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Tail use improves performance on soft substrates in models of early vertebrate land locomotors

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Science  08 Jul 2016:
Vol. 353, Issue 6295, pp. 154-158
DOI: 10.1126/science.aaf0984
  1. Fig. 1 Target and model systems for understanding early tetrapod locomotion on granular media.

    (A) A reconstruction of Ichthyostega (∼360 million years ago), an example of an early tetrapod body plan, by Raul Martin. (B) Skeletal reconstruction of Ichthyostega, an example of an early tetrapod body plan [from (20)], highlighting the pectoral limbs (green) and tail (blue). (C) The mudskipper (Periophthalmus barbarus), a biological model for early terrestrial locomotors. (D) A micro–computed tomography scan reconstruction of a mudskipper skeleton, highlighting the pectoral fin (green) and tail (blue). (E) The MuddyBot, a 3D printed robot developed to model the locomotion of crutching early tetrapods. Limbs are in green and the tail is in blue.

  2. Fig. 2 Mudskipper locomotion on granular media at different substrate inclines (θ).

    (A and B) Dorsal-view video frames of a mudskipper fish on dry, loose sand inclined at 0° (A) and 20° (B) (movies S1 and S2). Yellow solid lines along the longest tail fin ray and from between the eyes to the anterior edge of the dorsal fin are used to compute the tail angle (α2) in (E). The tail is not used propulsively in (A), although it moves slightly; in (B), the tail is used for propulsion. (C to E) Horizontal forward displacement per cycle (Δx) in body lengths (BL) for a single trial (C), vertical displacement (Δy, measured from eye) (D), and tail angle (α2) (E) of mudskippers on sand at 20° incline. Cycles without tail use are indicated by green regions; cycles with tail use are indicated by blue regions (determined from video inspection). Missing values of α2 are when the tail fin was out of view. (F) Δx at all inclines (θ) for steps without (green) and with (blue) tail use. Error bars denote SD. (G) Percentage of cycles with propulsive tail use across substrate inclines.

  3. Fig. 3 Robophysical experiments on granular media at various substrate inclines (θ).

    (A) 3D model of MuddyBot, showing ranges of motion for limb retraction (green arrow, 60°) and tail motion (blue arrow, 90°). Limb adduction (ψ, –5° to 20°, where 0° is horizontal) and limb supination (φ, 0° to 60°, where 0° is vertical to the limb) are labeled, with other arrows showing directions of limb and tail motion during thrust phase. (B and C) Kinematics of a single trial of MuddyBot (φ = 15°, ψ = 15°) moving for six cycles, without tail use (green) and with tail use (blue), on level (θ = 0°) (B) and inclined (θ = 20°) (C) poppy seeds. (D and E) First-step net displacement versus adduction and supination angles on θ = 0° (D) and θ = 20° (E) poppy seeds. Blue shading shows regions of identical supination angle for clarity. Vertical lines denote SD > 0.01. Gray shading indicates negative values.

  4. Fig. 4 Geometric mechanics model of MuddyBot locomotion.

    (A) A diagram of the simulation, showing the limb angle (α1) and tail angle (α2) as well as the reaction forces used to compute the local connection (see supplementary materials) between body deformation and body displacement. (B) The ratio of forces parallel and perpendicular to the limb surface during poppy seed drag experiments at various drag angles to the direction of motion, insertion depths, and substrate slopes. Intrusion depths are 1 cm (crosses) and 3 cm (circles), with θ = 0° (brown), 20° uphill (orange), and 20° downhill (green). The black line represents the ratio of perpendicular and parallel equations (fitted independently; see supplementary materials). (C) First-step displacement (without slip) of the robot and simulation at all inclines (ψ = 20°, φ = 0°), showing close agreement between the simulation and robot performance. Red and pink bars indicate the optimal and worst gaits, respectively. (D and E) Local connection vector field for θ = 0° (D) and θ = 20° (E) media, showing the limb only with tail dragging (purple) and tail gaits (light blue), as well as calculated optimal (red) and worst (pink) gaits.