From biology to engineering: how lessons from territorial animals inspire spatial coverage algorithms in robot swarms

Various animals, mammals in particular, display some form of territorial behaviour for which they make their presence conspicuous to others claiming exclusive ownership of regions of space. The signals employed to perform this form of spatial exclusion may be visual, auditory or olfactory depending on the species and the environment. When the mechanism of territorial exclusion occurs via marks deposited on the terrain (olfactory cues), one talks about stigmergy, a form of environment-mediated interaction often encountered in social insect societies.

To study the emergence of spatial segregation in stigmergic systems I have introduced a new type of collective animal movement model where alignment of the agents does not play any role. It is called the territorial random walker model as agents move freely as random walkers on a lattice, scent-marking the terrain wherever they go. As deposited marks remain active for a finite amount of time, each walker retreats upon encountering an active foreign scent. The emerging spatio-temporal dynamics of the system can be quite rich and can be studied at the meso-scale (the territories) as well as at the micro-scale (the agents).

At the meso-scale short-lived marks produce rapidly morphing and highly mobile territories, while long-lived marks yield slow territories with a narrowly defined shape distribution. More importantly the full dependence in territory mobility as a function of the time for which individual marks remain active is accompanied by a liquid-hexatic-solid transition akin to the Kosterlitz-Thouless melting scenario, apparently the first ecological model to predict such a transition.

The dynamics at the micro-scale is in general non-Markovian, but when population density is sufficiently large some mean-field analytic approaches have proved useful. By considering localized walls to mimic the sharp (retreat) interaction when an animal encounters a foreign scent, it is possible to represent via a Fokker-Planck formalism an animal roaming within neighbouring territorial boundaries. Application of this analytic model to movement data from a red fox population in Bristol, UK, is also shown.

Inspired by the findings on territorial dynamics, it is natural to ask whether it is possible to devise a swarm of independent and decentralised territorial robots. Given that building robots with actual marker reading and writing mechanisms is quite difficult in practice, inspiration comes from the behaviour of territorial birds which detect each other presence at a given location by chirping a challenge which is then countered. Rather than broadcasting a scent signal detectable by any individual passing by, the signalling occurs only between two individuals nearby. While the exclusion mechanism is not stigmergic anymore, it can still be exploited to segregate partially the robot population and limit spatial oversampling in search tasks. 

References

[1] A. Heiblum-Robles and L. Giuggioli, Phase transitions in stigmergic territorial systems, accepted.

[2] L. Giuggioli, I. Ayre, A. Heiblum Robles and G.A. Kaminka, From ants to birds: a novel bio-inspired approach to on-line area coverage, in Groß R et al. (eds) Distributed Autonomous Robotic Systems, Springer Proceedings in Advanced Robotics, vol 6, pp. 31-43 (2018).

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[5] J.R. Potts, S. Harris and L. Giuggioli, Quantifying behavioral changes in territorial animals caused by sudden population declines, Am. Nat. 182:e73-e82 (2013).

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[8] L. Giuggioli, J.R. Potts and S. Harris, Brownian walkers within subdiffusing territorial boundaries, Phys. Rev. E 83:061138/1-11 (2011).

[9] L. Giuggioli, J.R. Potts and S. Harris, Animal interactions and the emergence of territoriality, PLoS Comp. Biol. 7(3):e1002008/1-9 (2011).