Dactyls and Inward Gripping Stance for Amphibious Crab-Like Robots on Sand

Bioinspir. Biomim. 16 (2021) 026021 https://doi.org/10.1088/1748-3190/abdd94

PAPER Dactyls and inward gripping stance for amphibious crab-like RECEIVED 13 August 2020 robots on sand REVISED 26 October 2020 1,∗ 2 1 ACCEPTED FOR PUBLICATION Nicole M Graf , Alexander M Behr and Kathryn A Daltorio 19 January 2021 1 Department of Mechanical & Aerospace Engineering, Case Western Reserve University, Cleveland, United States of America 2 PUBLISHED Department of Computer Science, Case Western Reserve University, Cleveland, United States of America ∗ 1 March 2021 Author to whom any correspondence should be addressed. E-mail: [email protected] and [email protected]

Keywords: legged locomotion, marine animals, mobile robotics, sea-coast, underwater vehicles Supplementary material for this article is available online

Abstract Sandy beaches are areas that challenge robots of all sizes, especially smaller scale robots. Sand can hinder locomotion and waves apply hydrodynamic forces which can displace, reorient, or even invert the robot. Crab-like legs and gaits are well suited for this environment and could be used as inspiration for an improved design of robots operating in this terrain. Tapered, curved feet (similar to crab dactyl shape) paired with a distributed inward gripping method are hypothesized to enable better anchoring in sand to resist hydrodynamic forces. This work demonstrates that crab-like legs can withstand vertical forces that are larger than the body weight (e.g. in submerged sand, the force required to lift the robot can be up to 138% of the robot weight). Such legs help the robot hold its place against hydrodynamic forces imparted by waves (e.g. compared to displacement of 42.7 mm with the original feet, crab-like feet reduced displacement to 1.6 mm in lab wave tests). These feet are compatible with walking on sandy and rocky terrain (tested at three speeds: slow, medium, and fast), albeit at reduced speeds from traditional feet. This work shows potential for future robots to utilize tapered and curved feet to traverse challenging surf zone terrain where biological crabs thrive.

1. Introduction the feet puncture the sand [3]. In unsaturated sand, capillary forces can allow steep slopes to form that Crabs are adept at traversing the challenging terrain are stable for periods of time. The stability in this between dry sand and shallow water. In contrast, sand is obtained through capillary forces and is rein- it can be difficult to engineer robots for surf zones forced when moisture is added because this increases (areas of the ocean with depth less than 10 m). A both tensile strength and cohesion strength [4]. These major design challenge for amphibious locomotion strengths are not as present in dry and submerged is weight, which affects both robots and animals. A sand,causingtheseslopestofalltotheirnaturalangle heavy robot can better withstand relatively large wave of repose when interacted with [4]. forces but loses efficiency on dry sand. A light robot Some robots are capable of sand locomotion; often can move more quickly across dry sand because the utilizing wheels and wheel-like legs rather than the feet sink less into the sand but is more likely to capsize multi-jointed legs of crabs. An eccentric paddle mech- when impacted by waves. In this paper, the crab-like anism was developed to widen the range of terrain dactyls’ ability to increase the effective weight of the a wheeled robot can handle. This paddle works well body by applying distributed inward gripping [1, 2] in granular media, as the paddles will dig in then is examined. This will enable robots that are increas- push against the substrate to gain traction [5]. The ingly useful in this transitional area for environmental J8 Atlas is another wheeled robot that can success- monitoring, lifeguarding, tsunami or flood relief, and fully navigate difficult terrains [6]. Whegs IV looks to naval science. cockroaches along with animals that live in and out Sand is a complex substrate. One factor of the of water, such as salamanders, otters, frogs and pen- locomotion difficulty in granular media is its ability guins to create a robust robot that is easy to control to produce both fluid-like and solid-like forces when [7, 8]. The SeaOtter, an amphibious robotic crawler,

© 2021 IOP Publishing Ltd Bioinspir. Biomim. 16 (2021) 026021 NMGrafet al has been constructed to map out terrain and relay utilized this technique paired with a feedforward field information to deployment crews [9, 10]. Under- neural-network gait to allow a crab-like hexapod standing how crabs use their legs can enable legged robot to locomote on complex terrain under two robots with more diverse applications on rough nat- reflex mechanisms [36]. Mahapatra et al have exam- ural terrain, as adaptive gaits can allow the robot to ined the feet forces on hexapod robots to help find overcome obstacles and improve mobility [11]. Char- an optimal gait for minimizing the total power con- acteristics, such as the scale of the leg relative to grain sumed by the system [37–39]. size and mass of the robot are crucial components to Robots inspired by crabs have been developed creating a robot to navigate on granular media [12]. for marine applications. A horseshoe crab robot was While wheeled robots are typically easier to control developed with righting capabilities when knocked than legged robots, they are more limited by the sizes over from forces imparted on it by waves [40]. The of obstacles that they are able to overcome and are Crabster CR200 is a large underwater robot that is also sensitive to the grain size of the granular media able to counter strong tidal currents [41]. Greiner et al relative to the speed. developed an autonomous legged underwater vehicles More complex legs have several advantages in (ALUVs) to find mines in surf zones [42]. The Ursula rough terrain. First, they can climb over larger obsta- ALUV was able to walk underwater, but a faster and cles, dealing with highly uneven terrain [13]. Second, more efficient ALUV, Ariel, is able to walk sideways, theycanprobe theground toselect the strongest foot- imitating a crab’s gait [42, 43]. Khan et al have devel- fall locations [14]. Third, the foot itself be a special- oped an underwater manned sabed walking robot that ized end effector. For example, a recent robot uses is hexapod robot powered by a tether in a boat [44]. particle jamming in the foot to improves efficiency While ALUVs overcame some of the issues with surf and stability [15, 16]. They found that in order to sup- zone environments, they do not explore the effects of port forces tangential to the ground, the end effectors crab dactyls. While these crab-like robots have many are more useful when internally reinforced for shear. different applications, to the best of our knowledge, Here, we propose that shear forces can be important none of these other robots have tested the effects of not only for traction, but for additional stability in dactyl design. soft terrain. Here, the hypothesis is that a pointed foot design, Animals including insects [7, 17], turtles [8, 18], which might be a hinderance on dry ground com- otters [9], and salamanders [19] have been a source of pared to a traditional rounded foot, in fact provides inspiration for amphibious robots. Arthropods, such an advantage in generating a grip force with the sub- as crabs and lobsters, have many desirable traits that strate to resist disruptions caused by hydrodynamic can improve the way robots can traverse in sandy forces. environments. The evolution of varied gait patterns This builds on techniques studied in climbing for air and water is seen in arthropods, which help robots to improve ways crab-like robots grasp the these creatures navigate in tidal zones and amphibi- ground in order to improve the stability under hydro- ous habitats [20]. Their wide bodies, strong legs and dynamic forces. Climbing robots depend on over- tapered feet seem to have evolved multiple times in coming gravity through a variety of methods, many a process called carcinisation [21]. These adaptations of which involve spreading force over a larger area contribute to crabs’ success at navigating a wide vari- rather than a small contact point. Researchers are ety of environments. Crabs are the largest arthro- developing robots that have hooks along the con- pod to live in aquatic environments and on dry land tact area to distribute the force among the surface [22], a feat that puts stress on their hydrostatic skele- [45–47]. Others depend on grippers that use spe- tons [22–28]. A better understanding of these animals cific instances of spines to grab materials that they can help us build robots for transition between these are climbing on [48–50]. These methods reinforce the environments. benefits of spreading the force to create a grip that Arthropod legged walking has provided inspira- supports the robot. Some of these contact interfaces tion for robotic walking in several key areas. Joseph (e.g. hooks, directional adhesives, peeling, spines) can Ayers et al developed a robot based on the Ameri- support different amounts of force depending on the can lobster [29, 30]. This robot utilized the biome- direction of the total applied force. If there are mul- chanical and neurobiological features of a lobster tiple contact points, increasing the force by adding [31, 32]. Studying the gait patterns of crabs can also opposing shear forces can increase the total strength be useful. Some species of crabs, such as the grap- of the contact force in the normal direction. Animals sus tenuicrustatus, changes its posture and walking such as beetles can be observed to do this by align- pattern in air versus water [20, 33]. Cui et al ana- ing their legs to opposing patterns even when legs are lyzed the trajectory of the toe point of a hexapod missing [1]. This type of movement is used to help the robot through DH principles [34]. Researchers have spines engage and disengage in an alternating pattern developed central pattern generators to adapt over to obtain the appropriate forces to climb [1, 51]. This complex terrains [35]. This method can be benefi- strategy is called distributed inward gripping (DIG). cial to crab-like robots; for example, Wang et al have Here, the extent to which DIG can be applied to

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Figure 1. Amphibious hexapod robot uses crab-like dactyls (white) to walk from dry sand to sand submerged in water. crab-like dactyls to help maneuver in granular media sides to fit the wires that control each leg. The acrylic is determined. sides and holes for wires were sealed with hot glue The goal is to apply DIG to an amphibious robot and caulk, allowing the internal board to be water- and show that DIG can create an anchoring force to proofed while maintaining control of the servos. The help the robot maintain its position in wavy envi- waterproofed robot (figure 2(B)) was powered off- ronments. The shear loading from DIG increases board with a TEKPOWER DC regulated power supply the vertical force that can be supported by the grip (TP3005T) at 6 V. between the legs and the ground effectively stabiliz- ing the robot without adding weight. The robot plat- 2.2. Dactyl design form (figure 1), first developed in our preliminary The HEXY robot came with 6.35 mm thick acrylic feet conference paper [52] is tested in an automated wave that forms a circular foot with a diameter of 7.9 mm. tank to provide evidence that crab-like legs on gran- To evaluate how the robot would grip with different ular media can be used to resist hydrodynamic forces. feet, nine different designs were created and tested, The modified HEXY robot kit [53] can maintain its showninfigure3. position in a wavy environment significantly better These legs were designed to evaluate whether or than the non-modified robot (with 95% confidence). not the taper and overall profile commonly found on Mimicking crab dactyls and pairing them with DIG crab dactyls will help penetrate the sand. Dactyls #1–3 as presented in this paper could allow smaller legged are all the same length and thickness as the original robots to navigate the shorelines. flat foot, with an end profile of a rectangle, triangle, and smaller diameter circle, respectively. Dactyls four 2. Amphibious robot development through six have the same end profile as the dactyl above them in figure 3;however,thesedactylsalso To demonstrate the relative contribution of the crab- have a taper to mimic that of a crab. Dactyl #7 is like dactyls and inward gripping on sand, HEXY robot a larger version of Dactyl #4, inspired by a shovel. kit from ArcBotics (figure 2(A)), a hexapod with three Dactyls #8 and #9 were inspired by crabs, and after metal geared digital servos per leg (a total of 18 DOF), preliminary grip tests it was determined that Dactyl was modified. Specifically, the original ‘feet’ are cut #8 outperformed the others. Therefore, Dactyl #8, from blue acrylic and come with a rubber cap. The the original capped foot, and the uncapped foot were provided cap enlarges the contact area and friction used in the tests presented in this paper. between the foot and surface it is walking on, per- mitting the robot to navigate easier on smooth, hard 3. Control ground. The final robot has a weight of 1.2 kg and a height of 18 cm. 3.1. Grip definition From proximal to distal, the lengths of each link 2.1. Robot waterproofing are 101.6 mm, 25.4 mm, 50.8 mm, and 50.8 mm. The servos were treated with multiple layers of mod- Four grips (none/home position, small, medium, ified silicone conformal coating (MG chemicals) to and large) were examined throughout this process. make the servos watertight. After the solution dried, When the distances between the tips of the dactyls the servo output shafts were treated with lucas hi- decreases in stance, the robot drags its legs along the performance multi-purpose marine grease. This pair- ground. This motion buries the tip of the dactyls. ing protects the interior of the servo from any water The more translation tangentially along the ground, entering the casing. the deeper the tips of the dactyl go. The distances The electronics were mounted in a waterproof between the dactyl tips in each grip are shown in acrylic box that was modified by drilling holes on the figure 4.

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Figure 2. (A) Hexapod robot before waterprooﬁng shows white dactyls, blue HEXY legs, orange wires that connect joint actuators, and grip test harness (black loop) (B) amphibious robot has waterproof electronics box (clear), and silicone and marine grease coatings.

Figure 3. In preliminary evaluations, 11 different robot feet were compared. The crab-inspired foot #8, which will be referred to as Dactyl #8, due to its promising performance in both locomotion of the robot and the ability to grip. Throughout this paper, the effectiveness of the original capped foot, the ﬂat foot, and Dactyl #8 are compared. For more detail on the dactyl design, see: https://drive.google.com/drive/folders/1FO0Y5-ZF_YWyvaIpXRnmQ4A3R6rSreMl?usp=sharing (http://stacks.iop.org/BB/16/ 026021/mmedia).

3.2. Walking gaits 4. Characterization of resulting robot Based off of previous work in [52], the same slow, medium, and fast walking speeds were utilized, with a The robot is evaluated by a grip test, wave test, and stride length of 19.1 mm. The slow speed is the default a velocity test. First, the grip test determines the tripod gait setting for HEXY, with a delay of 600 ms amount of force it takes the robot to yield from dry, between each motion. Next, the fast speed was found wet, or submerged sand while performing either no by running the servo at the maximum working speed, grip, a small grip, a medium grip, or a large grip. Sec- resulting in a delay of 450 ms. The medium gait is the ond, in the wave test, the robot performs one of the average of the delays between the slow and fast speeds four grips in submerged sand, while a wave genera- (525 ms). tor produces ten waves. The amplitude of the robot’s

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Figure 4. The grip motions are shown here in air without sand for visibility. At the onset of stance (A) the distance between contralateral pairs of legs is approximately 20 cm. Gripping motions result in the distance being reduced to 74% for the small grip (B), 66% for the medium grip (C), and 63% for the large grip (D) with corresponding changes in dactyl angle.

Figure 5. A representative time-force proﬁle for Dactyl #8 in wet sand with a big grip shows that maximum extraction force is larger than the weight. When the winch stopped, there was a drop in the force. The maximum force was found by taking the maximum before the winch stopped, and the weight was found to be the average after settling.

motion during the waves, the displacement of the 4.1. Evaluation of vertical force (Ability to grip robot between each of the ten waves, and the net dis- the ground) placement of the robot between the beginning of the As in [49], Pavestone natural play sand was placed first wave and the end of the tenth wave are evaluated into a dry tank, a wet tank, and a submerged for a minimal value. Third, a velocity test was con- tank. Between every test, initial sand conditions were ducted on multiple surfaces with a slow, medium, and restored between by filling and flattening the divots in fast gait to ensure the robot could still locomote after the sand with a piece of metal screed. the alterations to the feet. For each test, the robot was set in the desired sand, All of the statistics were performed in R with reset, and performed either another reset or a small, ANOVA tests with an alpha of 0.05. These tests medium, or large grip. The robot was attached to resulted in the p-value [54]. The smaller the p-value, a force gauge (Nextech DFS50 Digital Force Gauge, the stronger the evidence is that there is a difference published resolution ±2.0 g force) with a cable in the performance of the dactyls and grips. secured to its body that supports the robots cen-

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Figure 6. After 30 trials in each configuration in (A) dry sand (B) wet sand (C) submerged sand, boxplots show that gripping is more effective with crab-like dactyls and in submerged sand. ter of mass. Then, the robot was pulled vertically by are in figure 6,andtheaveragesofthegriptestsare Paracord planet paracord connected to an ATV util- recorded in table 1. ity winch from badland winches, which was powered Dactyl #8 had higher weight percentages in each by an eTopxizu power supply (12 V 30 A) until it of the sands, reaching up to 153% of the robot’s yielded from the granular media. A 1.5-inch pulley weight with a large grip in submerged sand. Inward (National Hardware N233-247 3219BC wall/ceiling gripping is not always equally effective due to inher- mount single pulleys in zinc) that was attached to ent variation of sliding friction contacts and impreci- V-slot linear rails (openbuildspartstore.com)tocre- sion of actuation, however after 30 trials the curved ate a frame in order to guarantee that the robot dactyls enable significantly better performance than will be pulled vertically. The frame and winch were original feet. Even with this spread, the robot is con- eachsecuredwithtwoPittsburgh6-inchquickrelease sistently gripping better compared to the other two bar clamps. The force gauge recorded the load for types of feet. This increase in performance across every grip test (figure 5). The maximum value shows each tested terrain shows that the design of Dactyl when the sand yields. Note that in some cases a #8 performs better than the original foot with and second peak is visible when the winch stops, caus- without the cap. ing the robot to bounce. These secondary peaks are The robot could experience small increases ignored. in weight due to the sand friction along with The grip tests were conducted 30 times in each some sand stuck on the feet; however, this was sand with each foot type while the robot performed addressed by calculating the weight of the robot one of the four grips of interest. The results (as max- after each run. This was done by finding the average imum forces as percentages of the robot’s weight) robot weight after the winch stopped in order to

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Table 1. Performance of the grip tests of the robot with the grip force as a percentage of the robot’s weight.

Dry sand Wet sand Submerged sand No grip Small grip Med grip Large grip No grip Small grip Med grip Large grip No grip Small grip Med grip Large grip

Cap feet 108% 108% 110% 113% 111% 110% 110% 111% 109% 111% 111% 112% Flat feet 107% 110% 114% 114% 114% 119% 109% 107% 110% 114% 115% 117% Dactyl #8 103% 105% 112% 113% 105% 119% 120% 123% 105% 125% 134% 138%

Figure 7. Wave tank provides consist size waves to demonstrate effectiveness of dactyls to resist displacement.

Figure 8. Wave tank results for a trial of 10 waves for each feet with the robot performing a large grip. The robot’s displacement was tracked along the length of the tank, with the origin being at the point where the piston is attached to the board used to generate the waves. The starting point was subtracted from the position of the robot to have the displacements spread from 0 mm. The amplitudes are greatest with the original leg with the cap, are lessened with the original uncapped foot, and are the smallest with Dactyl #8. The displacements between each wave along with the total displacement from before the first wave to the end of the last wave also follow this trend. The displacements for all feet are in appendix A. incorporate any extra weight imparted by the sand. placed in the middle of the tank, then a metal rod This made the testing more conservative than in was inserted through a hole in the placement marker [52]. (figure 7). This lined up the hole in the placement An ANOVA test was applied to the no grip and marker with the center-point of the ‘X’ on the back large grip scenarios for Dactyl #8 and found that there of the modified HEXY robot. The robot then moved was a significant increase in grip force for the dry sand into one of the three grip positions or, for no grip −16 −16 (a p < 2.2 × 10 ), wet sand (1.231 × 10 ), and control data, the robot remained stationary. Waves × −16 submergedsand(p < 2.2 10 ). were generated with a period of 3.133 s. This period was selected by generating one wave and tracking 4.2. Wave displacement characterization the time that it took the crest of that wave to travel To show the effects of different feet under wave load- down the tank forward, backward, and forward to the ing, a wave generator was built for the lab tank. center point of the plate of the wave generator. This The wave generator is built with a CHLED piston ensures that at any given point, there will only be one (SC63X200) attached to a frame constructed from the wave in the tank. This permits us to run the test for same V-slot linear rails and clamps that were used multiple waves and then split the video to produce in the grip test. The piston was powered by a (Bos- multiple trials. After the robot was commanded to titch 150 psi) air compressor that was set to 100 psi. perform a grip, 10 waves were generated, displacing The stroke of the piston is 152.4 mm. The robot was the robot.

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Table 2. The averages and standard deviations of the robot’s displacement per each wave (similar to the data presented in ﬁgure 8 and appendix A of the test and as a total displacement (similar to the data presented in ﬁgure 9).

No grip Small grip Medium grip Large grip (mm) Per wave After 10 waves Per wave After 10 waves Per wave After 10 waves Per wave After 10 waves (n = 30) (n = 3) (n = 30) (n = 3) (n = 30) (n = 3) (n = 30) (n = 3)

Cap feet −4.8 ± 7.8 −20.5 ± 4.7 −6 ± 7.8 −23.8 ± 9.7 −7.6 ± 10.6 42.7 ± 2.5 −8.4 ± 9.0 −32.4 ± 8.6 Flat feet −2.8 ± 3.4 −5.7 ± 4.8 −3 ± 2.6 −14.7 ± 7.1 −5.0 ± 5.9 −11.5 ± 4.8 −5.7 ± 5.94 −18.3 ± 12.4 Dactyl #8 0.04 ± 3.2 7.4 ± 5.4 −0.6 ± 2.9 2.1 ± 5.3 −2.1 ± 3.1 −4.7 ± 5.6 −2.4 ± 2.6 −1.6 ± 7.8

Figure 9. After 3 sets of 10 waves (looking at 30 waves total), the trials for each foot’s performance in all 30 waves were averaged for each grip. This chart displays the average maximum displacement of the robot. The range is greater for the capped feet, diminishes for the ﬂat feet, and is the smallest for the crab dactyls.

The displacements were found by utilizing the uncapped foot it was 7.8 × 10−6.Allfourp-values program tracker (https://physlets.org/tracker/). The lead to the conclusion that the foot type, whether it robot’s absolute position over time in these trials is be original capped, original uncapped, or Dactyl #8, showninfigure8 and table 2. After several waves, has a statically significant impact on the amplitude. the robot experiences larger displacements because These p-values also show that Dactyl #8 significantly the hydrodynamic forces of the wave dislodged the minimized the amplitude of the displacements caused robot’s grip from the sand. The average net displace- by the waves. ment due to each wave and the total displacement was These results show that Dactyl #8 is significantly analyzed to examine the effects of the robot’s feet and better at resisting displacement than the other feet for grip. The average net displacement is the distance the all of the grips (no grip: p = 1.47 × 10−3,smallgrip: robot travels between each wave, while the total dis- p = 1.54 × 10−2,mediumgrip:p = 1.04 × 10−4,large placement is the difference between the initial posi- grip: p = 2.39 × 10−2). Overall, there is a significant tion and the displacement after the final wave. The difference in performance between the dactyl and the results of the wave test for each foot is in figure 9 other two feet. and table 2. When using Dactyl #8, the total displacements are close to an order of magnitude less. When 4.3. Walking speed characterization comparing the results for no grip and large grip, there In order to understand how the new dactyl altered the is a statistically significant difference in the ampli- robot’s locomotion, the robot walked 457.2 mm (18 tude (the total distance traveled forward and back- in) on linoleum, through the dry, wet, and submerged ward by the robot per wave) between both the orig- sand, and on a rock bed (figure 10). inal capped and uncapped feet and Dactyl #8. For The robot was able to travel this distance with each no grip, the p-value corresponding to the difference type of foot on all of the materials at all of the speeds in amplitudes between Dactyl #8 and the original except for Dactyl #8 with the fast gait on linoleum capped foot was 2.2 × 10−16 and between Dactyl #8 (figure 10). There is not enough friction between and the original uncapped foot resulted in a p-value of Dactyl #8 and the linoleum at the fast gait speed to 1.36 × 10−3.Forthelargegrip,thep-value cor- allow the robot to move forward. responding to the difference in amplitude between Even though the robot is still able to move, the Dactyl #8 and the original capped foot was 2.2 velocity is slowed when using Dactyl #8 by about 37% × 10−16 and between Dactyl #8 and the original on linoleum, 58%, 67% and 28% for dry, wet, and

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Figure 10. The robot’s speed was evaluated on several different substrates (n = 15): hard smooth linoleum tile (A), dry sand (B) wet sand, (C) and submerged sand with 25.4 mm of water above sand line which is enough to completely submerge feet of the robot (D), and rock bed (E).

Figure 11. (A) The robot walking in sandy area in cleveland edgewater park. (B) The robot walking in a rocky area at mentor headlands beach park. In each of these tests, the robot was walking with the slow gait (13 mm s−1). submerged sand, respectively, and 61% in the rock 5. Discussion and conclusions bed. Finally, it has been demonstrated that dactyls are The results found in this study show that DIG can be effective in walking on outdoor freshwater beaches successfully applied to robots maneuvering in granu- with waves (ﬁgure 11), with the slow gait in order lar media to create an anchoring force. This grip force to show the feasibility of this robot operating in out- is more effective when a crab-like dactyl is imple- door terrains. A version of this robot that is power mented as the foot of the robot. The grip of the robot autonomous but with wired control was tested. On helps minimize displacement due to outside forces, thesandybeach,therobotwasabletowalkintowaves such as waves. Furthermore, the displacement is sig- of frequency (approximately 0.23 Hz) on a day with niﬁcantly reduced when using Dactyl #8 because these wind speed (10 mph) into depths where the average feet are able to penetrate the sand better, causing the wave height was equal to robot body height. On the grip to have more effect. rocky beach, the robot was able to walk into waves The spread in the grip data is likely due to inherent of frequency approximately 0.35 Hz on a day with variation in sliding friction distance and imprecision wind speed (3 mph) where the average wave height of actuation. Servomotor torque is expected to be an was half the height of the robot. While the inherent important characteristic for future robots, as will gaits variability of outdoor testing makes precise tracking that improve utilization of dactyls for walking. and statistical analysis outside the scope of this paper, When considering non-wave environments, the these preliminary tests show promising potential for crab-like feet decreased the robot’s speed for the same crab-like robots to mimic biological crabs in natural gait pattern by about half of the speed of the origi- environments. nal capped foot. This could be due to a combination

9 Bioinspir. Biomim. 16 (2021) 026021 NMGrafet al of effects from friction, slip, and the dactyls not fully the displacement in waves could be a potential reason exiting the sand when taking a step. In the future, why crab dactyls are so unique. a new gait can be developed that is optimized for maneuvering in granular media, which would result Acknowledgments in an increased velocity. Even with the disadvantages of the slowed robot speeds with the implementation This research was sponsored by the Strategic Envi- of Dactyl #8, this work shows that the addition of ronmental Research and Development Program tapered feet can help the robot walk and maintain its (SERDP) SEED Grant #MR19-1369 and an Ofﬁce of position in shallow water, where making consistent Naval Research Young Investigator Award (Daltorio progress is challenging for robots that are light weight 2019). We would like to thank Yang Chen for her relative to wave forces. help in collecting the grip test data along with Chris Based on this work, smaller amphibious robots Wu and Nam Hoang for their help processing the can be utilized to complete the tasks of larger, more wave tests. We would like to thank Chenming Wei energy expensive robots. This can also increase the for her help conducting the wave tests. We would like range of depths being explored by robots, permit- to thank Megan Graf for assisting in the statistical ting shallower areas to be accessible by smaller robots. analysis of the different tests. We would also like These results also show a preliminary explanation for to thank Noah Napiewocki and Justin Wong for the proﬁle of the dactyls of biological crabs. The suc- constructing the wave tank. We would like to thank cess in obtaining an anchoring force that minimizes Emma Ries for her help in formatting this paper.

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Appendix A. Total wave test displacement performance

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