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On the periodic gait stability of a multi-actuated spring-mass hopper model via partial feedback linearization

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Abstract

Spring-loaded inverted pendulum (SLIP) template (and its various derivatives) could be considered as the mostly used and widely accepted models for describing legged locomotion. Despite their simple nature, as being a simple spring-mass model in dynamics perspective, the SLIP model and its derivatives are formulated as restricted three-body problem, whose non-integrability has been proved long before. Thus, researchers proceed with approximate analytical solutions or use partial feedback linearization when numerical integration is not preferred in their analysis. The key contributions of this paper can be divided into two parts. First, we propose a dissipative SLIP model, which we call as multi-actuated dissipative SLIP (MD-SLIP), with two extended actuators: one linear actuator attached serially to the leg spring and one rotary actuator attached to hip. The second contribution of this paper is a partial feedback linearization strategy by which we can cancel some nonlinear dynamics of the proposed model and obtain exact analytical solution for the equations of motion. This allows us to investigate stability characteristics of the hopping gait obtained from the MD-SLIP model. We illustrate the applicability of our solutions with open-loop and closed-loop hopping performances on rough terrain simulations.

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Acknowledgements

Hasan Hamzaçebi was supported by Aselsan Inc. and The Scientific and Technological Research Council of Turkey (TÜBİTAK). The authors would like to thank İsmail Uyanık for his invaluable comments and suggestions.

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  1. Department of Electrical and Electronics Engineering, Bilkent University, 06800, Bilkent, Ankara, Turkey

    Hasan Hamzaçebi & Ömer Morgül

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  1. Hasan Hamzaçebi
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  2. Ömer Morgül
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Correspondence to Hasan Hamzaçebi.

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Hamzaçebi, H., Morgül, Ö. On the periodic gait stability of a multi-actuated spring-mass hopper model via partial feedback linearization. Nonlinear Dyn 88, 1237–1256 (2017). https://doi.org/10.1007/s11071-016-3307-y

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  • DOI: https://doi.org/10.1007/s11071-016-3307-y

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