Morphological intelligence counters foot slipping in the desert locust and dynamic robots

Abstract

During dynamic terrestrial locomotion, animals use complex multifunctional feet to extract friction from the environment. However, whether roboticists assume sufficient surface friction for locomotion or actively compensate for slipping, they use relatively simple point-contact feet. We seek to understand and extract the morphological adaptations of animal feet that contribute to enhancing friction on diverse surfaces, such as the desert locust (Schistocerca gregaria) [Bennet-Clark HC (1975) J Exp Biol 63:53-83], which has both wet adhesive pads and spines. A buckling region in their knee to accommodate slipping [Bayley TG, Sutton GP, Burrows M (2012) J Exp Biol 215:1151-1161], slow nerve conduction velocity (0.5-3 m/s) [Pearson KG, Stein RB, Malhotra SK (1970) J Exp Biol 53:299-316], and an ecological pressure to enhance jumping performance for survival [Hawlena D, Kress H, Dufresne ER, Schmitz OJ (2011) Funct Ecol 25:279-288] further suggest that the locust operates near the limits of its surface friction, but without sufficient time to actively control its feet. Therefore, all surface adaptation must be through passive mechanics (morphological intelligence), which are unknown. Here, we report the slipping behavior, dynamic attachment, passive mechanics, and interplay between the spines and adhesive pads, studied through both biological and robotic experiments, which contribute to the locust's ability to jump robustly from diverse surfaces. We found slipping to be surface-dependent and common (e.g., wood 1.32 ± 1.19 slips per jump), yet the morphological intelligence of the feet produces a significant chance to reengage the surface (e.g., wood 1.10 ± 1.13 reengagements per jump). Additionally, a discovered noncontact-type jump, further studied robotically, broadens the applicability of the morphological adaptations to both static and dynamic attachment.

Keywords: friction; jump; locust; robot; slip.

Fig. 1.

The desert locust’s jumping behavior. (A) Side-view video snapshots of a desert locust (S. gregaria) jumping trial. (B) Photo of the locust’s hindfoot. (C) Body $XY$-motion during jumping trials where the locust had either no (none), type-2, type-1 (one leg), and type-1 (two legs) slips (males only; Trial Details). Tracking stops when the last foot leaves the surface. Jumping angles, ${\theta }_J<45^{°}$ (gray region), require friction coefficients >1, which are generally not achievable in the traditional Coulomb friction model.

Fig. 2.

Experiential surfaces compared with the locust. (A) Surface materials (3D surface profilometer micrographs). (Magnification: 100$\times$.) (B) Surface cross-sections compared with the locust’s spines and adhesive pads.

Fig. 3.

Locust slipping behavior. (A) Body accelerations during jumping trials where the locust had no (none), type-2, type-1 (one leg), and type-1 (two legs) slips (males only; Trial Details). Here, the shaded regions represent a SD around the mean. (B) Type-1 slip: two video snapshots where the foot does not reengage and leaves the surface. (C) Type-2 slip: two video snapshots where the foot reengages with a single spine. In B and C, motion of the red circle represents the approximate motion of the feature in the two images.

Fig. 4.

Locust experimental results per jump (per-leg rates are half), divided into slip type (type 1 or 2) and energy regions (planting, early, middle, or late). (A) Average slipping ratios (slips/jump) for each slip type on each material. (B) Material significance matrix, which compares the slipping ratios of each material within a single slip type and energy region of A, to determine significance of the differences in the means [e.g., type-1 slip and planting (upper left quadrant) presents the 10 unique significance measures between all five materials]. The diagonal values represent the slipping ratios (slips/jump), where zero values indicate that no slipping events were observed. *P $\le$ 0.05; **P $\le$ 0.01; ***P $\le$ 0.001. n represents the number of trials on each material.

Fig. 5.

Locust friction mechanisms. (A) The locust’s foot with spines and adhesive pads (3D surface profilometer micrograph). The passive two-axis joint allows for nearly 180° in the sagittal plane and a difference of −10° in the frontal plane. (Magnification: 100$\times$.) (B) Spine-asperity interaction plot which determines the potential increases in the effective loading angle ${\theta }_{SL}^{*}$ as a function of the spine tip radius, $r_s$, asperity radius, $r_a$, and asperity height, $h_a$. The average asperity radius ratios, $r_a/r_s$, of the tested materials are listed above the plot. (C) Adhesive pad interaction plot, which determines the passive loading coefficient, $C_{NF}$.

Fig. 6.

Robot experimental results of the SLIP foot. (A) Robotic SLIP foot diagram. (B) Contact jump (glass), where the foot preload is zero (high-speed video snapshots). (C) Noncontact jumps (sandstone), where the foot preload is zero (high-speed video snapshots). A type-3 slip, where the foot loading is greater than the surface friction but does not leave the surface, is shown. Motion of the red circle represents the approximate motion of the feature in the images. (D) Experimental results per jump (per leg rates are half) for the SLIP foot and each constituent part separated into contact and non-contact-type jumps. Feet include: SLIP, complete foot; SLIP-none, no pad or spines (3D-printed ABS pad base); SLIP-pad, no spines; and SLIP-spine, no pad. (E) Robot foot tracking of noncontact jumps, presenting the jumping-axis velocity, slip-axis velocity, and behaviors of symmetric and asymmetric feet, such as reorientation, contact, planting, bouncing, and mechanism traits such as variable cable friction. (F) Robot experiments, for flat and 45° surface angles, showing no loss of jumping performance. Robot experiments at twice the energy (80% increase in energy density due to an additional 13.2 g), comparing the flat performance to that of type-3 slipping on wood at a 45° surface angle, are shown (superimposed high-speed video snapshots).

Fig. 7.

Mass normalized translational jumping energy ($E_N$) for different types of slips (Trial Details and Slip Energy). (A) Locust: males only. (B) Robot: SLIP foot at a 45° surface angle. † Data are from the SLIP-none foot. (C) Simplified model (Slip Energy) for determining the ratio of translational and rotational energies in the event of a type-1 slip. (D) Locust: estimated $E_N$ as a function of the position, within the jumping cycle, in which a type-1 slip occurs. Assumed jumping angle is 45°. Energy regions (planting, early, middle, or late) are shown for an approximate leg length of 20 mm. Approximate position for the included type-1 (one leg) slip data from A is shown. Notes: Work is measured from jump initiation to foot separation, where each slip type is composed of slips from approximately the early knee angle region, to accentuate the energy losses, and covers all materials in which the behavior was observed. *P $\le$ 0.05; **P ≤ 0.01; ***P $\le$ 0.001; n.s., not significant. Variables: number of trials, n; contact-type jump, C; and non-contact-type jump, N.