Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

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


  1. Floreano, D. & Wood, R. J. Science, technology and the future of small autonomous drones. Nature 521, 460–466 (2015).

    Article  Google Scholar 

  2. Franceschini, N., Pichon, J.-M. & Blanes, C. From insect vision to robot vision. Philos. Trans. R. Soc. Lond. B 337, 283–294 (1992).

    Article  Google Scholar 

  3. Webb, B. Robots in invertebrate neuroscience. Nature 417, 359–363 (2002).

    Article  Google Scholar 

  4. Franceschini, N. Small brains, smart machines: from fly vision to robot vision and back again. Proc. IEEE 102, 751–781 (2014).

    Article  Google Scholar 

  5. Gibson, J. J. The Ecological Approach to Visual Perception (Houghton Mifflin, 1979).

  6. Collett, T. S. Insect vision: controlling actions through optic flow. Curr. Biol. 12, R615–R617 (2002).

    Article  Google Scholar 

  7. Srinivasan, M. V., Zhang, S. W., Chahl, J. S., Stange, G. & Garratt, M. An overview of insect-inspired guidance for application in ground and airborne platforms. Proc. Inst. Mech. Eng. G 218, 375–388 (2004).

    Article  Google Scholar 

  8. Srinivasan, M. V., Zhang, S.-W., Chahl, J. S., Barth, E. & Venkatesh, S. How honeybees make grazing landings on flat surfaces. Biol. Cybern. 83, 171–183 (2000).

    Article  Google Scholar 

  9. Baird, E., Boeddeker, N., Ibbotson, M. R. & Srinivasan, M. V. A universal strategy for visually guided landing. Proc. Natl Acad. Sci. USA 110, 18686–18691 (2013).

    Article  Google Scholar 

  10. Ruffier, F. & Franceschini, N. Visually guided micro-aerial vehicle: automatic take off, terrain following, landing and wind reaction. In Proc. 2004 IEEE International Conference on Robotics and Automation Vol. 3, 2339–2346 (IEEE, 2004).

  11. Herisse, B., Russotto, F. X., Hamel, T. & Mahony, R. Hovering flight and vertical landing control of a VTOL unmanned aerial vehicle using optical flow. In 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems 801–806 (2008);

  12. Alkowatly, M. T., Becerra, V. M. & Holderbaum, W. Bioinspired autonomous visual vertical control of a quadrotor unmanned aerial vehicle. J. Guid. Control Dyn. 38, 249–262 (2015).

    Article  Google Scholar 

  13. Van Breugel, F., Morgansen, K. & Dickinson, M. H. Monocular distance estimation from optic flow during active landing maneuvers. Bioinspir. Biomim 9, 2 (2014).

    Article  Google Scholar 

  14. Howard, D. & Kendoul, F. Towards evolved time to contact neurocontrollers for quadcopters. In Proc. Australasian Conference on Artificial Life and Computational Intelligence 336–347 (Springer, 2016).

  15. Scheper, K. Y. W. & de Croon, G. C. H. E. Evolution of robust high speed optical-flow-based landing for autonomous MAVs. Rob. Auton. Syst. (2020);

  16. Hagenaars, J. J., Paredes-Vallés, F., Bohté, S. M. & de Croon, G. C. H. E. Evolved neuromorphic control for high speed divergence-based landings of MAVs. Preprint at (2020).

  17. Santer, R. D., Rind, F. C., Stafford, R. & Simmons, P. J. Role of an identified looming-sensitive neuron in triggering a flying locust’s escape. J. Neurophysiol. 95, 3391–3400 (2006).

    Article  Google Scholar 

  18. Muijres, F. T., Elzinga, M. J., Melis, J. M. & Dickinson, M. H. Flies evade looming targets by executing rapid visually directed banked turns. Science 344, 172–177 (2014).

    Article  Google Scholar 

  19. Nelson, R. & Aloimonos, J. Obstacle avoidance using flow field divergence. Pattern Anal. Mach. I, 1102–1106 (1989).

    Article  Google Scholar 

  20. Green, W. E. & Oh, P. Y. Optic-flow-based collision avoidance. IEEE Robot. Autom. Mag. 15, 96–103 (2008).

    Article  Google Scholar 

  21. Conroy, J., Gremillion, G., Ranganathan, B. & Humbert, J. S. Implementation of wide-field integration of optic flow for autonomous quadrotor navigation. Auton. Robots 27, 189 (2009).

    Article  Google Scholar 

  22. Zingg, S., Scaramuzza, D., Weiss, S. & Siegwart, R. MAV navigation through indoor corridors using optical flow. In 2010 IEEE International Conference on Robotics and Automation 3361–3368 (IEEE, 2010).

  23. Milde, M. B. et al. Obstacle avoidance and target acquisition for robot navigation using a mixed signal analog/digital neuromorphic processing system. Front. Neurorobot. 11, 28 (2017).

    Article  Google Scholar 

  24. Rind, F. C., Santer, R. D., Blanchard, J. M. & Verschure, P. F. M. J. in Sensors and Sensing in Biology and Engineering (eds. Barth, F. G. et al.) 237–250 (Springer, 2003).

  25. Hyslop, A. M. & Humbert, J. S. Autonomous navigation in three-dimensional urban environments using wide-field integration of optic flow. J. Guid. Control Dyn. 33, 147–159 (2010).

    Article  Google Scholar 

  26. Serres, J. R. & Ruffier, F. Optic flow-based collision-free strategies: from insects to robots. Arthropod Struct. Dev. 46, 703–717 (2017).

    Article  Google Scholar 

  27. De Croon, G. C. H. E. Monocular distance estimation with optical flow maneuvers and efference copies: a stability-based strategy. Bioinspir. Biomim. 11, 1–18 (2016).

    Article  Google Scholar 

  28. Stevens, J.-L. & Mahony, R. Vision based forward sensitive reactive control for a quadrotor VTOL. In Proc. 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 5232–5238 (IEEE, 2018).

  29. Sanket, N. J., Singh, C. D., Ganguly, K., Fermüller, C. & Aloimonos, Y. GapFlyt: active vision based minimalist structure-less gap detection for quadrotor flight. IEEE Robot. Autom. Lett. 3, 2799–2806 (2018).

    Article  Google Scholar 

  30. Bertrand, O. J. N., Lindemann, J. P. & Egelhaaf, M. A bio-inspired collision avoidance model based on spatial information derived from motion detectors leads to common routes. PLoS Comput. Biol. 11, e1004339 (2015).

    Article  Google Scholar 

  31. Varma, M. & Zisserman, A. Texture classification: are filter banks necessary? In Proc. 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Vol. 2, II–691 (IEEE, 2003).

  32. Mitchell, T. et al. Machine learning. Annu. Rev. Comput. Sci 4, 417–433 (1990).

    Article  Google Scholar 

  33. Bishop, C. M. Pattern Recognition and Machine Learning (Springer, 2006).

  34. Qiu, W. et al. UnrealCV: virtual worlds for computer vision.In Proc. 25th ACM International Conference on Multimedia 1221–1224 (ACM, 2017);

  35. Mancini, M., Costante, G., Valigi, P. & Ciarfuglia, T. A. Fast robust monocular depth estimation for obstacle detection with fully convolutional networks. In Proc. 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 4296–4303 (IEEE, 2016).

  36. Mori, T. & Scherer, S. First results in detecting and avoiding frontal obstacles from a monocular camera for micro unmanned aerial vehicles. In Proc. IEEE International Conference on Robotics and Automation 1750–1757 (IEEE, 2013);

  37. Chaumette, F., Hutchinson, S. & Corke, P. in Springer Handbook of Robotics (eds. Siciliano, B. & Khatib, O.) 841–866 (Springer, 2016).

  38. Scaramuzza, D. & Fraundorfer, F. Visual odometry [tutorial]. IEEE Robot. Autom. Mag. 18, 80–92 (2011).

    Article  Google Scholar 

  39. Engel, J., Schöps, T. & Cremers, D. LSD-SLAM: large-scale direct monocular SLAM. In Proc. European Conference on Computer Vision (ECCV) 834–849 (Springer, 2014).

  40. Zhou, T., Brown, M., Snavely, N. & Lowe, D. G. Unsupervised learning of depth and ego-motion from video. In Proc. IEEE Conference on Computer Vision and Pattern Recognition 1851–1858 (IEEE, 2017).

  41. Gordon, A., Li, H., Jonschkowski, R. & Angelova, A. Depth from videos in the wild: unsupervised monocular depth learning from unknown cameras. Preprint at (2019).

  42. Gibson, J. J. The Perception of the Visual World (Houghton Mifflin, 1950).

  43. Brenner, E. & Smeets, J. B. J. Depth perception. Stevens’ Handb. Exp. Psychol. Cogn. Neurosci. 2, 1–30 (2018).

    Google Scholar 

  44. Lehrer, M. & Bianco, G. The turn-back-and-look behaviour: bee versus robot. Biol. Cybern. 83, 211–229 (2000).

    Article  Google Scholar 

  45. Stach, S., Benard, J. & Giurfa, M. Local-feature assembling in visual pattern recognition and generalization in honeybees. Nature 429, 758–761 (2004).

    Article  Google Scholar 

  46. Andel, D. & Wehner, R. Path integration in desert ants, Cataglyphis: how to make a homing ant run away from home. Proc. R. Soc. Lond. B 271, 1485–1489 (2004).

    Article  Google Scholar 

  47. Dyer, A. G., Neumeyer, C. & Chittka, L. Honeybee (Apis mellifera) vision can discriminate between and recognise images of human faces. J. Exp. Biol. 208, 4709–4714 (2005).

    Article  Google Scholar 

  48. Fry, S. N. & Wehner, R. Look and turn: landmark-based goal navigation in honey bees. J. Exp. Biol. 208, 3945–3955 (2005).

    Article  Google Scholar 

  49. Rosten, E., Porter, R. & Drummond, T. Faster and better: a machine learning approach to corner detection. IEEE Trans. Pattern Anal. Mach. Intell. 32, 105–119 (2010).

    Article  Google Scholar 

  50. de Croon, G. C. H. E. & Nolfi, S. ACT-CORNER: active corner finding for optic flow determination. In Proc. IEEE International Conference on Robotics and Automation (ICRA 2013) (IEEE, 2013);

  51. Lucas, B. D. & Kanade, T. An iterative image registration technique with an application to stereo vision. In Proc. International Joint Conference on Artificial Intelligence Vol. 81, 674–679 (ACM, 1981).

  52. Laws, K. I. Textured Image Segmentation. PhD thesis, Univ. Southern California (1980).

  53. Games, E. Unreal Simulator (Epic Games, 2020);

  54. Kisantal, M. Deep Reinforcement Learning for Goal-directed Visual Navigation (2018);

  55. Pulli, K., Baksheev, A., Kornyakov, K. & Eruhimov, V. Real-time computer vision with OpenCV. Commun. ACM 55, 61–69 (2012).

    Article  Google Scholar 

  56. Alcantarilla, P. F. & Solutions, T. Fast explicit diffusion for accelerated features in nonlinear scale spaces. IEEE Trans. Patt. Anal. Mach. Intell. 34, 1281–1298 (2011).

    Google Scholar 

  57. Farnebäck, G. Two-frame motion estimation based on polynomial expansion. In Proc. 13th Scandinavian Conference on Image Analysis 363–370 (ACM, 2003).

  58. Sanket, N. J., Singh, C. D., Fermüller, C. & Aloimonos, Y. PRGFlow: benchmarking SWAP-aware unified deep visual inertial odometry. Preprint at (2020).

  59. Wofk, D., Ma, F., Yang, T.-J., Karaman, S. & Sze, V. Fastdepth: fast monocular depth estimation on embedded systems. In Proc. 2019 International Conference on Robotics and Automation (ICRA) 6101–6108 (ICRA, 2019).

  60. Herissé, B., Hamel, T., Mahony, R. & Russotto, F.-X. The landing problem of a VTOL unmanned aerial vehicle on a moving platform using optical flow. In Proc. 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems 1600–1605 (2010);

  61. Ho, H. W., de Croon, G. C. H. E., van Kampen, E., Chu, Q. P. & Mulder, M. Adaptive gain control strategy for constant optical flow divergence landing. IEEE Trans. Robot. (2018);

Download references


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

Authors and Affiliations



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.

Ethics declarations

Competing interests

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.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing