Consensus Formation

Problem Statement

Consensus formation seeks distributed agreement on relative geometry using only neighbor communication.

Model and Formulation

Continuous consensus protocol:

$${\dot{x}}_i=-\sum _{j\in {\mathcal{N}}_i}{a}_{ij}(x_i-x_j-{\mathrm{\Delta }}_{ij})$$

where \Delta_{ij} encodes desired formation offsets.

Practical Notes

• Graph connectivity is a hard requirement for convergence.
• Consensus gain affects settling time versus oscillation.
• Communication delays can degrade phase alignment.

Implementation and Execution

python -m flybots.simulations.swarm.consensus_formation

Evidence

References

• Olfati-Saber and Murray, Consensus Problems in Networks of Agents (2004)
• Ren and Beard, Consensus Seeking in Multi-Agent Systems

Related Algorithms

• Virtual Structure
• Leader-Follower