Journal of Nonlinear Science

, Volume 27, Issue 4, pp 1121–1154 | Cite as

Locomotion Dynamics for Bio-inspired Robots with Soft Appendages: Application to Flapping Flight and Passive Swimming

  • Frédéric Boyer
  • Mathieu PorezEmail author
  • Ferhat Morsli
  • Yannick Morel


In animal locomotion, either in fish or flying insects, the use of flexible terminal organs or appendages greatly improves the performance of locomotion (thrust and lift). In this article, we propose a general unified framework for modeling and simulating the (bio-inspired) locomotion of robots using soft organs. The proposed approach is based on the model of Mobile Multibody Systems (MMS). The distributed flexibilities are modeled according to two major approaches: the Floating Frame Approach (FFA) and the Geometrically Exact Approach (GEA). Encompassing these two approaches in the Newton–Euler modeling formalism of robotics, this article proposes a unique modeling framework suited to the fast numerical integration of the dynamics of a MMS in both the FFA and the GEA. This general framework is applied on two illustrative examples drawn from bio-inspired locomotion: the passive swimming in von Karman Vortex Street, and the hovering flight with flexible flapping wings.


Soft robotics Locomotion Newton–Euler dynamics MAVs Fish-like robots 

Mathematics Subject Classification




The authors would like to thank all their colleagues and PHD students (whose names appear as coauthors of the referenced papers) who contributed over the last years to develop the specific cases of this general framework.

Supplementary material

Supplementary material 1 (mp4 5181 KB)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Frédéric Boyer
    • 1
  • Mathieu Porez
    • 1
    Email author
  • Ferhat Morsli
    • 2
  • Yannick Morel
    • 3
  1. 1.Automation, Production and Computer Sciences DepartmentEcole des Mines de NantesNantes Cedex 3France
  2. 2.Laboratory of Structure MechanicsEcole Militaire Polytechnique - BEBAlgerAlgeria
  3. 3.BioRobEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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