Supplementary Materials

Sidewinding with minimal slip: Snake and robot ascent of sandy slopes

Hamidreza Marvi, Chaohui Gong, Nick Gravish, Henry Astley, Matthew Travers, Ross L. Hatton, Joseph R. Mendelson III, Howie Choset, David L. Hu, Daniel I. Goldman

Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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  • Materials and Methods
  • Figs. S1 to S6
  • Table S1
  • Full Reference List

Images, Video, and Other Other Media

Movie S1
A sidewinder rattlesnake climbing on loose sand. The videos illustrate sidewinding motion of a snake on inclinations of 0, 10, and 20° at real-time speed followed by 4-times slower speed. The side by side videos show each trial from two different angles.
Movie S2
The CMU robot climbing loose sand at wave frequency of f = 0.08 Hz. At inclination of 10 degrees the robot pitched at contact length of l/L = 0.28 and slipped at l/L = 1. The CMU robot could successfully climb inclination of 10° at l/L = 0.55. The last two videos show the robot climbing inclinations of 5 and 20o at similar contact lengths successfully (l/L = 0.49 and 0.45, respectively). However, due to the presence of local slipping at the higher inclination angle (θ = 20°) the step length is shorter and thus the speed is slower
Movie S3
Movements of Other Crotaline Vipers on Horizontal and Inclined Sand. Sequence 1- A rock rattlesnake (Crotalus lepidus) uses lateral undulation on level sand. Sequence 2 - A speckled rattlesnake (Crotalus mitchellii) uses concertina with rectilinear locomotion on level sand (2x speed). Sequence 3 - A Mexican pitviper (Mixcoatlus melanurus) attempts to move using concertina locomotion on horizontal sand, but fails to make forward progress (3x speed). Sequence 4 - A pigmy rattlesnake (Sistrurus miliarius) attempts to move using lateral undulation on horizontal sand, but fails to make forward progress. Sequence 5 - A speckled rattlesnake (Crotalus mitchellii) uses concertina with rectilinear locomotion on 10° inclined sand (2x speed). Sequence 6 - A ridge-nosed rattlesnake (Crotalus willardi) attempts to move using lateral undulation on 10° inclined sand (uphill is upwards in the video), but fails to make forward progress. Sequence 7 - A Mexican pitviper (Mixcoatlus melanurus) attempts to move using concertina locomotion on 10o inclined sand, but fails to make forward progress. Sequence 8 - A pigmy rattlesnake (Sistrurus miliarius) attempts to move using lateral undulation on 10° inclined sand (uphill is upwards in the video), but fails to make forward progress.
Movie S4
Fluidizing sand using an air-fluidized bed. We constructed a setup to prepare a uniform and consistent state for the granular media before each trial. Our fluidized bed has a porous floor allowing the air to uniformly flow through the entire sand and letting it resettle into an equilibrium condition. As shown in this video, regardless of the initial state of the sand we were able to achieve a loosely packed granular media with a smooth surface after the fluidization process.
Movie S5
A sidewinder rattlesnake climbing loose sand at an inclination of 27°. The video is sped up 4 times and illustrates the extended contacts the snake makes during sidewinding motion on the highest possible angle (angle of maximum stability) on loose sand.