Autonomous functional movements in a tendon-driven limb via limited experience


Robots will become ubiquitously useful only when they require just a few attempts to teach themselves to perform different tasks, even with complex bodies and in dynamic environments. Vertebrates use sparse trial and error to learn multiple tasks, despite their intricate tendon-driven anatomies, which are particularly hard to control because they are simultaneously nonlinear, under-determined and over-determined. We demonstrate—in simulation and hardware—how a model-free, open-loop approach allows few-shot autonomous learning to produce effective movements in a three-tendon two-joint limb. We use a short period of motor babbling (to create an initial inverse map) followed by building functional habits by reinforcing high-reward behaviour and refinements of the inverse map in a movement’s neighbourhood. This biologically plausible algorithm, which we call G2P (general to particular), can potentially enable quick, robust and versatile adaptation in robots as well as shed light on the foundations of the enviable functional versatility of organisms.

A preprint version of the article is available at ArXiv.

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Fig. 1: The G2P algorithm.
Fig. 2: A run of the G2P algorithm, in detail, for the reward-driven treadmill task.
Fig. 3: Planar robotic tendon-driven limb.
Fig. 4: Treadmill task results.
Fig. 5: A run of the G2P algorithm in detail for the tracking of free cyclical movements.
Fig. 6: Distribution of joint angles visited during motor babbling versus those used to produce a free cyclical movement in air.

Data availability

The source code can be accessed at−2019-NMI.

All other data (run data for experiments as well as the 3D printing files) can be accessed at


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The authors thank H. Zhao for support in designing and manufacturing the physical system as well as support in the analysis of the limb kinematics, S. Kamalakkannan for support in designing and implementing the data acquisition system, and Y. Kahsai for Figs. 1 and 2. Research reported in this publication was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health under award numbers R01 AR-050520 and R01 AR-052345 to F.J.V.-C. This work was also supported by Department of Defense CDMRP Grant MR150091 and Award W911NF1820264 from the DARPA-L2M programme to F.J.V.-C. The authors acknowledge additional support for A.M. for Provost and Research Enhancement Fellowships from the Graduate School of the University of Southern California and fellowships for D.U.-M. from the Consejo Nacional de Ciencia y Tecnología (Mexico) and for B.C. from the NSF Graduate Research Fellowship Program. The content of this endeavour is solely the responsibility of the authors and does not represent the official views of the National Institutes of Health, the Department of Defense, The National Science Foundation nor the Consejo Nacional de Ciencia y Tecnología.

Author information




All authors contributed to the conception and design of the work and writing of the manuscript. A.M. led the development of the G2P algorithm, D.U.-M. led the construction of the robotic limb and B.A.C. led the data acquisition and analysis. F.J.V.-C. provided general direction for the project. All authors approved the final version of the manuscript and agree to be accountable for all aspects of the work. All persons designated as authors qualify for authorship, and all those who qualify for authorship are listed.

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Correspondence to Francisco J. Valero-Cuevas.

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Supplementary Information

Supplementary Materials and Methods, Supplementary Discussion, Supplementary Figures 1–7, Captions for Supplementary Videos 1,2

Supplementary Video 1

Video for Figs 4, 5a and 6

Supplementary Video 2

Video for additional experiments

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Marjaninejad, A., Urbina-Meléndez, D., Cohn, B.A. et al. Autonomous functional movements in a tendon-driven limb via limited experience. Nat Mach Intell 1, 144–154 (2019).

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