A Review of Modeling Methods for Swarm Robotic Systems

1
A Review of Modeling Methods for Swarm Robotic
Systems

• Kristina Lerman
• USC Information Sciences Institute
• Alcherio Martinoli
• Swarm-Intelligent Systems Group, EPFL
• Aram Galstyan
• USC Information Sciences Institute

2
(No Transcript)
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
Chemical Reaction Rate Equations
11
Robot Rate Equations
12
Robots are not molecules!
yes, but
13
Robot as a Stochastic Process

• Individual robots behavior subject to
• External forces
• may not be anticipated
• Noise
• fluctuations and random events in the environment
• Errors in sensors and actuators
• Other robots with complex trajectories
• Cant predict which robots will interact
• Randomness programmed into controllers
• e.g., avoidance
• Individual robots actions are so unpredictable,
  they might as well be considered stochastic

14
Controller as an FSA

• Robot is a stochastic Markov Process
• Reactive robots act based on input from sensors
• Controller Finite State Automaton (FSA)
• Robot controller for a simplified foraging
  scenario
• Box robots state action
• Arrows transitions between states
• External stimuli
• Timer

15
Stochastic Processes-based Modeling of Robot
Swarms

• Definitions
• p(n,t) probability robot is in state n at time
  t
• p(n,t) is also the fraction of robots in state n
• Markov property
• robots state at time tDt depends only on its
  state at time t
• Change in probability density

16
The Rate Equation

• Averaging both sides of Dp(n,t) over all robots
  gives the macroscopic Rate Equation
• Describes collective behavior
• with transition rates

17
Rate Equation

• Describes dynamics of average quantities
• Compare with results averaged over many
  experiments
• No need to know exact probability distributions
• Or exact robot trajectories
• Used to study a variety of systems in natural
  sciences
• Usually phenomenological
• Can be written down simply by assessing what
  important characteristics of the problem are

18
A Recipe for the Rate Equation
Initial conditions Ns(t0)N, Nh(0)0, Np(0)0
19
A Word on Coarse-graining
Avoid obstacle

search
Detect object

• Coarse-graining reduces the complexity of the
  model
• Helps construct a minimal model that explains
  experiments

20
Robot Swarm Applications
21
Stick-Pulling Experiments in Robots
(Ijspeert et al. 2001)

• Collaboration in a group of reactive robots
• Task completed only through collaboration
• Experiments with 2 6 Khepera robots
• Embodied simulations with up to 24 robots

22
Flowchart of the Robot Controller
23
Experimental Results

• Key observations
• Different dynamics for different ratio of robots
  to sticks
• Optimal gripping time parameter

24
Theoretical Results
Complete modelsimulations Martinoli et al., 2004
Minimal 2-state model Lerman et al., 2001
25
Robot Foraging

• Collect objects scattered in the arena and
  assemble them at a home location
• Single vs group of robots
• Benefits of a group
• robust to individual failure
• group can speed up collection
• Disadvantages of a group
• increased interference due to
• collision avoidance

Goldberg Mataric
26
Foraging Efficiency vs Group Size
Comparison with embodied simulations
Lerman Galstyan, 2002
27
Collective Clustering
Aggregation

• 20 seeds scattered in a 80X80 cm working area
  (red zone)
• Goal all the seed clustered in a single cluster,
  all the robots resting in the parking area
  (orange zone)

28
Mean Cluster Size and Active Workers
Comparison with embodied simulations

• Martinoli et al., 1999 Agassounon et al. 2004

29
Conclusions

• Macroscopic models of collective behavior based
  on theory of stochastic processes
• No need to know exact trajectories
• Allow quantitative analysis of collective
  behavior
• Results of mathematical models can be used in the
  design cycle to optimize robot controllers
• Caveats and simplifying assumptions to keep
  models tractable
• Models describe average swarm behavior
• Robots actions independent of one another
• Spatial uniformity
• Robot inhomogeneity not yet considered

30
Future Directions

• More realistic models
• Effects of noise
• Inhomogeneous robot characteristics
• Other systems
• Adaptation and learning
• Extended theory of stochastic processes to
  memory-based adaptation where robots change their
  behavior in response to series of observations of
  the other robots
• Other types of learning
• Reinforcement learning
• Pheromone-based stigmergy