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Orbital stabilization of an underactuated bipedal gait via nonlinear \({{\mathcal H}}_{\infty }\)-control using measurement feedback

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Abstract

The primary concern of the work is robust control of hybrid mechanical systems under unilateral constraints with underactuation degree one. Nonlinear \({{\mathcal H}}_{\infty }\) output feedback synthesis is developed in the hybrid setting, covering collision phenomena. Sufficient conditions are presented to ensure internal asymptotic stability while also attenuating external disturbances and plant uncertainties. The developed synthesis is applied to the orbital stabilization of an underactuated bipedal robot periodically touching the ground. Good performance of the closed-loop system is obtained not only in the presence of measurement noise and external disturbances, affecting the gait of the biped between collision time instants, but also under uncertainties at the velocity restitution when the ground collision occurs.

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Acknowledgments

The authors acknowledge the financial support of Campus France grant Eiffel and CONACYT Grant No.165958.

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Authors and Affiliations

  1. CICESE, Carretera Ensenada-Tijuana No. 3918, Zona Playitas, C.P. 22860, Ensenada, B.C., Mexico

    Oscar Montano & Yury Orlov

  2. L’IRCCyN, 1, Rue de la Noe, BP 92101, 44321, Nantes Cedex 3, France

    Yannick Aoustin & Christine Chevallereau

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  1. Oscar Montano
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  2. Yury Orlov
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  4. Christine Chevallereau
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Correspondence to Yannick Aoustin.

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Montano, O., Orlov, Y., Aoustin, Y. et al. Orbital stabilization of an underactuated bipedal gait via nonlinear \({{\mathcal H}}_{\infty }\)-control using measurement feedback. Auton Robot 41, 1277–1295 (2017). https://doi.org/10.1007/s10514-015-9543-z

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