Undulatory swimming in sand: Experimental and simulation studies of a robotic sandfish

Ryan D. Maladen, Yang Ding, Paul B. Umbanhowar, Daniel I. Goldman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


A previous study of a sand-swimming lizard, the sandfish, revealed that it swims within granular media at speeds up to 0.4 body-lengths/cycle using body undulations (approximately a single period sinusoidal traveling wave) without limb use. Inspired by the organism, we develop a numerical model of a robot swimming in a simulated granular medium to guide the design of a physical device. Both in simulation and experiment the robot swims limblessly subsurface at speeds up to 0.3 body-lengths/cycle and, like the animal, increases its speed by increasing its oscillation frequency. The performance of the robot measured in terms of its wave efficiency η, the ratio of its forward speed to wave speed, is 0.34 ± 0.02, within 8% of the simulation prediction. Both in simulation and experiment, η increases with increasing particle-particle friction but decreases with increasing body-particle friction. On a flat, rigid surface the robot fails to move forward, as expected, due to the frictional isotropy between the interacting surfaces. However, the surface and subsurface performance of the robot on low friction particles are comparable. Our work provides a validated simulation tool and the design of a robot that can move on or within yielding terrestrial substrates.

Original languageEnglish (US)
Pages (from-to)793-805
Number of pages13
JournalInternational Journal of Robotics Research
Issue number7
StatePublished - Jun 2011


  • Bioinspired
  • Limbless
  • Modeling
  • Sand
  • Subsurface
  • Swimming

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Mechanical Engineering
  • Artificial Intelligence
  • Electrical and Electronic Engineering
  • Applied Mathematics


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