Properties continued Co-existence of several stable states (multistability) Fluctuations are amplified, implying many stable points in state space may be reached; e.g. example of identical food sources. Mass recruitment in ants is based solely upon traillaying trail following Depends upon attractors in space and initial conditions.

30 SO Properties continued Existence of bifurcations when parameters are varied. Behavior changes dramatically at bifurcations. Macrotermes (termite) uses soil pellets impregnated with pheromone for pillar building.two phases: Non-coordinated when random deposits occur. When critical size, coordination phase and pillars emerge. Existence of initial deposits stimulates (+ve feedback) others to collect materials for pillar building. Diffusion of pheromone is also key. Autocatalytic or snow ball effect.

31 Stigmergy Interactions between agents can be: Direct Indirect Direct: obvious, easily observable Antennation (antenna touching) Exchange of food, liquids Mandibular contact Indirect: more subtle Usually through environment, which is an active component of system Stigmergy (Grasse)

32 Stigmergy From Greek: Stigma (sting) Ergon (work) Explains Macrotermes observed nest building behaviour Coordination of activities is implicit, through the actual pillar structure Nest contruction occurs through: Building strips and pillars with soil pellets and mortar Arches are then created between pillars Gaps are then filled to create walls

33 From Swarm Intelligence Bonabeau et al. Nest Building (Figure 1.13) Sematectonic Communication

34 Stigmergy Individuals modify the environment in response to the local state (some aspect). Future behavior is then modified by that altered environmental state. Movement allows interesting patterns to develop. Achieves coordination of individual and collective behavior.

35 Other Examples of Stigmergy Recruitment: ensure sufficient resources are allocated to a task. Trail laying: the stronger the trail, the more ants will tend to follow it rather than deviate from it. Nest cleaning: the more ants clean, the less ants need to clean (NOT IN MY HOUSE!) Pile formation: how ants create piles of dead ants, larvae, or sand. Wasp nest building: specific configurations of bricks stimulate more bricks to be added to the structure. Insect coordinate for carrying prey. When ants change position they change forces on the prey, causing other ants to change their alignment. (NOT PHEROMONE HERE, THE ENVIRONMENT IS THE PREY).

36 Advantages of Stigmergy Direct communication is not required for coordination Don t need to know agent locations Little, or no, global information is required No single agent is responsible for problem solving: Individual agent loss is tolerated Environment is dynamic: Stigmergy has built-in ability to deal with changing environments Very flexible, colony, not individuals respond to environmental perturbations.

37 Areas of Application Software agents are interesting but Swarm-based robotics rapidly accelerating Also referred to as reactive collective robotics See: Journal of Autonomous Robots Why? Colonies of robots make individuals simpler Reduces communication complexity Scales better Decentralized Cheaper Nice talk or Project here

38 Swarm Robotic limitations Can end up with stagnation or deadlock No referee to pull the protagonists apart! Solution, being emergent can be difficult to program What are the individual rules of behavior? Learn? GP, RL Little or no theory to guide us Heterogeneous agent systems are particularly difficult to develop

39 So, why bother? Symbolic AI failures: Brittle Domain theory requirements Frame problem Failure of first order logics Higher order logic theories being domain specific with limited natural plausibility Scalability

40 So, why bother? Rise of connectionism Domain theory not symbolic, and can be learned Alife has emergence as guiding principle Appreciation and understanding of collective behaviour has increased Learning from Nature

41 Where s it going? Deveza: odor sensing for robot guidance A literal implementation of pheromones Russell: heat trails Electromagnetic pheromones Prescott and Ibbotson: paper trails Robots dispense tissue

42 Potential Applications Satellite repair NASA multi-robot system for investigating the solar system and beyond Self-organize to optimize imaging performance Ship maintenance Underwater robots clean ships collectively Kube: microsurgery