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Integration of deep learning and soft robotics for a biomimetic approach to nonlinear sensing


Traditional approaches to sensing have often been aimed at simple sensor characteristics to make interpretation of the sensor outputs easier, but this has also limited the quality of the encoded sensory information. Integrating a complex sensor with deep learning could hence be a strategy for removing current limitations on the information that sensory inputs can carry. Here, we demonstrate this concept with a soft-robotic sensor that mimics fast non-rigid deformation of the ears in certain bat species. We show that a deep convolutional neural network can use the nonlinear Doppler shift signatures generated by these motions to estimate the direction of a sound source with an estimation error of ~0.5°. Previously, determining the direction of a sound source based on pressure receivers required either multiple frequencies or multiple receivers. Our current results demonstrate a third approach that makes do with only a single frequency and a single receiver.

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Fig. 1: Experimental set-up.
Fig. 2: Doppler shift signatures associated with different directions.
Fig. 3: Diagram of the CNN architecture.
Fig. 4: Deep learning of direction finding from Doppler signatures.
Fig. 5: Accuracy of direction finding with a dynamic soft-robotic pinna.
Fig. 6: Direction-finding approaches.

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Data availability

The original sound recordings are available from the corresponding author upon reasonable request. The training datasets (spectrograms derived from the recordings) are available via Code Ocean at Source data are provided with this paper.

Code availability

All source code for the CNN is available via Code Ocean at


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This research has been supported by the Office of Naval Research (award no. N00014-17-1-2376 to R.M.), the National Science Foundation (award no. 1362886 to R.M.), the Naval Engineering Education Consortium (award no. N001741910001 to R.M.) and a fellowship from the China Scholarship Council to X.Y.

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Authors and Affiliations



R.M. and X.Y. conceived and designed the experiments. X.Y. performed the experiments. X.Y. and R.M. analysed the results. X.Y. and R.M. wrote the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Rolf Müller.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Machine Intelligence thanks Deepak Gala and Ming Zhong 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.

Supplementary information

Supplementary Video 1

This video shows an example of fast ear motions in a female Pratt’s roundleaf bat (Hipposideros pratti). The video was recorded at a frame rate of 200 Hz, and it is first played back using the original sequence of frames and then a second time slowed down 10 times.

Supplementary Video 2

Hardware-in-the-loop implementation of the direction-finding approach: The pinna capable of fast deformations is mounted on a pan-tilt unit and the speaker emits a single ultrasonic frequency (90 kHz), and the deep neural network tries to align the pinna with the loudspeaker so that the laser pointer mounted next to the pinna is aimed at the piece of paper next to the speaker. This video is a demonstration and does not depict the experimental procedure described in the text.

Source data

Source Data Fig. 5

Source data that includes prediction and measurement errors for Fig. 5.

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Yin, X., Müller, R. Integration of deep learning and soft robotics for a biomimetic approach to nonlinear sensing. Nat Mach Intell 3, 507–512 (2021).

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