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.

Show MeSH
Comparison of properties of the kilobot swarm for different values of the avoidance radius .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).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4219724&req=5

pone-0111542-g009: Comparison of properties of the kilobot swarm for different values of the avoidance radius .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).

Mentions: The results are presented in Fig. 9, which displays the jump probabilities (top panels), the splitting probability (bottom left panel) and the decision time (bottom right panel) for avoidance distances (blue), (red), and (green). In the bottom panels, the markers indicate the results extracted directly from the experiment records while the curves are computed from the solution of the Master equation (10). Generally, the variance is high and a clear trend is hard to recognize in the plot. This is expected, as the number of experiments we performed is low (31 experiments for each ). The jump probabilities exhibit a tendency to promote an emerging decision: if a majority of “red'' robots is present (), is high and the process will further move towards the consensus “red'' (and vice versa).


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

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

Comparison of properties of the kilobot swarm for different values of the avoidance radius .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).
© Copyright Policy
Related In: Results  -  Collection

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

pone-0111542-g009: Comparison of properties of the kilobot swarm for different values of the avoidance radius .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).
Mentions: The results are presented in Fig. 9, which displays the jump probabilities (top panels), the splitting probability (bottom left panel) and the decision time (bottom right panel) for avoidance distances (blue), (red), and (green). In the bottom panels, the markers indicate the results extracted directly from the experiment records while the curves are computed from the solution of the Master equation (10). Generally, the variance is high and a clear trend is hard to recognize in the plot. This is expected, as the number of experiments we performed is low (31 experiments for each ). The jump probabilities exhibit a tendency to promote an emerging decision: if a majority of “red'' robots is present (), is high and the process will further move towards the consensus “red'' (and vice versa).

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