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Differential game theory for versatile physical human–robot interaction


The last decades have seen a surge of robots working in contact with humans. However, until now these contact robots have made little use of the opportunities offered by physical interaction and lack a systematic methodology to produce versatile behaviours. Here, we develop an interactive robot controller able to understand the control strategy of the human user and react optimally to their movements. We demonstrate that combining an observer with a differential game theory controller can induce a stable interaction between the two partners, precisely identify each other’s control law, and allow them to successfully perform the task with minimum effort. Simulations and experiments with human subjects demonstrate these properties and illustrate how this controller can induce different representative interaction strategies.

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Fig. 1: Simulation of an arm reaching with the GT interactive controller.
Fig. 2: Simulated arm reaching training for motor recovery.
Fig. 3: Adaptation of assistance to reaching experiment.

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Code availability

The code that supports the findings of this study is available from the corresponding authors upon reasonable request.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.


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We thank J. Eden, T. Mylvaganam, N. P. Perez, Q.-C. Pham and K. P. Tee for their careful reading and comments on the manuscript. This research was supported in part by the European Commission grant EU-H2020 COGIMON (644727), UK EPSRC MOTION grant EP/NO29003/1 and Singapore MOE Tier1 grant RG48/17.

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Authors and Affiliations



Control concepts: Y.L. and E.B.; algorithm and simulation: Y.L.; set-up: F.G. and D.C.; experiments: G.C.; results analysis: Y.L., G.C. and E.B.; manuscript writing: Y.L. and E.B. All authors have read and edited the manuscript, and agree with its content.

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Correspondence to Y. Li or E. Burdet.

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The authors declare no competing interests.

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Guidelines for study procedures were provided by Imperial College London.

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Li, Y., Carboni, G., Gonzalez, F. et al. Differential game theory for versatile physical human–robot interaction. Nat Mach Intell 1, 36–43 (2019).

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