Incremental Social Learning Applied to Robot Swarms
Chapter 5 of Incremental Social Learning in Swarm Intelligence Systems





Table of Contents
  1. Shortest Path Selection Video
  2. Probability of Reaching Consensus
    1. By Latency Ratio
    2. By Number of Teams
  3. Number of Team Formations needed to reach Consensus
    1. By Latency Ratio
    2. By Number of Teams
  4. Discrimination Ability

Shortest Path Selection

This video shows the collective decision-making process that results from the application of the majority-rule opinion dynamics model with differential latency.

The environment consists of two areas between which the robots must transport objects collectively. These two areas are at the top and bottom parts of a video frame. Connecting these two areas there are two corridors of different length. Each team of robots must choose between these two corridors to go to the target area. At each decision point, there is an LED that helps robots know in which direction to turn. For simplcity, objects are removed from the simulation as soon as they are transported to the target area. Something similar happens with robots once they go back to the starting area.

In this example, a population of 32 robots and 8 teams are used. Initially, 16 robots prefer the left path and 16 robots prefer the right path. Every time a team is formed (at random), the local majority determines which path the team will follow. At the end of the simulation the population achieves consensus on the left path. Note: The speed of the video is 4 times the normal speed of the simulation.

Download the video in AVI format.

Probability of Reaching Consensus

The following figures show the probability of reaching consensus as a function of the initial fraction of agents favoring the opinion associated with the shortest latency period.

Results grouped by the ratio of the duration of latency periods

9 agents
1 Team2 Teams3 Teams
90 agents
10 Teams20 Teams30 Teams
900 agents
100 Teams200 Teams300 Teams

Results grouped by the number of teams

9 agents
Latency Ratio = 1Latency Ratio = 2Latency Ratio = 3Latency Ratio = 4
90 agents
Latency Ratio = 1Latency Ratio = 2Latency Ratio = 3Latency Ratio = 4
900 agents
Latency Ratio = 1Latency Ratio = 2Latency Ratio = 3Latency Ratio = 4

Number of Team Formations needed to reach Consensus

The following figures show the average number of team formations needed to reach consensus as a function of the initial fraction of agents favoring the opinion associated with the shortest latency period.

Results grouped by the ratio of the duration of latency periods

9 agents
1 Team2 Teams
90 agents
1 Team10 Teams20 Teams
900 agents
1 Team100 Teams200 Teams

Results grouped by the number of teams

9 agents
Latency Ratio = 1Latency Ratio = 2Latency Ratio = 3Latency Ratio = 4
90 agents
Latency Ratio = 1Latency Ratio = 2Latency Ratio = 3Latency Ratio = 4
900 agents
Latency Ratio = 1Latency Ratio = 2Latency Ratio = 3Latency Ratio = 4

Discrimination Ability

The probability of reaching consensus on the opinion associated with the shortest latency period and the average number of team formations needed to do it as a function of different levels of overlap between latency period duration distributions.

11 agents
1 Team2 Teams3 Teams
92 agents
10 Teams20 Teams30 Teams
902 agents
100 Teams200 Teams300 Teams