Limits...
Multiscale modelling and analysis of collective decision making in swarm robotics.

Vigelius M, Meyer B, Pascoe G - PLoS ONE (2014)

Bottom Line: Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model.Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process.Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable.

View Article: PubMed Central - PubMed

Affiliation: FIT Centre for Research in Intelligent Systems, Monash University, Melbourne, Australia.

ABSTRACT
We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable.

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Comparison of swarm properties for different values of the avoidance radius .Shown are results for  (blue curves and markers),  (red curves and markers),  (green curves and markers) and  (black curves and markers). All other simulation parameters are given in Table 1. (top panels) Parameters  (left) and  (right) for the stochastic differential equation as inferred from the simulation results for the virtual swarm. (bottom left panel) Splitting probability , as estimated directly from the simulation output [cf. Eq. (53)] (markers) and computed using the integrated stationary distribution Eq. (54) (curves). (bottom right panel) Decision time  as estimated from the simulation output [Eq. 58] (markers) and computed from the FPE coefficients [Eq. (59)] (curves).
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pone-0111542-g006: Comparison of swarm properties for different values of the avoidance radius .Shown are results for (blue curves and markers), (red curves and markers), (green curves and markers) and (black curves and markers). All other simulation parameters are given in Table 1. (top panels) Parameters (left) and (right) for the stochastic differential equation as inferred from the simulation results for the virtual swarm. (bottom left panel) Splitting probability , as estimated directly from the simulation output [cf. Eq. (53)] (markers) and computed using the integrated stationary distribution Eq. (54) (curves). (bottom right panel) Decision time as estimated from the simulation output [Eq. 58] (markers) and computed from the FPE coefficients [Eq. (59)] (curves).

Mentions: In order to investigate how spatial inhomogeneities affect the validity of our approach, we perform numerical experiments where we vary over a range of values. In Fig. 6, we compare swarm properties for (blue curves and markers), (red curves and markers), (green curves and markers) and (black curves and markers). All other simulation parameters are as in Table 1. Shown are the SDE coefficients (top panels), the splitting probability (bottom left panel) and the decision time (bottom right panel).


Multiscale modelling and analysis of collective decision making in swarm robotics.

Vigelius M, Meyer B, Pascoe G - PLoS ONE (2014)

Comparison of swarm properties for different values of the avoidance radius .Shown are results for  (blue curves and markers),  (red curves and markers),  (green curves and markers) and  (black curves and markers). All other simulation parameters are given in Table 1. (top panels) Parameters  (left) and  (right) for the stochastic differential equation as inferred from the simulation results for the virtual swarm. (bottom left panel) Splitting probability , as estimated directly from the simulation output [cf. Eq. (53)] (markers) and computed using the integrated stationary distribution Eq. (54) (curves). (bottom right panel) Decision time  as estimated from the simulation output [Eq. 58] (markers) and computed from the FPE coefficients [Eq. (59)] (curves).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4219724&req=5

pone-0111542-g006: Comparison of swarm properties for different values of the avoidance radius .Shown are results for (blue curves and markers), (red curves and markers), (green curves and markers) and (black curves and markers). All other simulation parameters are given in Table 1. (top panels) Parameters (left) and (right) for the stochastic differential equation as inferred from the simulation results for the virtual swarm. (bottom left panel) Splitting probability , as estimated directly from the simulation output [cf. Eq. (53)] (markers) and computed using the integrated stationary distribution Eq. (54) (curves). (bottom right panel) Decision time as estimated from the simulation output [Eq. 58] (markers) and computed from the FPE coefficients [Eq. (59)] (curves).
Mentions: In order to investigate how spatial inhomogeneities affect the validity of our approach, we perform numerical experiments where we vary over a range of values. In Fig. 6, we compare swarm properties for (blue curves and markers), (red curves and markers), (green curves and markers) and (black curves and markers). All other simulation parameters are as in Table 1. Shown are the SDE coefficients (top panels), the splitting probability (bottom left panel) and the decision time (bottom right panel).

Bottom Line: Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model.Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process.Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable.

View Article: PubMed Central - PubMed

Affiliation: FIT Centre for Research in Intelligent Systems, Monash University, Melbourne, Australia.

ABSTRACT
We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable.

Show MeSH