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 properties of a flame simulation designed to mimic the kilobot swarm for different values of the avoidance radius .Also compare Fig. 9). Shown are results for  (blue curves and markers),  (red curves and markers) and  (green curve and markers). The experimental setup is described in Section "Kilobot experiments'' (subsection 1). (top panels) Jump probabilities  (left) and  (right) for the Master equation (10) as inferred from the experiment records [Eq. (63)]. (bottom left panel) Splitting probability , as estimated directly from the experimental records [cf. Eq. (53)] (markers) and computed using the solution of the Master equation Eq. (68) (curves). (bottom right panel) Decision time  as estimated from the experiment records [Eq. 58] (markers) and computed from the Master equation [Eq. (69)] (curves). The simulation parameters are given in table 2.
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pone-0111542-g010: Comparison of properties of a flame simulation designed to mimic the kilobot swarm for different values of the avoidance radius .Also compare Fig. 9). Shown are results for (blue curves and markers), (red curves and markers) and (green curve and markers). The experimental setup is described in Section "Kilobot experiments'' (subsection 1). (top panels) Jump probabilities (left) and (right) for the Master equation (10) as inferred from the experiment records [Eq. (63)]. (bottom left panel) Splitting probability , as estimated directly from the experimental records [cf. Eq. (53)] (markers) and computed using the solution of the Master equation Eq. (68) (curves). (bottom right panel) Decision time as estimated from the experiment records [Eq. 58] (markers) and computed from the Master equation [Eq. (69)] (curves). The simulation parameters are given in table 2.

Mentions: For comparison, we use flame to simulate a swarm with the same parameters as the kilobot swarm (Table 2). The results are presented in Figure 10. The splitting probability (bottom left panel in the figure) exhibits the same mismatch between the simulation data (markers) and the integrated solution (curve) despite the fact that the number of experiments is significantly higher (). Again, we attribute the discrepancy to spatial correlations (see subsection 5 in Section “Microscopic approach: Virtual swarm'').


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

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

Comparison of properties of a flame simulation designed to mimic the kilobot swarm for different values of the avoidance radius .Also compare Fig. 9). Shown are results for  (blue curves and markers),  (red curves and markers) and  (green curve and markers). The experimental setup is described in Section "Kilobot experiments'' (subsection 1). (top panels) Jump probabilities  (left) and  (right) for the Master equation (10) as inferred from the experiment records [Eq. (63)]. (bottom left panel) Splitting probability , as estimated directly from the experimental records [cf. Eq. (53)] (markers) and computed using the solution of the Master equation Eq. (68) (curves). (bottom right panel) Decision time  as estimated from the experiment records [Eq. 58] (markers) and computed from the Master equation [Eq. (69)] (curves). The simulation parameters are given in table 2.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0111542-g010: Comparison of properties of a flame simulation designed to mimic the kilobot swarm for different values of the avoidance radius .Also compare Fig. 9). Shown are results for (blue curves and markers), (red curves and markers) and (green curve and markers). The experimental setup is described in Section "Kilobot experiments'' (subsection 1). (top panels) Jump probabilities (left) and (right) for the Master equation (10) as inferred from the experiment records [Eq. (63)]. (bottom left panel) Splitting probability , as estimated directly from the experimental records [cf. Eq. (53)] (markers) and computed using the solution of the Master equation Eq. (68) (curves). (bottom right panel) Decision time as estimated from the experiment records [Eq. 58] (markers) and computed from the Master equation [Eq. (69)] (curves). The simulation parameters are given in table 2.
Mentions: For comparison, we use flame to simulate a swarm with the same parameters as the kilobot swarm (Table 2). The results are presented in Figure 10. The splitting probability (bottom left panel in the figure) exhibits the same mismatch between the simulation data (markers) and the integrated solution (curve) despite the fact that the number of experiments is significantly higher (). Again, we attribute the discrepancy to spatial correlations (see subsection 5 in Section “Microscopic approach: Virtual swarm'').

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