Morphological Intelligence Counters Foot Slipping in the Desert Locust and Dynamic Robots

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

Matthew A. Woodwarda and Metin Sittia,1

aPhysical Intelligence Department, Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany

Edited by John A. Rogers, Northwestern University, Evanston, IL, and approved July 20, 2018 (received for review March 10, 2018)

During dynamic terrestrial locomotion, animals use complex mul- including hydrophobic glass (contact angles of 94.7◦/84.0◦, n = tifunctional feet to extract friction from the environment. How- 119), hydrophilic glass (contact angles of 32.6◦/21.6◦, n = 111), ever, whether roboticists assume sufficient surface friction for wood (sawn pine, n = 113), sandstone (n = 112), and mesh (steel, locomotion or actively compensate for slipping, they use rel- n = 95), where n represents the number of trials (Fig. 2, Table 1, atively simple point-contact feet. We seek to understand and and Surface Preparation). These materials were selected to both extract the morphological adaptations of animal feet that con- challenge and isolate the two major attachment mechanisms of tribute to enhancing friction on diverse surfaces, such as the the locust: the spines, whose contribution to surface friction is desert locust (Schistocerca gregaria) [Bennet-Clark HC (1975) J Exp unknown, and wet adhesive pads (Fig. 1B). We proposed that Biol 63:53–83], which has both wet adhesive pads and spines. A the glass would sufficiently isolate the adhesive pad behavior buckling region in their knee to accommodate slipping [Bayley TG, and the change in wettability would challenge the wet adhesion, Sutton GP,Burrows M (2012) J Exp Biol 215:1151–1161], slow nerve whereas the wood, sandstone, and mesh would sufficiently iso- conduction velocity (0.5–3 m/s) [Pearson KG, Stein RB, Malhotra late the spine behavior, and the change in surface roughness and SK (1970) J Exp Biol 53:299–316], and an ecological pressure to cohesion would challenge the spine friction (42). We recorded enhance jumping performance for survival [Hawlena D, Kress H, the foot behavior for each material with a high-speed camera; Dufresne ER, Schmitz OJ (2011) Funct Ecol 25:279–288] further sug- further details are presented in Locust Experiments. Initial obser- gest that the locust operates near the limits of its surface friction, vations of the jumping angles (Fig. 1C) and accelerations (Fig. but without sufficient time to actively control its feet. Therefore, 3A) suggest that the locust’s feet exhibit frictional properties all surface adaptation must be through passive mechanics (mor- beyond that predicted by the traditional Coulomb friction model. phological intelligence), which are unknown. Here, we report the To quantify the performance of the locust’s feet on each sur- slipping behavior, dynamic attachment, passive mechanics, and face, individual slipping events were counted and categorized by interplay between the spines and adhesive pads, studied through whether the foot reengaged the surface after the slip as (type 1 both biological and robotic experiments, which contribute to the or 2) slips and the potential energy lost as (planting, early, mid- locust’s ability to jump robustly from diverse surfaces. We found dle, or late) slips (Fig. 4). The slip-type categories include type-1 slipping to be surface-dependent and common (e.g., wood 1.32 ± slips, where all remaining energy is lost, and type-2 slips, where 1.19 slips per jump), yet the morphological intelligence of the feet a slip and reengagement occur, resulting in minimal energy lost produces a significant chance to reengage the surface (e.g., wood (Fig. 3 B and C); reengaging the surface occurs when the foot 1.10 ± 1.13 reengagements per jump). Additionally, a discovered comes to rest after a slip event. The potential energy lost divides noncontact-type jump, further studied robotically, broadens the applicability of the morphological adaptations to both static and dynamic attachment. Significance

locust | robot | slip | friction | jump Animals in natural environments necessarily come into contact with surfaces having differing orientations and materials. However, not much is known about how their feet contribute errestrial locomotion emerges from interaction with one’s to friction, particularly in the case of dual-attachment mech- Tenvironment (1), which is further complicated by the diver- anisms and passive mechanics (morphological intelligence). sity of surface materials and dynamic timescales. Locomotion We study the desert locust’s (Schistocerca gregaria) mor- studies have explored dynamics with point-contact feet (2–10), phology, spines and adhesive pads, and jumping behavior rigid, rough (11–13), mesh (14), and smooth (15, 16) sur- to extract traits that contribute to enhancing friction. Our faces, deformable (17) surfaces, granular (18–25) surfaces, and results demonstrate the potential contribution of morpholog- obstructed environments (26, 27) elucidating traversing behav- ical intelligence to solving complex dynamic locomotion prob- iors, optimal strategies, and new environmental material models lems. We anticipate that this study will inspire further research (28). However, interactions tend to dissipate energy, which is of the strategies used by animals to interact dynamically with well studied for granular surfaces [environmental dissipation diverse surfaces. Furthermore, the concepts presented can be (28)], but not for rigid surfaces (body dissipation) which, through easily adapted to, for the enhancement of, existing simple slipping, tend to dissipate energy in the tissues (29). Scansorial miniature and state-of-the-art large-legged terrestrial robots. robots using either spines (30–32) or gecko-inspired dry adhesives (33–36) have demonstrated the frictional properties of each Author contributions: M.A.W. and M.S. designed research; M.A.W. performed research; of these attachment mechanisms on rigid surfaces. However, M.A.W. contributed new reagents/analytic tools; M.A.W. analyzed data; and M.A.W. and the diversity of surfaces in the environment sometimes neces- M.S. wrote the paper. sitates multiple attachment mechanisms, and, whereas humans The authors declare no conﬂict of interest. have developed shoes for ice, grass, wood, rock, track, slip, and This article is a PNAS Direct Submission. stick, animal feet must be multifunctional. This open access article is distributed under Creative Commons Attribution- Desert locusts (1, 37–40) [Schistocerca gregaria; female, 2.32 ± NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). 0.31 g; male, 1.67 ± 0.14 g; t(30) = 10.0, P = 0.00] escape-jumped 1To whom correspondence should be addressed. Email: [email protected] (41) from an elevated platform in response to a rapid approach This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. from behind by the experimenter (Fig. 1A, Movie S1, and Ani- 1073/pnas.1804239115/-/DCSupplemental. mals and Statistics). The surface material is one of ﬁve selected, Published online August 22, 2018.

E8358–E8367 | PNAS | vol. 115 | no. 36 www.pnas.org/cgi/doi/10.1073/pnas.1804239115 Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 o ohsai n yai ufc neatos h lower The interactions. surface dynamic and designed are static feet locust’s both the the for of of that that suggests adaptations S2A), morphological with 4A; Fig. the along Appendix, Fig. (SI discovery, behavior behavior, This jump noncontact (overall 4B). Fig. surface data, discovered the the statistical for reengage not to if robustness possibility low proba- very high the suggest yet would common, bility be would slipping that reasoned We Discussion and Results locust a the of uses that which to 6A, structure 44)], (Fig. leg (43, and jump [MultiMo-Bat catapult-type platform developed similar were robotic feet robotic the traits locust, for morphological the on of investigate inves- modification to To difficult and jump). (contact importance surface the the the which tigate with in jump contact a in with begins compared foot rest, to the comes occurs slip foot with a the jump) sometimes before and (noncontact contact, contact sufficient without in or feet surface, their initiate without occasionally robotic plant- jump locusts that The a the discovery region. the and from this comes minimal, slip within ing is lift-off predict energy dynamics remaining platform from the excluded be as henceforth will analyses, slips Late of kinematics platform. the robotic from the come fractions energy potential the where angle, 135] knee of by loss defined energy tial ranges, energy four θ into events slip the friction Coulomb traditional the in achievable not model. generally are which ihrn nn) ye2 ye1(n e) n ye1(w es lp (males slips angles, legs) (two Jumping type-1 and leg), locust’s (one the only; type-1 of type-2, Photo (none), (B) no trial. either jumping ) gregaria (C (S. locust hindfoot. desert a of shots 1. Fig. odadadSitti and Woodward 10 mm A k agsa h ne ftesi,wihrpeettepoten- the represent which slip, the of onset the at ranges , ◦ .Takn tp hntels otlae h surface. the leaves foot last the when stops Tracking Details). Trial 3,06% and 0.6]%, [38, = C ieve ie snap- video Side-view (A) behavior. jumping locust’s desert The and Foot, Robotic

Body ) Vertical Motion (mm) 20 30 10 15 25 35 0 5 0 θ J XY < θ θ J 45 k mto uigjmigtil hr h outhad locust the where trials jumping during -motion >45 Type-1 (2Legs) Type-1 (1Leg) Type-2 None 5 [0] ◦ o 1 mm ◦ ga ein,rqiefito coefficients friction require region), (gray Horizontal Motion(mm) 10 ≈100%, θ k 15 180] [135, oi S2). Movie 15 θ 20 k B 0 45] [0, ◦ Hindfoot Adhesive Pads 06 ],respectively, 0]%, [0.6, = 25 ◦ 10 38]%, [100, = 30 θ 35 J <45 o 40 Spines θ k [45, >1, hneo ye1siso h og ufcs(od 0.22 (wood, surfaces rough 0.24 the on sandstone, slips type-1 of chance e’ aitladfotlpae Fg 5A, the (Fig. from planes measured frontal A angles and characteristic sagittal two leg’s by defined tibia, Spines. 4B). (Fig. surfaces dynamically with two interacting the difficulty that equal suggesting have mechanisms not, friction did smooth slips and type-1 planting rough the the surfaces, showed between slips differences type-1 significant middle pervasive and early whereas However, friction. 0.88 glass, 0.83 glass, (hydrophobic surfaces smooth n a ofimdb h outeprmns nwihasig- a slips type-2 which 4.0, mean in (1.10 the wood experiments, between for locust observed was the difference rates by slip nificant higher confirmed in was result would and reasoned we which Interaction), wood, roughness: stone, area (mean asperities (r tip spine the 13.4 of load- model nondimensional the a increasing developed angles effectively surface, differing fric- angle, overall have enhance ing the which to of asperities, that able with than are interacting Spines by (14). running tion rapid surfaces for used challenging and S1) on section Appendix, (SI forefeet the h icvr fatoai asv on Fg 5 (Fig. joint to passive two-axis adapted a by of supported instead discovery further surface the was are conclusion 3D This spines a asperities. existing the using hold surface that wood suggested the profilometer on indentations spine any decreas- 0.02 1.17 mesh, the [wood, surfaces 0.59 however, rough sandstone, asperity; increasingly vs. an on rates create slip or ing of enhance loss to wood minimal in resulting conditions, rough- energy. of jumping dynamic range broad a and on asperities nesses hold and find to developed (0.22 0.3, wood = t(222) on slips 1 rs-etoscmae ihtelcs’ pnsadahsv pads. adhesive and spines locust’s the 100× with (Magnification: compared cross-sections micrographs). profilometer surface (3D 2. Fig. B A h pnsmyb bet eert h otsraeo the of surface soft the penetrate to able be may spines The Height (μm) and P 200 400 600 Y-Axis (mm) radii, asperity and µm) ufc materials Surface (A) locust. the with compared surfaces Experiential S n al ) oetal dpe rmtoese on seen those from adapted potentially 2), Table and B, .0(i.4.Hwvr h iia hneo type- of chance similar the However, 4). (Fig. 0.00 = 0 4 2 0 h outssie rtuefo h itledo the of end distal the from protrude spines locust’s The a 0 01 75.13 = θ ± ± SL ∗ Mesh Mesh P .0 ute ugs pcaiainfrspine-based for specialization suggest further 0.70) 0.14, oamr ufc-epniua retto.We orientation. surface-perpendicular more a to , 1 .4 ugse httelcs’ pnsaewell are spines locust’s the that suggested 0.74, = ± ± )sol els tbe(i.5B (Fig. stable less be should µm) .3 n adtn (0.56 sandstone and 1.13) 18 6.6, = t(118) Spine Tip ≈23um .7 n eh 0.0 mesh, and 0.47; ± 010101 0 0.90, adtn Wood Sandstone adtn Wood Sandstone ± 1 20 4.2, = t(210) .4 n adtn (0.24 sandstone and 0.44) X-Axis (mm) X-Axis (mm) r a P 0 hc rdce htsmaller that predicted which , PNAS .0 n alr oidentify to failure and 0.00] = Adhesive Pad≈0.5→1mm 1 | ± P ± o.115 vol. .)cmae othe to compared 0.0) .0 adtn vs. sandstone 0.00; = S i.S1 Fig. Appendix, SI .6 n hydrophilic and 0.66; a 0 ,wihconnects which A), 10. = ± Glass Glass | 0.89), 1 o 36 no. 6 Surface (B) .) s ;sand- µm; and 23.3 = 22 = t(212) ± ± ± | (μm) Height 0.47), Spine 0 100 200 300 400 500 600 0.44; E8359 1.17, ±

BIOPHYSICS AND ENGINEERING COMPUTATIONAL BIOLOGY Table 1. Summary of surface roughness properties attachment mechanism. Spines effectively increase the contact Material S , µm R , µm Maximum height, µm angle between the foot and surface, reducing the necessary fric- a a tion coefficient, but still relying on the applied load. Conversely, Glass* 0.02 0.01 0.19 pad-based friction is a function of both the applied load and the Wood (pine) 10.60 0.68 212.07 adhesion; however, the normal load required for adhesion is typ- Sandstone 75.13 1.16 581.12 ically at least an order of magnitude less than the frictional force Mesh (steel) 174.26 1.15 665.39 produced for flat adhesives and greater than that for structured adhesives (46, 57, 58). In this way, the locust has developed a The arithmetic mean area roughness, S (asperities), arithmetic mean line a strategy, whereby the spines receive the majority of the force to roughness discretized by the average spine tip radius of 23 µm, Ra (friction), and height range of each material. maximize their friction and chance of interlocking, and the adhe- *The transparency and reflectivity may have added noise to the sive pads rely instead on passive loading to saturate the adhesion measurements. and enhance friction. Balancing the performance of the attachment mechanisms is achieved by changing the configuration, magnitude, and distri- the spine to the tibia. This joint introduces compliance into each bution of the locust’s applied forces (applied FA ≈ 200 mN, spine, allowing each to locate the valley of an asperity through adhesive pads FA⊥ ≈ 45 mN, spines FA⊥ ≈ 86 mN; maximum ◦ changing its sagittal-plane angle up to ≈ 180 and increasing its per foot), where the robot (applied FA ≈ 10.8 N, adhesive pads ◦ contact angle by ≈ 10 , thus enhancing its hold (45). FA⊥ ≈ 4.7 N, spines FA⊥ ≈ 2.8 N; maximum per foot) had 54 times more force than the locust (Foot Forces), where FA⊥ is Adhesive Pads. The locust’s first tarsal segment contains three the force perpendicular to the surface. First, the robotic “multi- separate adhesive pads (Fig. 1B) which rely on preloading to Surface Locust-Inspired Passively-adaptable” (SLIP) foot had generate friction (46). However, the spines, attached to the tibia both the spines and adhesive pad mounted on the first tarsal and positioned more distally than the ankle joint, limit the defor- segment, allowing both to maintain a prescribed orientation mation of the relatively soft adhesive pads [effective modulus of throughout all leg angles, eliminating the loss of spine interac- 300 kPa (47)] and thus the direct loading (Fig. 5A). The max- tion at low jumping angles and high knee angles (SI Appendix, imum deformation force (45 mN), assuming spherical hertzian Fig. S1B). Second, whereas the locust’s ≈66% of the perpendic- contact and complete deformation of the hemispherical pads, ular force was not sufficient for penetration of the wood surface, is only 32.3% of the maximum load per foot. We therefore the robot easily penetrated the surface at ≈37%, allowing for reasoned that the foot morphology may indirectly enhance the stable mechanical interlocks on the soft wood surface. Finally, loading of the pads. This was confirmed by analysis of the the remaining force was then redistributed to the adhesive pads torque on the first tarsal segment, where the model (Adhesive Pad Interaction) produced a loading coefficient, CNF , which suggested that the locust can indirectly enhance its pad loading as a A 300 function of the friction coefficient (Fig. 5C). The low margin pre- None Type-2 dicted in the model and transition between static and dynamics Type-1 (1 Leg) ) regimes during slipping, which tends to reduce the interaction 2 200 Type-1 (2 Legs) strength, would suggest, contrary to our observations (Fig. 4), that reengagement is impossible. The solution may be in the leg 100 structure and jumping behavior of the locust, similar to that of the robotic platform, which produces an increasing force over approximately the first half of the jumping cycle (Fig. 3A). This 0 increase in applied force may be compensating for the reduced

interaction strength, making the observed reengagements of the Body Acceleration (m/s adhesive pads possible. -100 The desert locust’s adhesive pads secrete an emulsion of 0 10203040 “lipidic nano-droplets dispersed in an aqueous liquid” (48) pas- Body Motion (mm) sively during the deformation of its sponge-like cuticle, as with other insects (49). However, the wet adhesion of the locust B Type-1 Slip C Type-2 Slip showed no specialization for hydrophobic or hydrophilic surfaces (natural examples in refs. 50–52), as evidenced by the similar chance of type-1 [hydrophobic glass 0.83 ± 0.66 and hydrophilic glass 0.88 ± 0.70, t(224) = 0.6, P = 0.57] and type-2 [hydrophobic glass 0.34 ± 0.66 and hydrophilic glass 0.23 ± 0.46, t(212) = 1.6, P = 0.11] slips (Fig. 4). This corroborated results for climbing aphids (53) and confirmed a supposition for locusts (48), which suggests that the emulsion can tolerate changes in surface wettability without affecting its overall adhesive properties. Furthermore, as unstable (coalescing) emulsions lead to surface films (demulsification) that may reduce friction (54), the result suggests that either that the locust’s emulsion is stable (dis- 0 10 mm 0 1 mm persed) or renewed sufficiently often to remain dispersed until use. The dispersed droplets each create a lipid–water interface Fig. 3. Locust slipping behavior. (A) Body accelerations during jumping tri- allowing a number of capillary bridges (55, 56) between the foot als 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 and surface to form, thereby enhancing friction through contact SD around the mean. (B) Type-1 slip: two video snapshots where the foot pinning and viscous forces. 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 Coupled Attachment Mechanisms. The difference in the loading the red circle represents the approximate motion of the feature in the two behavior corresponds well with the particular needs of each images.

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nietegco hc utatvl eahisfe (35). feet its detach two, actively the prop- must to separating which quickly gecko, passively it front the surface, initiated, unlike from entire was peel the peeling through to once agated cases, observed both was In the 6A) back. of (Fig. large peeling pad robot’s circumferential the rectangular whereas use 5A), (Fig. interface. to pads spherical the observed approximately through was cracks of locust propagation The the adhesive’s resist the to and contact ability highly surface intimate gecko’s continu- limiting adhe- the large, surfaces, unlike relatively The ous have robot, spines. (46), and adhesives the locust fibrillar a the of discretized that both removal of indicating for pads liftoff, required sive at been was slightly have force foot sandstone), only)] small the Nonem- (robot (e.g., perturb wood robot. to asperities [e.g., observed and the spines locust escape embedded the whereas simply in spines mechanisms bedded both for sively Detachment. grains. supported sandstone Therefore, that the to of not. forces cohesion (30, interaction the were spines by individual several robot the between reduce the load to the of 45) share to forces significant robot the foot the requiring lim- strength, the the interaction in within materials’ both increase surface on were the forces pads of maximum adhesive its the and while spines that locust’s suggests the This 0.60 6D). robot (contact, (Fig. the type-3 face whereas of surfaces, observed chance 1.60 glass higher noncontact, were the much occurrences on a only few showed and a locust less Only the is load. in strength applied surface-interaction the the than when occurs which 6C), and Slip. Type-3 deiepd 3 ufc rfioee irgah.Tepsietwo-axis passive 180 The nearly micrograph). for allows profilometer joint surface (3D pads adhesive 5. Fig. ltwihdtrie h oeta nrae nteefcielaigangle height, loading effective the in increases θ potential 100× the determines (Magnification: which plot plane. frontal the in il r itdaoetepo.( C plot. coefficient, loading the passive the above determines listed are rials BC SL ∗ Asperity Height Ratio, ha/ra 0 1 2 safnto ftesietpradius, tip spine the of function a as 012345678 Wood (0.5) Glass (8.6e ,tp- lp r hto otnossipn (Fig. slipping continuous of that are slips type-3 S3), Movie A seiyRadiusRatio,r Asperity X-Axis (mm) h h outsfo ihsie and spines with foot locust’s The (A) mechanisms. friction Locust

Locust, Robot 0 1 2 3 a 01234 h vrg seiyrdu ratios, radius asperity average The . L1 M2 L2 Sagittal -4 i.S2B Fig. Appendix, (SI locust the in observed First Plane ) eahetfo h ufc sacmlse pas- accomplished is surface the from Detachment Mesh (7.5) Sandstone (3.2) M1 Interlocking Mechanical ± θ*>90 SL .4 lp,abi nyo h adtn sur- sandstone the on only albeit slips, 0.84) θ*<45 SL a o /r ◦ s ntesgta ln n ifrneof difference a and plane sagittal the in o Y-Axis (mm) Frontal Plane θ* 0 20 40 60 80 100 120 Passive Joint,2-Axis deiepditrcinpo,which plot, interaction pad Adhesive ) SL +θ -θ

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Spine Frontal Plane (0.0 ms) (7.1 ms) (9.3 ms) (41.4 ms) (57.1 ms) D Planting Early Middle Late Materials: 1) Wood (pine) 2) Sandstone 3) Glass (hydrophilic) SLIP SLIP-none SLIP-pad SLIP-spine Type-1 Type-2 Type-3 Type-1 Type-2 Type-3 Type-1 Type-2 Type-3 Type-1 Type-2 Type-3 3 2 2 3 Co

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) 4 Cable 4 4.52 m 4.21 m /s Friction Reorientation Contact and Loading Bouncing 2.63 m 2.75 m 3 3 Leg Ground 2.58 m 2.58 m Contact ABS (2X Energy, Flat) ABS (2X Energy, Wood (2X Energy, 45 deg) (2X Energy, Wood ABS (Flat) Sandstone (45 deg) Wood (45 deg) Wood Glass (45 deg) 2 2 Planting Middle

Foot Velocity (m Type-2 Type-2 1 1

0 0

-1 -1 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 Foot Motion (m) Foot Motion (m)

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).

Foot Asymmetry. We posited that the locust’s asymmetric foot, jumps (Fig. 6 C and E, symmetric). This was confirmed by robotic while working well for contact jumps, would have difficulty reori- experiments (SI Appendix, Fig. S3), where the initial misalign- enting to significantly misaligned surfaces during noncontact ment was set at 45◦, and the foot was not only observed to slip,

E8362 | www.pnas.org/cgi/doi/10.1073/pnas.1804239115 Woodward and Sitti Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 L1 .A 7A). (Fig. 7 cases (Fig. (none) no-slip model and simplified by leg) (one confirmed type-1 experimentally stage was early This contact. in only the as is 7C), leg (Fig. body single the a on to torque common a symmetry, introducing animals, sagittal-plane most the break they as formance locust, the (calculated, of robot cases and slip leg) (one the in type-1 difference significant signifi- the in 7 future by resulted [Fig. as slips loss left type-1 energy single are cant previous, and the energy Unlike significant work. remove may higher velocities whereas velocities, foot-sliding slow relatively represented robot, the in loss 0.09, locust, = t(9) the of cases slip (E type-2 energies jumping translational 7 (Fig. Performance. Jumping surfaces. diverse on locomotion terrestrial independently 6F dynamic (Fig. support and configuration desired continuously both a to maintain allowed to pad This reorient adhesive leg. and further and spines had pad, the foot adhesive SLIP spines, robotic (SI the the angle decoupled leg whereas the S1B), to Fig. loading. coupled Appendix, were during orientations rotation spine foot thermal locust’s minimize stiffer The to case, used this were in to surface; pads tends the plastic which from pad, away adhesive spines the the rotations of pull torque caused pad loading potentially passive was the adhesive This by 6). Fig. and decoupled, (coupled, S4; spines slipping Fig. type-1 Appendix, significant the showed experiments and where coupled robotic were feet by several confirmed attach- combined was of the This of mechanisms. performance the ment rotational to their integral decoupling is thus motions, segments, separate on pads sive foot symmetric Decoupling. robot’s Rotational the simi- whereas be misalignment. greater surface, must much the tolerate orientation can of morphology the that distances, to short lar from plant can (symmetric rates metric resulted rotational which foot lever-arm, 6E, increased shorter (Fig. a in contact to initial due the was after This surface asymmetric). the off bounced also but planes. specified the from measured are angles *The L2 M2 M1 Spine characteristics Spine 2. Table odadadSitti and Woodward of (F force shear N average an 7.7 to verified was foot SLIP robotic of force shear center and leg was the which (≈ between mass of distance of the effect by the rota- accentuated motion, into further in translational, converted energy resulted of more slips instead but Earlier tional, loss, cycle. energy more jumping only the not in of position significance slip’s the the demonstrated and degradation performance ye1sismyas aea de feto h upn per- jumping the on effect added an have also may slips Type-1 medial. M, lateral; L, nttl aho h outsfe a upr naverage an support can feet locust’s the of each total, In 0 euto ntelocust’s the in reduction >50% 7 e/) hssget ht lhuhtelcs’ foot locust’s the although that, suggests This deg/s). ≈370 A A⊥ and oywidth/2). body P ≈ .3 ye3sissoe iia iia energy minimal similar showed slips Type-3 0.93. = ye2,a vdne ytesmlrnormalized similar the by evidenced as type-2), B, . )o h og n mohsrae.The surfaces. smooth and rough the on N) 7.7 F Ak 3 1.47, = t(3) aitlplane, Sagittal ≈ −155.3 −136.8 ye2sisrsl nmnmleeg loss energy minimal in result slips Type-2 lpEnergy). Slip h oiinn ftesie n adhe- and spines the of positioning The 4 N(F mN 149 126.3 144.1 A C and and ± ± ± ± 2)=1.26, = t(27) ye1(n e),a evidenced as leg)], (one type-1 B, 9.5 9.1 8.0 10.1 P nlst e planes* leg to Angles D .4 oee,teeresults these however, 0.24; = ◦ and N A⊥ E ften-lp(oe and (none) no-slip the of ) N E ≈ N atrdthe captured Energy) Slip ften-lp(oe and (none) no-slip the of bevdbtenthe between observed , 1)=7.86, = t(14) 3 N,weesthe whereas mN), 131 P 6 e/,asym- deg/s, ≈160 .2 n robot, and 0.22, = rna plane, Frontal opassively to ) 47.7 51.2 42.6 41.0 P ± ± ± ± 0.00, = F 8.8 8.4 12.6 7.9 Ak SI ≈ ◦ two-tailed Statistics. (n sandstone (F mechanisms decreasing with ment ( However, friction. angle Coulomb jump than more on rely 45 mis- of a angle jump, to or mechanisms alignment, attachment the verified experiments robot (n (n glass philic (n glass hydrophilic (n (two glass type-1 hydrophilic region: early the from transition (n the glass hydrophilic after leg): just were trials dle (n (n stone (n glass hydrophobic (n glass hydrophilic none: where type, slip each for case worst singu- the given n approximated a the for These energy produce event. jumping would slip the these lar in as effects ranges, similar angle and knee observable early most or planting the in ring Details. Trial with VK-X200) (Keyence nm. 0.1 profilometer surface 3D x high-resolution a with proper softness. Imaging. to relative its cut for and chosen store pine, hardware smooth-cut was local wood a The from size. purchased were mesh steel plasma, Kr a air using by follows: con- measured 80 and as octadecylsilane, at process methoxy(dimethy) glass densation silanization and cleaned butylamine the a in of through immersion some altered of fabricate To chemistry was drying. surface slides for the acetone, gas glass, follows: argon hydrophobic as and the was water, sequence deionized the alcohol, solvents; isopropyl polarity varying with slide Preparation. Surface second. per v641) frames Phantom 1,400 at (VisionResearch, trials jumping camera the viewing digital recorded the to high-speed perpendicular itself The specifically align direction. to were locust dimensions the platform encourage various The to testing selected jump. for locust’s modified be the plat- could of surface small parameters the a center, which the on In placed, event. was the form of viewing unrestricted allowing while before important especially pads, adhesive trials. their smooth-surface clean temperature to them average allowed an also to up 30.5 warmed of The were thermometer. and cold-blooded, lamp heat being a locusts, with terrarium acrylic empty an to rarium was Experiments. Grass Locust conducted. locusts. were the to trials of provided experimental food period no of acclimation source where a main d, supply. the by 5 food abated plentiful than was and less deficiency lamp no nutritional heat or with terrarium stress a Any in housed and store Animals. Methods and Materials and surfaces. events diverse slipping on the locomotion of robust many preserve of severity physical the absence the reduce the into of can in encoded system part yet, intelligence as locust, morphological but desert control, anomaly, the of an of locomotion as dynamic not the slipping highlights study This Summary attachment. maintain to enhanced interaction requiring spine models, and adhesion spine-interaction and adhesive the − ersnstenme ftrials. of number the represents ) nldn lnig( planting including 2), = i.7B Fig. 7A and 3A, 1C, Figs. jump, each after locusts the contain to constructed was box acrylic An ) n ye1(n e) yrpii ls (n glass hydrophilic leg): (one type-1 and 3); = axis ◦ and ) n ye1(n e) yrpii ls (n glass hydrophilic leg): (one 1 type and 3); = C eeotie rmalclpet local a from obtained were gregaria) (S. locusts desert The h ufc n outfo opooyposwr generated were plots morphology foot locust and surface The h eotdsaitclvle eeotie rmtwo-sample, from obtained were values statistical reported The a h olwn ufc radw e lptp:nn (C): none type: slip per breakdown surface following the had t eoebigtaserdt h etn erru.Ti process This terrarium. testing the to transferred being before et,weesignificance, where tests, h eetdjm rasec a nyasnl lpeetoccur- event slip single a only had each trials jump selected The 1). = y ) od(n wood 5), = − < axis ◦ C 45 ) od(n wood 4), = h eetlcsswr rnfre rmtermi ter- main their from transferred were locusts desert The ) od(n wood 6), = h dacn n eeigcnatage were angles contact receding and advancing The . h yrpii ls a rprdb laigaglass a cleaning by prepared was glass hydrophilic The ) yrpii ls (n glass hydrophilic 1), = eouin f130n and nm 1,390 of resolutions ◦ s-rpSaeAaye.Tewo,snsoe and sandstone, wood, The Analyzer. Shape uss-Drop a h olwn ufc radw e lptype: slip per breakdown surface following the had ¨ oe nraigbre nteattach- the on burden increasing comes ) 6). = ) adtn (n sandstone 5), = Ak( n ) n adtn (n sandstone and 1), = ) al (n early 1), = max ) n adtn (n sandstone and 4), = ) = ) n adtn ( sandstone and 9), = ◦ twihpitatcmn must attachment point which at , a endas defined was p, F PNAS A( ) n ide(n middle and 3), = max ) n eh( mesh and 6), = ) od(n wood 2), = | ) o.115 vol. cos(θ ) od(n wood 1), = ) ye3 sandstone 3: type 1); = z − J P )adsandstone and 4) = ,cpue by captured )), ) ye2 hydro- 2: type 1); = axis | ≤ n 0,adsand- and 10), = o 36 no. .5wt null a with 0.05 ) oe(N): none 4); = eouin of resolutions n ) h mid- The 2). = ) ye2: type 6); = ) and 1), = | E8363

BIOPHYSICS AND ENGINEERING COMPUTATIONAL BIOLOGY A Locust Slips hypothesis of equal mean values. The effective degrees of freedom were approximated with the Welch–Satterthwaite equation, and all reported ± *** values represent a SD. All reported statistical data follow the following tem- *** plate: t(n1) = n2, P = n3, where n1 is the effective degrees of freedom, n2 is n.s. the t-critical value, and n3 is the signiﬁcance or P value. 7

6 Spine Orientation. Comparing the sagittal-plane angles of the correspond- ing medial (M) and lateral (L) spines, M1, L1, t(18) = 2.44, P = 0.03, and M2, (J/kg)

N 5 L2, P = 0.03 and t(17) = 2.86, P = 0.01, showed low signiﬁcant differences in the angles, whereas the frontal-plane angles only showed a signiﬁcant 4 difference, albeit low, between M1 and L1, t(18) = 2.85, P = 0.01, indicat- ergy, E 3 * ing only a minor probability of spine asymmetry. However, the angles did indicate that all of the spine would be oriented to interact with the surface

malized Translational 2 r during jumping (Table 2). Jump En No 1 SI Appendix, Fig. S1B shows the relationship between leg, θL, spine, θS, jumping, θJ, and spine loading, θSL = θJ, angles, where θS ≤ 0 indicates that 0 the spine tip is no longer able to interact with the surface. The passive joints None Type-2 Type-1 Type-1 which connect the spines to the tibia give them the freedom to change (n=17) (n=12) (1 Leg) (2 Legs) ◦ (n=6) (n=3) their sagittal-plane angle from the initial positions (Table 2) to nearly 180 B (SI Appendix, Fig. S1B, SP = 180◦). This suggests that the spines can passively Robot Slips locate stable positions on the surface as they are loaded. These joints also allow for approximately −10◦ of rotation in the frontal plane (SI Appendix, *** Fig. S1B, FP-10◦). Therefore, as the spines are loaded, their effective spine n.s. n.s. angle is reduced, broadening the leg angle range over which they can 25 n.s. interact with the surface. This joint will also include some damping, which can be used to reduce the impulse caused by the spine reengaging after 20 a slip, increasing the chance of a successful reengagement. In all, locusts (J/kg)

N have developed spines that can interact with the surface even in extreme ◦ ◦ 15 cases; for example, a horizontal jump (θJ = 0 and initial θL = 90 ) resulted ◦ ◦ in spine angles of θS ∈ [38.8 , 59 ], permitting strong surface interaction. Spine placement, however, typically only allows the more distal medial and 10

alized Translational lateral spines to interact with the surface. m

Jump Energy, E 5 Nor Spine Interaction. The performance of spines is strongly related to the roughness characteristics of the surface, spine angle θS, and spine loading 0 angle θ . We have included surfaces with overhanging asperities and, for None None Type-2 Type-3 Type-1 Type-1 SL our purposes, will calculate an effective increase to the spine loading angle (C) (N) (C) (C) (1 Legs,C) (2 Legs,C) for round asperities as: (n=19) (n=9) (n=7) (n=3) (calculated) (n=3)

−1 C θ*SL = cos (1 − (PpPs)/(1 + Ps)), [1] x FA /2 FA /2 where Ps ∈ [0, ∞] is the asperity radius ratio, ra/rs, and Pp ∈ [0, 2] is the ψ FA Symmetric asperity height ratio, ha/ra, with asperity radius, ra, asperity height, ha, and * ◦ ψ spine radius, rs (Fig. 5B). Mechanical interlocking occurs at θSL + θSL ≥ 90 , ◦ R Mg whereas θSL + θ*SL < 90 reduces the required friction coefficient; for exam- L/2 θJ ple, Sa(wood) = 10.6 µm ⇒ Ps = 10.6/23.3 results in effective increase in the Asymmetric ◦ ◦ spine loading angles of θ*SL (Pp = 2) = 68 and θ*SL (Pp = 1) = 46.6 requiring 10 mm L (Type-1 Slip) a friction coefficient µ = 0.40 and µ = 0.95, respectively, for a horizontal ◦ jump (θJ = 0 ). A friction coefficient of µ = 0.40 is within generally achievable limits, demonstrating that even at extreme jumping angles, the locust’s D None Locust Slips spines greatly enhance the surface friction. We expect the spines to find 6 Type-2 asperities with increasing likelihood on the wood, sandstone, and mesh. The )

g glass, however, does not produce any usable asperities, and therefore the k 5 adhesive pad performance can be isolated. (J/ N 4

, E Adhesive Pad Interaction. Using the morphology (SI Appendix, Fig. S1A) and gy r 3 summing the torques about pad P1 yields an expression for the torque on e segment S1 as follows, En 2

1 MA + FA sin θJrA(µ cos φ − sin φ) + µFadhrA cos φ Jump Normalized Translational Early Middle

Planting Late 0 = Rpr2x + Rp(r2x /r3x )r3x [2] 0 1020304050 Type-1 (1 Leg) Slip at Body Position (mm) where FA is the applied ankle force, MA is the applied ankle torque, and rA is the distance between P1 and the ankle joint JA. Then, Rp is the reac- Mass normalized translational jumping energy ( ) for different Fig. 7. EN tion force at pad P2, Rp(r2x /r3x ) is the reaction force at pad P3, and r2x types of slips ( and ). ( ) Locust: males only. ( ) Robot: Trial Details Slip Energy A B and r3x are the x-distances between pads P1-P2 and P1-P3, respectively. The SLIP foot at a 45◦ surface angle. † Data are from the SLIP-none foot. (C) frictional, µFA sin θJ, and adhesive, µFadh, forces have been substituted in Simpliﬁed model (Slip Energy) for determining the ratio of translational for the applied horizontal force to limit it to that supported by the sur- and rotational energies in the event of a type-1 slip. (D) Locust: estimated face friction. The left side is then related to the applied loads, and the EN 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. angle region, to accentuate the energy losses, and covers all materials in Approximate position for the included type-1 (one leg) slip data from A is which the behavior was observed. ∗P ≤ 0.05; ∗∗P ≤ 0.01; ∗∗∗P ≤ 0.001; shown. Notes: Work is measured from jump initiation to foot separation, n.s., not signiﬁcant. Variables: number of trials, n; contact-type jump, C; and where each slip type is composed of slips from approximately the early knee non-contact-type jump, N.

E8364 | www.pnas.org/cgi/doi/10.1073/pnas.1804239115 Woodward and Sitti Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 odadadSitti and Woodward xrce rmtelcs’ ot h pnsaeselpn one ta at mounted in pins S3 determined steel experimentally are modulus spines h)]—material The foot. locust’s 45 the poor from locust’s extracted the Foot. by Robotic evidenced as lower, much surfaces. smooth loco- been on during permanence have achieved value may actual motion the Therefore, configuration. idealized as sured J/m 0.015 eutn oko deinvle r sflos cflx0-0=1.207 = 00-10 Ecoflex The follows: area. as contact using are J/m values by and 0.036 adhesion calculated measure- curve of was the trials work force-displacement adhesion resulting before of of adhesive stabilize set work measured initial to the the Finally, an adhesion taken. where the were tested, allow ments were to material conducted pads Three the were indenter. foot on hemispherical elastomer 4-mm sites a soft separate using the by 00-20) of Ecoflex curves (Smooth-On, force-displacement pull-off sured Adhesion. of Work pads whereas adhesion, additional for loading and pad the increase to difficult; used angle the load, of under measurement however, exact makes pads by adhesive governed deformable is unloading and loading between tion coefficient, friction angle, the between relationship the presents coefficient, zero, load than frictional less vs. normal the 1.17 00-20, (Ecoflex Adhesion). material pad J/m adhesive (6 foot’s pads SLIP locust’s the of sion glass, of ratios E Poisson’s and moduli elastic radius, the pad effective the where +x rmtekinematics, the from Forces. Foot , Appendix (SI axis center-of-mass the legs, robot’s along S5 the is Fig. of produced sides force two the the bio- synchronize ensuring ten- to use (60), which 100% gears nymphs, immediately. created (Issus) and interact opposite logically planthopper to region mm from spines taken distal the 1 is the allowing surface. inspiration of Finally, of force, the little deformation thickness requires engage initial a spines kPa, to the has 55.2 spines locust, of pad the the modulus of adhesive for sile that deformed the to be similar as is must However, pad pad adhesive the and slipping. spines during where including the jump, of the loading throughout The surface the to orient sively given is force maximum The surface. flat a from punch (59), flat by a of force jumping the where pads, adhesive the of loading range passive angle the side, right r eope rmec te swl steleg, the as well as is other pad each pad, from adhesive The decoupled the feet. are of the dynamics on rotational The fluid with loading. joint, a ankle maintaining the of about forces adhesive Waals symmetric difficultly der elastomeric the van The instead eliminate using asperities. dry, to own are 00-20) its Ecoflex create (Smooth-On, pads to surfaces soft etrate vertically, and mm) (±1 p wihalwsfcetfedmt oebt horizontally both move to freedom sufficient allow —which ◦ o Eq. For h deieforce, adhesive The drcin,adtefito coefficient friction the and -direction), ν P p w ( mm 1×3 [cross-section beams flexural to attached and angle epciey eemn h eair h fetv oko adhe- of work effective The behavior. the determine respectively, , ilgnrlyntcontribute. not generally will 5 hr h optimal the where φ, B and 2 2 J/m ∼6 cflx0-0=1.168 = 00-20 Ecoflex , hra rmltrtr,telcs’ oko deinwsmea- was adhesion of work locust’s the literature, from whereas , F F 2 A adh δ θ opoueangtv oqe nodn h deiepads, adhesive the unloading torque, negative a produce to ⇒ = h oo’ pnsadahsv a ocsaedetermined are forces pad adhesive and spines robot’s The C p J = ). noprtsalo h features the of all incorporates 6A, Fig. foot, SLIP The ∈ = K C NF s1 2 q [ 7Telcs,hwvr a esrdi uhmore much a in measured was however, locust, The 47 ,90 0, x x h oko deinwscluae ietyfo mea- from directly calculated was adhesion of work The f < 6π otherwise 0 1 f = + ,asmn h deini lasatatv.Fg 5C Fig. attractive. always is adhesion the assuming 0, φ r ◦ x p 3 K F F ] f KW prahszr.Apidaketorque, ankle Applied zero. approaches A , p1 adh θ − P + SV K (x 1-J x a eapoiae yteplofadhesive pulloff the by approximated be can , adh s1 ofidaprte n togeog open- to enough strong and asperities find to , K f p0 P − p1 + A 1-J > 2 , x nl range angle x K 4)i rae hnfietmsta fthe of that times five than greater is (47) ) p0 ± A r p0 0 p1 p , nl is angle δ fetv oko adhesion, of work effective , )δ .2 J/m 0.128 δ p K p p + + + = φ K K −72 ≈ δ K pb 3 4 µ pb pb pb " φ x eemn h odn behavior. loading the determine C δ (x pb0 = 2 1 φ = pb NF n hra lsi 0.142 = plastic thermal and , f − ∈ E δ tan E − ◦ = p pb g otherwise 0 1 ν [ hsesrn asv pad passive ensuring thus , −90 x p 2 (µ ν −1 , pb0 θ g + x L φ n h deiepad, adhesive the and , cos f loigec opas- to each allowing , n h transi- the and (−1/µ) ◦ )δ = − ± 1 90 , section Appendix, SI θ pb − φ tan E x PV .3J/m 0.13 g pb0 − ◦ ν n spines, and , n the and µ, ] g −1 2 sin > (φ > # −1 h highly The µ. 0 θ ,ms be must φ), , M SH , 2 W si the in is 0 , A = okof Work adh a be can , ±4.8 P and , 1-J θ SV [4] [3] P × ± ± ◦ A 4 , hr ahi oee ssml pigaddsac eoefl a contact, pad full before distance and spring x simple as modeled is each where F ocsaedfie as, modulus, defined are elastic forces spine, robot’s including, the Finally, parameters relationships. the define pad adhesive the E and m, 0.0182 ftelcs SI ot i.6 ope foot, coupled 6; Fig. foot, (SLIP locust the of foot primary SLIP the the of after performance the tested reduce mechanism. was attachment could material which each jumps spines, undergone that the had ensured damage adhe- order the or damage conducted The and dull contaminate were sive. could could wood cleaning sandstone and sandstone or and the to modifications whereas glass designed no was the order as trials; foot The foot, between approximate respectively. SLIP m/s, the 0 the where and sequence, challenge 3.4 the was in velocity surface contact- impact then, each and, on noncontact glass, the jumps and first, type for, wood, conducted (Dynam- sandstone, were glass, testing trials follows: 10 uniform as where was and sequence foot testing the The ics). of sim- angle v641) dynamically Phantom jumping A (VisionResearch, model. a rig, friction at jumping Coulomb conducted ilar traditional were the trials using achieve of series specific of a foot, SLIP Experiments. Robot robot. and locust the for software) Matlab (custom tracking of model contact hertz the spheres, by determined elastic is two force pad adhesive locust’s The modulus, elastic including parameters, area, of arm moment MPa, lever 173.25 the where a n ufc,rsetvl,adteasmdfl eipeedeforma- hemisphere force, full applied assumed the and tion, respectively, surface, and pad and radii, the where ute hlegsteSI ett neatwt h ufc,adw would we This and jumps. surface, the noncontact with of as interact rates to jump, feet slip non-contact-type SLIP accen- type-2 the the is early challenges of further which higher changes mechanism the velocity cable by It surface. sudden evidenced the the the in from away by friction pulling tuated nonuniform foot by the as caused observed is is this event; slip Fig. the morphology. foot the not and 6E mechanism storage energy the by caused energy. of loss minor in a scratches slip higher only linear in a approximately with resulting resist produced as sandstone, sandstone, These observed the to cm, jumps. the 1.5–2.5 created noncontact in approximately dynamic been of observed more observed had the only regularly in friction were was occurrence sufficient slips 2) load Type-3 type before applied (planting slipping. period slip some situation. the initial required difficult an during most mechanisms friction, the create attachment simulate to both experiments to jump preload as contact zero However, the at unknown, is conducted foot were locust’s the of preloading p0 A p1 itt h oa otdisplacement, foot total the dictate , h oo hwdmc oedtriitcjmigbhvo hnthat than behavior jumping deterministic more much showed robot The h ihocrec ferytp- lp o ocnatjms(i.6 is 6) (Fig. jumps noncontact for slips type-2 early of occurrence high The h ple force, applied The eosrtstetpclsde rpofi otvlct hc precedes which velocity foot in drop-off sudden typical the demonstrates θ itnebfr akn aeilengagement, material backing before distance , = J ν x = 6ka area, kPa, 55.16 surf p 45 = n esl moduli, tensile and , ◦ R twihpittencsayfito ofceti ifiutto difficult is coefficient friction necessary the point which at , p2 eemn h a odn.Te,sbrcinfo h total the from subtraction Then, loading. pad the determine , F A eemnstelcs’ pn loading. spine locust’s the determines , a sdt aiiaeobservation facilitate to used was S5A, Fig. Appendix, SI R p2 K oeprmnal hrceietepromneo the of performance the characterize experimentally To x F F p2 = p K 3 s1 p1 s1 = = ⇒ ⇒ A F = 290 = A p1 = 9π 1 uigjmigi acltdtruhfeature through calculated is jumping during , K K π = − s1 6E p1 F K R and µm 2 E 2L p2 2.39 x p2 p2 p2 (x ν F s1 f p2 p 2 2 s1 3 f = >> << , (R I E s1 − I p2

, p2 × s1 , x = K R 16 p0 = 16R 10 + 9π surf surf R ) 0 P and kPa 300 2.76 R −4 surf R K + 2 PNAS x p2 K surf p2 K surf f p1 K p2 R 2 h pigcntnsare, constants spring The . x m pb )(K surf × p 3 = = 2 ! (x n thickness, and , R 10 p2 | 0.5 E p2 1 i.S4 Fig. Appendix, SI f p1 π −12 − − + oso’ ratios, Poisson’s , L o.115 vol. , E p1 F A x K surf ν s1 p1 pb0 surf 2 surf n deiepad, adhesive and , E m x pb0 surf , ). 4 ) , n length, and , 2 n ple load, applied and , o h adhesive the for , | o 36 no. L s1 = ν 0 m, 0.001 .A the As ). | p2 E8365 = E L s1 s1 F 0.5 [6] [5] [7] p1 = = ,

BIOPHYSICS AND ENGINEERING COMPUTATIONAL BIOLOGY expect improved results if the legs were locked and the cable unwound rig and the robot, with only a small variation in the bouncing frequency of before the jump. the foot (SI Appendix, section S2). Finally, the SLIP feet were tested on the MultiMo-Bat (Fig. 6F) to vali- date the system integration and performance. The MultMo-Bat was tested Slip Energy. The mass normalized translational jump energies, presented first on a flat Acrylonitrile butadiene styrene (ABS) surface and then on in Fig. 7 A and B, were calculated by numerical integration (trapezoidal ◦ angled (θJ = 45 ) glass, sandstone, and wood surfaces, where the behavior rule) from the acceleration data. To ensure uniformity, only male trials were matched that of the constrained jumping rig trials (Fig. 6F). Body pos- included (Trial Details). ture on the angled surface, as with the locust, was maintained through Assuming the locust as a uniform cylinder, the rotational inertia (I) as a a combination of foot and body contacts. The MultiMo-Bat produced a function of jumping angle (θJ) is calculated as follows, maximum jumping height of 2.75 m, with similar jumping heights for all Z L/2 Z π Z R cases, where the jumping energy density (J/kg) is approximately equal to 2 the jumping rig. Increasing the jumping energy density by 80% (Fig. 6F) I = ρrd drdφd` −L/2 −π 0 propelled the MultiMo-Bat up to the maximum height of 4.52 m. Continued slipping was observed on the angled wood surface due to the significant where, d = ` cos(θJ) − r sin(φ) sin(θJ), increase in tip loading; however, the passive confirmation of the SLIP foot M = πLρR2; allowed the MultiMo-Bat to extract sufficient energy to propel itself up to 1 2 2 2 2 heights >4 m. I = M L cos (θJ) + 3R sin (θJ) [10] 12 Dynamics. To analyze the robotic foot’s interaction with the surface, a jump- where the length of the body (L), effective radius (R), jumping angle (θJ), ing rig was developed which simulates the dynamics of the robot, but within effective density (ρ), and mass (M) define the relationship. The variation in a more observable configuration. The configuration, SI Appendix, Fig. S5 the rotational inertia comes from the assumption that a type-1 slip would A and B, was designed to be dynamically similar to that of the robot, SI hinder the locust’s ability to properly align its body. The ratio of the trans- Appendix, Fig. S5C, which is governed by lational to total energy, PT = ET /(ET + ER), caused by a type-1 slip, for the !0.5 locust is then, r − r 2 ¨ 2 1 2 mBr1 = 2k1 L − [8] !−1 2 12 F2 R2 P = A + 1 [11] TL 2 2 2 2 2 (FA − Mg) L cos (θJ) + 3R sin (θJ) 2!0.5 2 r1 − r2 mF¨r2 = −2k1 L − − k2r2 − c2r˙2, 2 and the robot, having constant rotational inertia (I), is then,

whereas the jumping rig is governed by !−1 F2 MR2 P = A + 1 , [12] TR 2 mB¨r1 = −k2(r1 − r2) − c2(r˙1 − r˙2) [9] I(FA − Mg)

2!0.5 2 r2 mF¨r2 = 2k1 L − + k2(r1 − r2) + c2(r˙1 − r˙2), where the translational energy (ET ), rotational energy (ER), applied force 2 2 (FA), and the gravitational constant (g = 9.81 m/s ) deﬁne the ratios. These

where r1 and r2 represent to position of the two masses, main body, allow for estimation of the effects of a type-1 slip (locust, Fig. 7B) at differ- mB = 55.4 g, and foot, mF = 4.8 g. The robot’s k1 = 291.2 N/m and L = ent points of the jumping cycle, from the no-slip (none) cases presented in 135.8 mm are the stiffness of the main power spring and the leg length, Fig. 7 A and C as, 9 respectively. The ground interaction is governed by k2 = 10 N/m and Z a Z b c2 = 88.4 Ns/m, which are the stiffness and damping coefficient, respec- ( ) = ¨ + ¨ EN a xdx xPTL, R dx [13] tively. Note that all values represent half of the robot, as only one leg is 0 a being tested. The ground stiffness was chosen to be arbitrarily large com- where the body position at the onset of the type-1 slip (a), body position pared with k1, whereas the damping coefficient c2 was calculated from at liftoff (b), and body position along motion axis (x) define the behavior. the experimentally determined coefficient of restitution, COR = 0.8929, of Comparing the normalized translational jumping energy of the predicted the 3D-printed ABS material (Stratasys uPrintSE Plus, ABSplus), discussed in and actual type-1 (one leg) slips of the locust shows good agreement (Fig. SI Appendix, section S3. The gravitational potential contributed little to 7D), which allows for approximation of the effect to the robotic platform the jumping dynamics, as the accelerations were an order of magnitude [Fig. 7B, type-1 (one leg)]. greater over short periods (≈[25,50] ms) (Fig. 3A). Therefore, the orientation of the trials played an insignificant role in the dynamics during the foot ACKNOWLEDGMENTS. We thank Byung-Wook Park for creation of the contact. hydrophobic glass surfaces, Dirk Drotlef for work of adhesion measure- A comparison of the dynamics, SI Appendix, Fig. S5D, showed good ments, and Davide Bray for assistance with the biological experiments. This agreement between the magnitude and damping responses of the testing work is supported by the Max Planck Society.

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E8366 | www.pnas.org/cgi/doi/10.1073/pnas.1804239115 Woodward and Sitti Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 0 iC se T oda I(02 ut-ucinlfo s uigrnigi the in running during use foot Multi-functional (2012) DI Goldman ST, Hsieh C, Li 20. 1 iC hn ,GlmnD 21)Atrayaiso egdlcmto ngranular on locomotion legged of terradynamics A (2013) DI Goldman T, Zhang C, Li 21. 8 oo ,GlmnD 21)Bnahorfe:Srtge o oooini granular in con- locomotion for Strategies in feet: our rapidly Beneath (2015) crawl DI Goldman crevices, A, Hosoi traverse 28. Cockroaches robots (2016) and RJ animals Full in K, shapes Jayaram streamlined 27. Terradynamically (2015) al. et C, Li 26. sand: extension in Burrow (2005) swimming E Undulatory Landis BP, (2009) Boudreau B, DI Johnson PA, Goldman Jumars C, KM, terres- Dorgan Li Flipper-driven 24. Y, (2013) Ding RD, DI Maladen Goldman 23. PB, Umbanhowar N, Mazouchova 22. 0 ebesA,Abc T uksyM 21)Lnig ecigadtkn f from off taking and perching Landing, (2011) MR Cutkosky AT, Asbeck AL, Desbiens 30. contains hindlegs locust in region buckling A (2012) M Burrows GP, Sutton TG, Bayley 29. boring. and burrowing of biomechanics The (2015) KM Dorgan 25. 5 i ,e l 20)Sot etclsraecibn ihdrcinladhesion. directional Scal- with climbing toe: surface vertical gecko’s Smooth The (2008) al. (2013) et S, MR Kim Cutkosky 35. AT, Asbeck EV, Eason EW, Hawkes smooth 34. near-vertical vertical of on climbing Dynamic climbing (2012) and RS perching Fearing AG, for Gillies robot P, Birkmeyer multimodal A 33. (2016) al. et MT, recon- durable Pope the D.R.O.P. 32. of summary Video (2012) A Parness C, Mckenzie S, Paul 31. 8 ete J(97 h outjm I.Srcua pcaiain ftemetathoracic the of specializations Structural III. jump locust The (1977) WJ Heitler locust 38. the of and jump the recovery of energetics Adhesion The (1975) II: HC Bennet-Clark Waalbot 37. 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BIOPHYSICS AND ENGINEERING COMPUTATIONAL BIOLOGY