Nonlinear Dynamics

, Volume 89, Issue 4, pp 2739–2751 | Cite as

Motion analysis of two-link nonholonomic swimmers

  • Salah BazziEmail author
  • Elie Shammas
  • Daniel Asmar
  • Matthew T. Mason
Original Paper


This paper presents a tool for analyzing the motion of two-link nonholonomic swimmers. We refer to these systems as Land-sharks, which are a generalization of the well known Roller Racers. By exploiting the symmetry of the system, we are able to reduce the equations of motion and construct the scaled momentum evolution equation. This unveils a very useful and intuitive Land-shark motion analysis tool based on the partitioning of the mass and geometry parameter space. In particular, this partitioning reveals that, as opposed to the Roller Racer, the Land-shark’s momentum can be increased and decreased, i.e., the system can be stopped. This is done through the use of steering, which is the system’s only input. Furthermore, we explore the problem of modeling frictional slip by assessing the applicability of a previously proposed friction model to the oscillatory locomotion of the Land-shark. Results show that the proposed friction model is generally applicable to two-link nonholonomic mechanical systems, which is an important step toward establishing the generality of the friction model for nonholonomic mechanical systems.


Geometric mechanics Nonholonomic motion planning Frictional slip Robotic locomotion 



This work is supported by the Lebanese National Council for Scientific Research (LNCSR), the University Research Board (URB) of the American University of Beirut, and the Munib and Angela Masri Institute. The authors would like to thank the reviewers for their insightful comments, which helped in improving the work presented in this paper.

Supplementary material

Supplementary material 1 (mp4 3494 KB)


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Salah Bazzi
    • 1
    Email author
  • Elie Shammas
    • 1
  • Daniel Asmar
    • 1
  • Matthew T. Mason
    • 2
  1. 1.Vision and Robotics Lab, Department of Mechanical EngineeringAmerican University of BeirutBeirutLebanon
  2. 2.Robotics InstituteCarnegie Mellon UniversityPittsburghUSA

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