# Un dispositif expérimental pour découpler des invariants optiques dans le contrôle de l'altitude des abeilles

Aimie Berger Dauxère, Gilles Montagne, Julien Serres

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Aimie Berger Dauxère, Gilles Montagne, Julien Serres. Un dispositif expérimental pour découpler des invariants optiques dans le contrôle de l'altitude des abeilles. 17ème Journée de l'École Doctorale Sciences du Mouvement Humain ED463 (JEDSMH 2022), Jun 2022, Nice, France. 2022, 17ème Journée de l'École Doctorale Sciences du Mouvement Humain ED463 (JEDSMH 2022). hal-03793157

HAL Id: hal-03793157

https://hal.science/hal-03793157

Submitted on 30 Sep 2022

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Distributed under a Creative Commons Attribution 4.0 International License
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## Bases and aims

**Optic flow:** vector field of the apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an agent and the scene.

**Optical invariants:** particular properties of the optic flow unaltered when the agent is moving.
Two optical invariants are particularly relevant for a ground-following task:

* optical speed rate of change $\dot{\omega}$ [used by bees and pilots]

* splay angle rate of change $\dot{s}$ [used by pilots]

**Aims:**
(1) To determine if bees also use splay angle rate of change for performing ground-following tasks
(2) To set the priority and weight system by which bees use these two optical invariants to control their altitude

<figure><img src="image_3.png" /><figcaption>Optic flow field perceived by a flying agent (Gibson 1950, 1979)</figcaption></figure>

<figure><img src="image_4.png" /></figure>

## Optical speed (OS) experienced by a flying agent

OS ($\omega$) is the speed of environment's image scrolling the retina when an agent is moving.

* OS increases for an agent going down ($\dot{\omega} > 0$)

* OS decreases for an agent going up ($\dot{\omega} < 0$)

--> optical speed rate of change ($\dot{\omega}$) is informative about altitude change

altitude

<figure><img src="image_5.png" /></figure>

$\dot{\omega} = \text{OS}$

$\dot{\omega} = \text{OS rate of change}$

$Vx = \text{agent's speed}$

$z = \text{agent's altitude}$

To maintain a constant flight altitude --> keep $\dot{\omega} = 0$

observed in bees [1, 2, 3, 4, 7]

<figure><img src="image_6.png" /></figure>

## Splay angle rate of change experienced by a flying agent

Base lines join at the image's focus of expansion forming the splay angle ($\dot{s}$):

* angle's value increases in the visual field of an agent going down ($\dot{s} > 0$)

* angle's value decreases in the visual field of an agent going up ($\dot{s} < 0$)

--> splay angle rate of change ($\dot{s}$) is informative about altitude change

altitude

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

horizon
base line

$s = \frac{1}{2} \text{ angle formed by base lines}$

To maintain a constant flight altitude --> keep $\dot{s} = 0$

observed in humans [5, 6]

<figure><img src="image_10.png" /></figure>

## Experimental setup

<figure><img src="image_11.png" /></figure>

Weak OS available
Regular splay angle

Weak OS available
Narrow splay angle

<figure><img src="image_12.png" /></figure>

## Highlights

* An experimental setup was designed to investigate whether the splay angle rate of change is implicated in bees' altitude control

* A flight tunnel was built enabling specific manipulations of two optical invariants

* Splay angle rate of change is used by bees to control their altitude in a ground-following task

<figure><img src="image_13.png" /></figure>

## Predictions and results

<figure><img src="image_14.png" /></figure>

* A bee perceiving a splay's enlargement will interpret a loss of altitude, so it will go up to maintain a null splay angle rate of change ($s=0$).

* A bee perceiving a splay's narrowing will interpret a gain in altitude, so it will go down to maintain a null splay angle rate of change.

* A bee perceiving weak OS will take into account splay angle's rate of change in priority so it will show broader altitude changes.

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

[1] J. Lecoeur, M. Dacke, D. Floreano and E. Baird (2019), Scientific Reports (9) 7707

[2] G. Portelli, J.R Serres and F.Ruffier (2017), Scientific Reports (7) 9231

[3] J.R Serres and F.Ruffier (2017), Arthropod Structure & Development (46) 5, 703-717

[4] M.V Srinivasan (2011), Current Opinion in Neurobiology (24) 4, 535-543

[5] A.P Duchon and W.H Warren (2002), Psychological Sciences (13) 3, 272-278

[6] J.M Flach, R. Warren, S.A Garness, L. Kelly and T.Stanard (1997), Journal of Experimental Psychology (23) 6, 1764-1782

[7] J.R Serres, A.H.P. Morice, C. Blary, R. Millot, G. Montagne and F. Ruffier (2022), Biology Letters (18) 3, 20210534