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Enhancing optical-flow-based control by learning visual appearance cues for flying robots


Flying insects employ elegant optical-flow-based strategies to solve complex tasks such as landing or obstacle avoidance. Roboticists have mimicked these strategies on flying robots with only limited success, because optical flow (1) cannot disentangle distance from velocity and (2) is less informative in the highly important flight direction. Here, we propose a solution to these fundamental shortcomings by having robots learn to estimate distances to objects by their visual appearance. The learning process obtains supervised targets from a stability-based distance estimation approach. We have successfully implemented the process on a small flying robot. For the task of landing, it results in faster, smooth landings. For the task of obstacle avoidance, it results in higher success rates at higher flight speeds. Our results yield improved robotic visual navigation capabilities and lead to a novel hypothesis on insect intelligence: behaviours that were described as optical-flow-based and hardwired actually benefit from learning processes.

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Fig. 1: Fundamental optical flow problems and the proposed solution.
Fig. 2: Landing results.
Fig. 3: Simulated obstacle avoidance experiments.
Fig. 4: Real-world obstacle avoidance experiments.

Data availability

All data are publicly available at

Code availability

All code bases (in C, Python and MATLAB) that have been used in the experiments are publicly available at


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We thank M. Kisantal for creating the UnrealCV environment that was used in this work. We also thank F. Muijres, M. Karasek and M. Wisse for their valuable feedback on earlier versions of the manuscript.

Author information




All authors contributed to the conception of the project and were involved in the analysis of the results and revising and editing the manuscript. G.C.H.E.d.C. programmed the majority of the software, with help from C.D.W. for the implementation in Paparazzi for the real-world experiments. G.C.H.E.d.C. performed all simulation and real-world experiments. G.C.H.E.d.C. created all graphics for the figures.

Corresponding author

Correspondence to G. C. H. E. de Croon.

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The authors declare no competing interests.

Additional information

Peer review information Nature Machine Intelligence thanks Yiannis Aloimonos and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Landing performance for different landing strategies.

For each strategy we show the height (red lines), and the divergence (purple lines) over time. Thick solid lines show the average over 5 landings, while the grey area shows the sampled standard deviation. All landings aimed for a divergence of D*=-0.3 and started in hover, that is, at D=0. a, Landing with a fixed gain K (as in, for example,60), resulting in oscillations close to the surface. b, Landing with an adaptive gain as in61. The performance during landing is good, but slowly increasing the gain takes a rather long time (in the order of 14 seconds). c, Landing with the proposed self-supervised learning strategy. It can immediately start landing and has a good performance all the way down. Note the quicker landings with respect to a fixed gain and the absence of evident oscillations in the divergence.

Extended Data Fig. 2 Dense distance estimation from optical flow and oscillations.

First (top) row: Dense horizontal optical flow images, determined with the Farnebäck algorithm57. Second row: Histogram of each optical flow image. The x-axis represents the optical flow in pixels/frame. Third row: Corresponding dense gain (distance) images. Fourth row: Histogram of each gain image. Although the optical flow changes substantially during oscillatory motion of the flying robot (rows 1–2), the gain values are of comparable magnitude (rows 3–4). Smaller optical flow does lead to noisier gain estimates.

Extended Data Fig. 3 Example images from the Unreal simulator.

These images are taken at 960 × 960 pixel resolution. The environment contains a variety of trees and lighting conditions. The border of the environment is a smooth, grey, stone wall (bottom right screenshot). The flowers on the ground and the leaves of the trees move in the wind. The simulated flying robot perceives the environment at a 240 × 240 pixel resolution.

Extended Data Fig. 4 Distance-collision curves for the four different avoidance methods.

The curves are obtained by varying the parameters of the methods that balance false positives (turning when it is not necessary) and false negatives (not detecting an obstacle). For the predictive gain method this is the gain threshold, for the divergence methods that use optical flow vectors or feature size increases it is the divergence threshold, and for the fixed gain method it is the control gain. The numbers next to the graphs are threshold / parameter values. Per parameter value, N=30 runs have been performed, and the error bars show the standard error \(\sigma /\sqrt N\). The stars indicate the operating points shown in Fig. 3 in the main article.

Supplementary information

Supplementary Information

Supplementary Information, including sections and associated figures.

Supplementary Video 1

Overview video of the article.

Supplementary Video 2

Long video with raw experimental footage.

Supplementary Video 3

Video that shows both a landing with a fixed control gain and one with the proposed method.

Supplementary Video 4

Video of simulation experiments.

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de Croon, G.C.H.E., De Wagter, C. & Seidl, T. Enhancing optical-flow-based control by learning visual appearance cues for flying robots. Nat Mach Intell 3, 33–41 (2021).

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