Oscillations make a self-scaled model for honeybees’ visual odometer reliable regardless of flight trajectory

Abstract

Honeybees foraging and recruiting nest-mates by performing the waggle dance need to be able to gauge the flight distance to the food source regardless of the wind and terrain conditions. Previous authors have hypothesized that the foragers’ visual odometer mathematically integrates the angular velocity of the ground image sweeping backward across their ventral viewfield, known as translational optic flow. The question arises as to how mathematical integration of optic flow (usually expressed in radians/s) can reliably encode distances, regardless of the height and speed of flight. The vertical self-oscillatory movements observed in honeybees trigger expansions and contractions of the optic flow vector field, yielding an additional visual cue called optic flow divergence. We have developed a self-scaled model for the visual odometer in which the translational optic flow is scaled by the visually estimated current clearance from the ground. In simulation, this model, which we have called SOFIa, was found to be reliable in a large range of flight trajectories, terrains and wind conditions. It reduced the statistical dispersion of the estimated flight distances approximately 10-fold in comparison with the mathematically integrated raw optic flow model. The SOFIa model can be directly implemented in robotic applications based on minimalistic visual equipment.

Indoor and outdoor in-flight odometry based solely on optic flows with oscillatory trajectories

“…IV. The SOFIa visual odometer method A model for the honeybee's visual odometer called SOFIa (Self-scaled Optic Flow time-based Integration model) was tested in simulations [2]. The SOFIa model is based on the integration of the local translational optic flow ω T scaled by the estimated distance with respect to the ground ĥ:…”

“…A SOFIa (Self-scaled Optic Flow time-based Integration) model has been previously tested as a means of modeling the visual odometer of honeybees with simulations [2] as well as with preliminary indoor flights [3]. The SOFIa method to estimate the distance traveled is based on the integration of the local translational optic flow scaled by the drone's flight height, determined by means of an EKF taking the local optic flow divergence as measurement [2]. The SOFIa model was found to be about 10 times more accurate than the values obtained in simulations based on the raw mathematical integration of the optic flow [2].…”

“…The SOFIa method to estimate the distance traveled is based on the integration of the local translational optic flow scaled by the drone's flight height, determined by means of an EKF taking the local optic flow divergence as measurement [2]. The SOFIa model was found to be about 10 times more accurate than the values obtained in simulations based on the raw mathematical integration of the optic flow [2]. Using an integration scheme of this kind can therefore be regarded as a minimalistic dead reckoning method based on the optic flow.…”

Floor and ceiling mirror configurations to study altitude control in honeybees

“…The minimum sized section of a rectangular tunnel sets the honeybees' forward speed [5,7]; therefore, the forward and upward axes of the honeybee's flight control system can be decoupled [2]. Consequently, in a tunnel where the width is smaller than the height, the width sets the honeybees' forward speed (see also [8][9][10][11] for a description of the visuomotor modelling in honeybees). Similarly, honeybees, which have be trained to follow the tunnel ceiling, when encountering a 'dorsal ditch' in the middle of the tunnel configuration [4] responded to this new configuration by rising quickly and hugging the new, higher ceiling, while maintaining a similar forward speed, distance to the ceiling, and dorsal optic flow to those observed during the training step.…”

Corridor 3D Navigation of a Fully-Actuated Multirotor by Means of Bee-Inspired Optic Flow Regulation

“…Moreover, the authors of [10] have used OF divergence to asses, via an Extended Kalman Filter (EKF), the distance from a given surface by means of two OF sensors set on a back-and-forth oscillating chariot. In [11], a model of the honeybee's visual odometer is assessed in simulations by scaling of the integration of the translational OF via the estimation of the flight height. One may find that OF can be confidently used in conjunction with other control and navigation techniques (e.g.…”