Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum

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SHAHBAZI M., SARANLI U., BABUSKA R., LOPES G. A. D.

BIOINSPIRATION & BIOMIMETICS, cilt.12, sa.1, 2017 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 1
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1088/1748-3190/12/1/016003
  • Dergi Adı: BIOINSPIRATION & BIOMIMETICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: bio-inspired walking, spring-loaded inverted pendulum, double-stance, analytical approximation, damping, WALKING, LOCOMOTION, MAP
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of nonnegligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.