Optimization of two- and three-link snakelike locomotion.

We analyze two- and three-link planar snakelike locomotion and optimize the motion for efficiency. The locomoting system consists of two or three identical inextensible links connected via hinge joints, and the angles between the links are actuated as prescribed periodic functions of time. An essential feature of snake locomotion is frictional anisotropy: The forward, backward, and transverse coefficients of friction differ. The dynamics are studied analytically and numerically for small and large amplitudes of the internal angles. Efficiency is defined as the ratio between distance traveled and the energy expended within one period, i.e., the inverse of the cost of locomotion. The optimal set of coefficients of friction to maximize efficiency consists of a large backward coefficient of friction and a small transverse coefficient of friction, compared to the forward coefficient of friction. For the two-link case with a symmetrical motion, efficiency is maximized when the internal angle amplitude is approximately π/2 for a sufficiently large transverse coefficient. For the three-link case, the efficiency-maximizing paths are triangles in the parameter space of internal angles.

• Publication year

  2012

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2012-12-01

• Fields of study

  Mathematics, Physics, Medicine, Engineering

• Identifiers
  DOI 10.1103/PhysRevE.87.022711arXiv 1212.0062PMID 23496552
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• SLITHERING LOCOMOTION

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  2004influential reference
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  1993cited by this paper
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  1992cited by this paper
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  1990cited by this paper
• Mathematics Applied to Continuum Mechanics

  1977cited by this paper
• TERRESTRIAL LOCOMOTION WITHOUT LIMBS

  1962cited by this paper
• The mechanism of locomotion in snakes.

  1946cited by this paper
• ON THE LOCOMOTION OF SNAKES.

  1932cited by this paper

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  2020cites this paper
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  2018cites this paper
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  2016cites this paper
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  2016cites this paper
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  2016cites this paper
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  2015cites this paper
• Controllability and optimization of deformable bodies in fluids: from biology to robotics

  2015cites this paper
• Incorporating frictional anisotropy in the design of a robotic snake through the exploitation of scales

  2015cites this paper
• Crawling scallop: friction-based locomotion with one degree of freedom.

  2013cites this paper
• Optimizing snake locomotion in the plane. II. Large transverse friction

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  2013cites this paper
• The role of functional surfaces in the locomotion of snakes

  2013cites this paper
• Optimizing snake locomotion on an inclined plane.

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