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A. Thoma et al.
A reason for this might be that the bumblebee is not able to survey the entire situation
because the obstacle is blocking the whole field of view. While reorienting and searching
for a solution, the bee might see the upper corner of the obstacle first and choose to fly
over the obstacle in some cases. An analysis of the recordings supports this statement.
If the obstacle is very close to the gate, the bees show a searching behavior.
Investigation of the dependency of the behavior on the distance between gate and
obstacle with the HV index (Fig. 2) indicates a positive, linear relationship between
distance and decision. The optimal climb performance of bumblebees might be the
controlling factor here. Analyses of flapping-wing aerodynamics indicate that forward
flight is more efficient than hover flight [29]. Therefore, increasing altitude while flying
forward is energetically more efficient than climbing vertically. This is the same for
rotary wings, e.g., quadcopters or helicopters [30], leading to the conclusion that a UAV
should evade a close obstacle horizontally to keep a certain minimal forward flight speed
while an obstacle in greater distance should be overflown.
The slope of the three different obstacle types also indicates a dependency on the size
of the obstacle. However, only two positions per obstacle were investigated. Nonetheless,
these preliminary results show that an extended investigation on the dependency of the
evasion maneuver on the obstacle dimensions is worth a more in-depth investigation.
Additionally, the question arises, if the distance itself is the triggering parameter at all
or if other parameters derived from the distance, e.g., obstacle height to distance ratio,
are triggering a specific behavior.
Therefore, logistic regression was performed. It showed that the behavior of the
bumblebees is predictable with an accuracy of more than 80% with the distance between
obstacle and entrance gate itself as the sole parameter. The investigated ratio of obstacle
width-to-height, height-to-distance, or width-to-distance does not influence the accuracy.
However, it is possible that the differences in the ratios were not varied enough to show a
measurable effect on the behavior. Additionally, the distance between gate and obstacle
was often such that the decision of the bee was unambiguous. Therefore, additional
experiments need to be conducted to investigate this further. The data points of Fig. 2
are not sufficient without further research for new findings derived from the slopes of
the three different obstacle types, either.
The other evaluated parameters do not improve the accuracy of the linear regression
at all. It is reasonable that the distance between tunnel sidewall and obstacle, as well as
tunnel ceiling and obstacle, does not have a positive influence on the accuracy of the
prediction model. The bumblebees cannot see the tunnel itself. Even though they know
that there is a barrier from previous flights, there is no visual feedback, and therefore
any effect on their behavior is doubtful.
Finally, the parameters speed and velocity do also not improve the predictability
according to the logistic regression model. The confined space around the obstacle might
explain this. The average flight speed in all recordings was relatively low, indicating that
the bumblebees maneuvered carefully. The bees also had to fly through the gates, which
the bees usually did with moderate velocity.
A. Thoma et al.
A reason for this might be that the bumblebee is not able to survey the entire situation
because the obstacle is blocking the whole field of view. While reorienting and searching
for a solution, the bee might see the upper corner of the obstacle first and choose to fly
over the obstacle in some cases. An analysis of the recordings supports this statement.
If the obstacle is very close to the gate, the bees show a searching behavior.
Investigation of the dependency of the behavior on the distance between gate and
obstacle with the HV index (Fig. 2) indicates a positive, linear relationship between
distance and decision. The optimal climb performance of bumblebees might be the
controlling factor here. Analyses of flapping-wing aerodynamics indicate that forward
flight is more efficient than hover flight [29]. Therefore, increasing altitude while flying
forward is energetically more efficient than climbing vertically. This is the same for
rotary wings, e.g., quadcopters or helicopters [30], leading to the conclusion that a UAV
should evade a close obstacle horizontally to keep a certain minimal forward flight speed
while an obstacle in greater distance should be overflown.
The slope of the three different obstacle types also indicates a dependency on the size
of the obstacle. However, only two positions per obstacle were investigated. Nonetheless,
these preliminary results show that an extended investigation on the dependency of the
evasion maneuver on the obstacle dimensions is worth a more in-depth investigation.
Additionally, the question arises, if the distance itself is the triggering parameter at all
or if other parameters derived from the distance, e.g., obstacle height to distance ratio,
are triggering a specific behavior.
Therefore, logistic regression was performed. It showed that the behavior of the
bumblebees is predictable with an accuracy of more than 80% with the distance between
obstacle and entrance gate itself as the sole parameter. The investigated ratio of obstacle
width-to-height, height-to-distance, or width-to-distance does not influence the accuracy.
However, it is possible that the differences in the ratios were not varied enough to show a
measurable effect on the behavior. Additionally, the distance between gate and obstacle
was often such that the decision of the bee was unambiguous. Therefore, additional
experiments need to be conducted to investigate this further. The data points of Fig. 2
are not sufficient without further research for new findings derived from the slopes of
the three different obstacle types, either.
The other evaluated parameters do not improve the accuracy of the linear regression
at all. It is reasonable that the distance between tunnel sidewall and obstacle, as well as
tunnel ceiling and obstacle, does not have a positive influence on the accuracy of the
prediction model. The bumblebees cannot see the tunnel itself. Even though they know
that there is a barrier from previous flights, there is no visual feedback, and therefore
any effect on their behavior is doubtful.
Finally, the parameters speed and velocity do also not improve the predictability
according to the logistic regression model. The confined space around the obstacle might
explain this. The average flight speed in all recordings was relatively low, indicating that
the bumblebees maneuvered carefully. The bees also had to fly through the gates, which
the bees usually did with moderate velocity.