in Self-Organised Robot Colonies

2008

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29 pages

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Abstract

Abstract Swarm robotics draws inspiration from decentralised, self-organising biological systems in general and from the collective behaviour of social insects in particular. In social insect colonies, many tasks are performed by higher-order entities, such as groups and teams whose task solving capacities transcend those of the individual participants. In this paper, we investigate the emergence of such higher-order entities using a colony of up to 12 physical robots.

Figures (17)

Figure 1: Illustration of the division of labour to accomplish the foraging task under constraints C,, Co, C3 and Cy. The overall task is a partitioned task. It splits into three (sub-) tasks— path formation, recruitment and retrieval—that are organised sequentially (indicated by arrows). Recruitment requires some robots to follow the path from the nest to the prey and grasp either the prey directly or other robots already gripped onto it. Retrieval requires those robots that are gripped onto the prey and/or to each other, to transport the prey along the path back to the nest. Individual tasks, group tasks and team tasks are framed respectively by dotted, dashed and solid lines. IRIDIA — Technical Report Series: TR/IRIDIA/2008-005

Figure 2: Overview of the hardware. (a) The s-bot robot. (b) Image taken by the omni-directional camera of the s-bot. It shows other s-bots and an s-toy (at various distances), all of which have activated their LEDs in red. (c) One of the two s-toys, which is used both as a nest and as a prey.

Figure 3: State diagram of the finite state machine that controls each s-bot. Circles represent states (i.e., behaviours). Edge labels specify conditions that trigger transitions between the corresponding states. The initial state is search chain. P.. (and P..) is a boolean variable, which is set to True with probability P.. (P.-), and False otherwise. The value of P.. (P.-) determines the rate at which s-bots join (leave) a chain.

Figure 4: The concept of CDP (cyclic directional patterns) chains. The small coloured circles represent s-bots that have formed a CDP-chain that connects the nest with the prey. Three colours are sufficient to give a directionality to the chain. The large circles surrounding the s-bots indicate their perceptual range. The small uncoloured circle represents an explorer s-bot following the chain towards the prey. The three vectors drawn on top of the chain members represent the motor schema that leads to an overall alignment of the chain. The two vectors drawn on top of the explorer s-bot represent the motor schemas that lead to a tangential trajectory along the chain.

Table 1: Number of s-bots required to accomplish sub-tasks path formation (Np), recruitment (N,) and retrieval (N;,) for different initial distances (D in cm) between the nest and the prey.

Figure 6: Time until the n-th s-bot finds either the nest or a chain (which provides a path to the nest) for the first set of experiments with (N,D) = (2,30), (4,60) and (8, 120).

n Table 2: Summary of the results for the first set of experiments. We investigated three setups (N, D) with a linear relationship between group size N and distance D: (2,30), (4,60) and (8, 120). The value of T, denotes the time it takes the s-bots to form the path, T; denotes the time it takes the first two s-bots to be recruited, and JT; denotes the time it takes the s-bots to transport the prey to the nest. All results are given in seconds. with 8 s-bots, five of them are candidate for recruitment (while only 2 are required), whereas in the system with 2 s-bots (4 s-bots) only 2 (4) are candidate for recruitment (see Table 1). Another possible explanation is linked to an effect of the formed chain: the larger the group size, the more s-bots take part in the chain formation process, in this way extending the area from which a path to the nest can be found by those s-bots still performing the initial random walk. This accelerates the process of gathering s-bots at the nest.

Table 4: Number of s-bots that are part of the path formed between nest and prey (if any) in setups (N, D) of the second set of experiments.

Table 5: Completion times (in s) of sub-tasks path formation (T,), recruitment (T,), and transpor (T;) in setups (NV, D) of the second set of experiments. If no value is given the respective sub-tas] was not successfully completed.

Table 6: Completion time (in s) of the overall foraging task in setups (V, D) of the second set of experiments. If no value is given the overall task was not successfully completed.

Figure 7: State diagrams for four selected setups (NV, D) from the second set of experiments: (a) (12,150), (b) (12,240), (c) (7,150) and (d) (7,240). The respective grey levels indicate the number of s-bots in states search chain, explore chain and recovery, join chain, assemble, transport target and transport blind.

Figure 9: Number of distinct behavioural roles (i.e., states) an s-bot performed during a trial (see Figure 3). Data from all s-bots and all trials of the second set of experiments.

Figure 10: Number of times an s-bot changed its behavioural role (i.e., states) during a trial. Data from all s-bots and all trials of the second set of experiments.