SymmetricalDataSecurity: Bird-inspired dynamic grasping and perching in arboreal environments

Bird-inspired grasping mechanism design

SNAG comprises a bird-inspired bipedal foot and leg system (

). It is mounted on a quadrotor aerial platform to control its flight. The grasping mechanism structure consists of three-dimensional (3D) printed segments. Jointed subcomponents are primarily printed in place to facilitate fast iteration, assembly, and repair. SNAG can be mounted on a variety of aerial platforms. Similar to the legs and feet of birds, the grasping mechanism handles surface variability upon contact for perching robustly, enabling the aerial approach phase to be stereotyped for all surfaces during landing. Similar to some birds of prey, SNAG can also dynamically catch objects with the same legs and feet used for perching. Movie 1 demonstrates SNAG’s core functionality and many of its key biomimetic design features. The first design iterations relied on more traditional engineering solutions, which underperformed. Only after 20 design iterations that increasingly mimicked bird legs and feet (see fig. S1 for the design evolution) did we reach a design that could reliably land similar to birds do (design and construction details: data files S1 and S7 and text S4).

Movie 1. Demonstration of SNAG’s core functions and key design features.

The robot leg and grasper design are inspired by the functional anatomy of the bird hindlimb (

Fig. 2, A and B

). The rigid structures in bird legs and toes are made up of bone and cartilage, linked together by ligaments and actuated by muscles through tendon connections (

). Analogously, the robot’s rigid structures are made from hard plastic, and grasping is actuated using Spectra tendons with tuned springs in series driven by one motor per leg (text S4). The dimensions of the extended leg length, toe lengths, and claw sizes were all isometrically scaled by mass from two peregrine (

Falco peregrinus

) cadavers for a ~750-g quadcopter including the mass of the SNAG grasper. We chose peregrine falcons because of their eye-catching grasp performance, which they attain with a leg length and leg mass that is typical for birds of similar body mass (text S4) (

). The SNAG grasping mechanism with its electronics has a mass of about 250 g. Each leg is about 50 g, or 6.7% of the mass of the quadcopter in flight. This structural leg mass is proportionally similar to that of the legs of many birds (

). Because birds’ thighs tend to stay close to the body at all times during landing and catching (

), we simplified the robot leg design to resemble just the section of the bird’s leg from the knee to the foot; we refer to the most proximal joint on the robot as the hip rather than the knee (

Fig. 2B

). The section of the grasping mechanism rigidly connected to the body holds the two actuators per leg. This design parallels how the major grasping muscles in bird legs are located more proximally than the feet (

). These muscles are situated above the ankle and connected to the toes via tendons (

). On the robot, a servomotor in the hip orients the leg in the sagittal plane at a target perch or object and also balances the robot’s center of gravity during perching. The second motor stores energy in a spring, which is released upon impact with an object through a quick-release mechanism in the body (

Fig. 2C

). The quick release is mechanically triggered through a tendon as the leg collapses (text S4). The foot motor can reverse direction to restore and reload the leg and foot to their resting positions. The foot motor is nonbackdrivable, so it can hold grasping forces passively. The robot’s legs consist of an upper and lower parallel mechanism that collapse prismatically (

Fig. 2, A and B

). The tendon that flexes the toes runs through the leg with a spring in series.

Fig. 2. Bird-inspired grasping mechanism design.

(
A
) The robot’s leg and grasper design are inspired by the functional anatomy of the avian hindlimb [drawing adapted from (
44
,
71
)]. The key dimensions are primarily scaled isometrically based off peregrine falcon legs. We integrated analogs of the avian DFM (
7
) and TLM (
7
) to improve grasping performance. (
B
) For each leg, the mechanism uses one motor for generating grasp force through a spring and another for sagittal leg motion that orients the feet at a target surface and balances the robot after perching. Triggered on impact, a quick release (
C
) releases stored energy to the tendons running along the leg, feet, and toes to the claws. Simultaneously, the grasp force is amplified by the DFM (
D
). The toes wrap around the object upon impact within 50 ms, after which the mechanism locks with the TLM. (
E
) The underactuated toes conform to complex surfaces through a tendon differential that distributes the grasping force over the toes, which each exert force on the surface via distributed toe pad friction and claws latched on asperities. For takeoff, the foot motor reverses direction to reset the entire mechanism. (
F
) The low-weight avian-inspired mechanism enables SNAG to rapidly generate high forces to dynamically grasp complex surfaces. As in birds, the most massive parts are located proximally to the body (
42
), which improves agility (data file S7). Numbered parts in (B) to (E) are defined in (F).

The robot’s legs incorporate two key internal mechanisms found in many bird legs, which have been hypothesized to improve grasping performance: the digital flexor mechanism (DFM) and the tendon locking mechanism (TLM) (

Fig. 2, A and D

) (

). In the DFM, some of the tendons that flex the toes are routed around the ankle such that these tendons tension when the leg bends at the ankle. Although this mechanism has been shown to be insufficient for enabling automatic passive perching or passively curling the toes, it may still be mechanically beneficial for birds because it creates some initial stretch in the muscle, which may facilitate effective contraction (

). By routing the tendon around the ankle in the robot, similar to (

–

), SNAG mechanically embodies the DFM principles to (i) absorb impact energy as the collapsing leg stretches the tendon to the feet, similar to how the tendons in bird legs absorb initial impact energy (

), and (ii) transform the impact energy into squeeze force. Critically, passively absorbing the impact momentum with tendon-spring stretch allows the grasping mechanism to apply more grip force than the actuators could provide alone. In the TLM in birds, tendons passing through each toe interact with locking features in their associated tendon sheaths. So, when the foot actively closes, these features can lock the toe on the surface (

). SNAG incorporates a TLM analog with a locking ratchet in the ankle. This mechanism enables SNAG to maintain the extra grip force from the DFM when the leg collapses, preventing elastic rebound. When the foot motor resets the grasping mechanism for takeoff, the ratchet unlocks, allowing the leg to extend back into its resting position.

Similar to birds, SNAG’s feet feature tendon-driven jointed toes with toe pads that generate friction and claws that latch onto surface asperities, which together enable SNAG to grasp complex surfaces reliably and securely (

Fig. 2E

) (

). The claws are 3D printed to be the same shape and size as those of an isometrically scaled peregrine falcon. Similar to bird claws, the claw geometry is sharp enough to engage with surface asperities, but not so sharp that the tip penetrates too deep into the surface and gets stuck, enabling both reliable grasping and releasing. In birds, the toe pads comprise a rough podothecal pad covering subcutaneous fatty tissue (

). This structure likely improves the grip; the toe pad can deform to adapt to large surface features, while the rough outer layer interlocks with the smaller surface features with relatively little tangential compliance (text S4 lists further functions). To recreate a similar toe pad structure, each phalanx in SNAG’s feet contacts the surface through a deformable rubber bumper covered with a grip tape (text S4). From pilot experiments, this design remains high friction despite dirt, lichen, moss, and moisture commonly found on trees in forests, whereas smooth high-friction surfaces commonly used in robotics and engineering, such as rubber, lose grip. Overall, the hierarchical conforming structure of the jointed toes, sharp curved claws, toe pad protuberances, and rough skin complements the fractal nature of rough surfaces (

Fig. 2E

) (

). To actuate all of the toes with a single tendon from the leg, a tendon differential connects each claw to share the load equally across the toes. Similar to the mechanism birds appear to have to extend their claws (

), elastic bands behind the joints passively extend the toes when the foot motor relaxes the main tendon. Similar to the design of underactuated hands (

), it is important that the stiffness of the elastic bands is such that toes begin to curl at the more proximal joints before the distal joints when grasping an object. This allows the foot to conform well to the surface during the grasp and prevents the toes from getting stuck on surface features upon release.

The perching process commences when the hip motors rotate the legs toward the target perch and the foot motors wind up to store energy in their main springs (

Fig. 2F

). When the robot impacts the surface, the legs begin to collapse. The DFM absorbs the robot’s flight energy and passively transforms it into grasp forces, which cause the toes to wrap the surface. Simultaneously, the quick release triggers and unleashes the stored energy to amplify the forces that flex the toes, which conform at high speed to the surface within 50 ms. As the leg collapses, the ratcheting TLM passively locks the posture of the leg. During perching, an accelerometer in the right foot triggers the leg to begin balancing soon after making contact (text S4), which is accomplished through active rotation of the body about the hip. The accelerometer senses the angle of the foot relative to the direction of gravity, which we found to be a good proxy for the angle of the foot on the perch. For takeoff, initiated by the flight controller, the leg reorients to direct the quadrotor to a stable flight orientation, and the foot motor reverses direction to unlock the ankle, reset the quick release, and provide slack to the toes over about 20 s. During takeoff, SNAG relies on its rotors to propel itself away from the surface, similarly to how hummingbirds rely heavily on their wings to propel themselves from a perch (

Grasp parameter sufficiency region

The tradeoffs birds and robots make when transitioning from the air to a perch determine the contact conditions they must handle upon touchdown (

). For example, landing velocities that are too high may injure the bird or damage the robot and allow less time for closed-loop feedback control. On the other hand, lower speeds result in reaching the destination later, which costs elevated slow-flight aerodynamic energy and makes the body more sensitive to approach errors induced by gusts. Landing birds and robots must balance these tradeoffs when selecting appropriate landing dynamics.

During landing, a suite of variables determines bird and robot perching success, including hardware design, kinematics, surface features, and balancing behavior after contact (

Fig. 3A

). Kinematic variables include the impact velocity, the angle of the body and the leg, and the angle and location at which the foot contacts the perch. Hardware parameters include dimensions and mass as well as the way the legs absorb energy. Behaviorally, after grasping a perch, birds use the feet and legs to adjust their footing and control the center of mass to balance. To accomplish this, SNAG uses an active hip joint to balance, but it cannot adjust its footing as birds do. Because these variables all interact in landing, adjustments to one can sometimes be compensated for by others to maintain sufficiency.

Fig. 3. The grasp parameter sufficiency region for perching.

(A) Perching success is determined by leg and foot design, kinematics, surface features, and balancing behavior after contact. (B) All variable combinations that meet the requirements to grasp and hold onto the surface for the impact condition fall into the sufficiency region. For each variable, holding all others constant, there is an upper and lower bound. As an example, the curve within the green region indicates the upper and lower bound for the impact velocity angle. The drivers behind these bounds include the dynamics, surface friction, leg motor torque, and leg spring and structure stiffness. Much of the energy in the direction of the vector from the hip to the feet will be absorbed by the springs in the legs. The energy perpendicular to that vector will be, in part, absorbed in rotating the center of mass of the robot, raising the height of the center of mass, system compliance, slipping on the surface, and play in the mechanism. (C) Our multiparameter model predicts the perching sufficiency range in parametric space. The 3D sufficiency subspace illustrating the approach speed (v), the approach angle (θ_v), and the leg extension angle (θ_leg) shows how they are required to interact to result in perching success. The colors were selected for visualization purposes: The amount of red, green, and blue in each face corresponds to the degree of velocity angle, velocity magnitude, and leg angle, respectively, relative to their extremes.

Ultimately, a successful landing is determined by whether the multibody dynamics, robot hardware, robot behavior, and surface conditions are suitable. The definition of a “successful landing” depends on context. For example, certain birds and bats can perch upside down, and we observed during pilot testing on small-diameter branches that SNAG can successfully stay attached to a perch by swinging underneath a branch similar to a bat. However, for our bird-inspired purposes, we define a successful landing as one in which the robot’s center of mass remains above the center of the perch similar to most birds. With this definition, some amount of slip on the surface is allowable and can be beneficial for dissipating energy and stochastically finding better asperities as the claws scrape along the surface (

). For this definition, there are limits on the kinematic parameters that will result in a successful landing, such as bounds on the velocity magnitude and angle (

Fig. 3B

). Traditionally, the state-space regions that satisfy kinematic and velocity constraints for successful perching are referred to as landing envelopes (

–

). We can augment this notion of a landing envelope with all the other landing variables, including robot balancing behavior, which we term the “perching sufficiency region.” Specifically, the perching sufficiency region is defined as the high-dimensional space of all of the variables that result in successful perching (

Fig. 3C

). This definition not only enables us to quantitatively study the effects of different kinematics and balancing behaviors when landing but also allows us to evaluate the effects of different toe arrangements across bird species. For example, different balancing algorithms or foot designs can modify the allowable velocity range on contact, shifting the perching sufficiency bounds.

Our planar perching sufficiency model defines the boundaries of the perching sufficiency region by placing limits on the linear and angular momenta, along with constraints on the foot misalignment and range of leg motion (Materials and Methods). We observed in pilot experiments that the robot’s feet slipping too far forward or backward on the perch was the primary perching failure mode, which we model using angular momentum

$HLx=−v(mleg(lleg,com*sin(θleg−θv)+sin(θv)*(−d2*cos(θleg))+cos(θv)*(d2*sin(θleg)))−mbody(lbody*sin(θleg−θv−θbal)−lleg,eq*sin(θleg−θv)−sin(θv)*(−d2*cos(θleg))+cos(θv)*(d2*sin(θleg))))$

(1)

where the variables are as follows:

, speed;

m_body

, body mass;

m_leg

, leg mass; θ

_leg

, angle of the leg; θ

, angle of the velocity;

, perch diameter;

l_body

, body length; θ

_bal

, balance angle;

l_{leg, eq}

, extended leg length; and

l_{leg, com}

, projected location of the center of mass on the axis of the legs (

Fig. 3A

, Materials and Methods, and data files S2 and S4). We estimate the limits on the angular momentum upon contact with the perch,

H_Lx

, by corroborating this mathematical model (

Fig. 3A

) with our experimental perching data (

Figs. 4

). The model’s other four constraints beyond surface slip ensure that the robot collides with enough momentum to collapse the leg, the robot collides softly enough to avoid damage, the foot is reasonably aligned with the perch to ensure a good grasp, and the robot has enough balance angle range before hitting the angle limit to balance effectively. We use 2D slices from this model to visually illustrate how the variables interact in determining perching sufficiency. The simplicity of the model allows us to gain critical intuition into the key considerations that govern perching.

Fig. 4. Experimental investigation of perching sufficiency: The effect of toe arrangement, quick-release trigger timing, and foot ejection.

(
A
) To study SNAG’s grasp sufficiency region and to understand the roles of the hardware, kinematic, behavior, and perch parameters, we set up a series of controlled collisions with tree branches in which we varied the impact and surface conditions. The robot is attached to an elastic band-driven rail system that launches it into the air immediately before impact with the perch. (
B
) To test how perching success depends on bird foot morphology, we tested the two most common toe arrangements: anisodactyl, three toes in the front and one toe in the back (e.g., parrotlets and woodpeckers), and zygodactyl, two toes in the front and two toes in the back (e.g., peregrine falcons). (Background of the bird foot images was removed for clarity.) (
C
) To determine whether more toes on one side helps the robot absorb angular momentum in the opposite direction, we tested both toe arrangements at different perching impact speeds and, thus, proportionally larger angular momentum (
Fig. 3A
). The nominal velocity angle at impact was kept constant and representative for bird landing, 10°. We observed no difference on the first section of a natural perch, a tree branch, and we observed a small shift in successful perching speeds on the second perch section. Open circles indicate perching success, whereas crosses indicate failure. The min/max differences for the upper and lower thresholds on the second perch section are 0.04/0.23 m/s and 0/0.16 m/s, respectively. (
D
) A key hardware design parameter that influences the grasp sufficiency region is the timing of the quick-release trigger. If the trigger is too early, then the leg becomes too stiff to collapse, resulting in a failed landing. However, a late trigger can cause less energy to be absorbed by the legs, which increases the likelihood of damage to the robot. (
E
) Last, improper foot and leg hardware design (such as claw forces or rebound forces that are too high) can also cause the foot to eject from the surface. (Numbers in the bottom-left corner indicate the trial number; data file S3.)

Fig. 5. Experimental investigation of perching sufficiency: The effect of balance behavior after contact.

(A) We experimentally verified the perching stability that three different balance algorithms afford: The first control scheme maintains a fixed leg angle, the second is open loop, and the third is closed loop (control loop details are in Materials and Methods). The fixed leg angle scheme commands a relatively high balance angle during landing, whereas the open-loop and closed-loop algorithms rotate the body forward, which much reduces the balance angle. (B) For the same conditions, the fixed leg angle resulted in a failed landing, whereas the open-loop and closed-loop algorithms resulted in a successful landing because the robot was able to place its center of gravity near the top of the perch. The white bar with pink dots on the robot body enables kinematic tracking and serves as a scale bar.

Fig. 6. Experimental investigation of perching sufficiency: The effect of leg orientation, foot placement, impact velocity, and surface conditions.

The perching sufficiency space is divided into the following five regions: 1, success (green); 2, angular-momentum upper-bound constraint violated (dark brown); 3, angular-momentum lower-bound constraint violated (light brown); 4, linear-momentum upper-bound constraint violated (dark yellow); 5, two or more constraints violated (gray). A description of the model can be found in Materials and Methods. (A) A 2D slice of the perching sufficiency region shows how foot misalignment versus leg angle affects the robot’s ability to perch. Perching fails when the magnitude of the foot misalignment is too large (red cross that borders regions 2 and 3) and when leg angles become too large, breaking the body angular-momentum upper-bound constraint (red crosses near the middle of region 2). The blue dots indicate successful landing experiments, and the red crosses indicate failed trials. The photos illustrate how foot misalignment causes the toes to curl before contacting the surface. (B) The robot faces both linear and angular momentum constraints, illustrated by a 2D slice of perching sufficiency plotted as a function of velocity magnitude (speed) versus velocity angle. To distinguish the linear and angular momentum constraints, we linearly interpolate the leg angle based on the velocity angle, using 10°/45° and 90°/0° (θ_v/θ_leg) as end points. Because there are small kinematic variations from trial to trial, we also ran the model with the specific kinematics of each trial, and the successes and failures agreed in all cases. The magenta dots correspond to using the fixed leg algorithm as opposed to the closed-loop algorithm in blue and red. There is an obscured magenta dot under the blue dot at (90,0). (C) Branch diameter and surface friction also influence perching performance. SNAG successfully lands on all four surfaces tested: a small (38 mm)–, medium (64 mm)–, and large (165 mm)–diameter perch of the same oak tree species as well as a 64-mm-diameter alder tree perch (text S5). (D) Many branches in nature have an inclination (are angled in a vertical plane), which SNAG can accommodate with its independent passive energy absorption in both legs. The demonstration here shows a vertical landing on a branch at a moderate inclination angle.

Experimental investigation of the perching sufficiency region

To study SNAG’s perching performance and corroborate how the kinematic, hardware, behavior, and perch parameters drive its perching sufficiency parameter region, we set up a series of controlled perching experiments (

Fig. 4A

and Materials and Methods). The experimental setup precisely launched the robot by pulling it along a rail with an elastic band, until it was released into the air immediately before its foot impacted the surface, which triggered SNAG to grasp the perch. For these tests, the robot did not use its rotors because the rail system allowed for high precision in specifying and varying the kinematics at contact. We focused on how foot morphology, balancing strategy, landing velocity, impact angle, leg angle, and surface properties affect perching across branches of different sizes and textures (table S1). For these tests, we selected impact conditions in the realm of what birds experience by focusing on tree branches to perch and a range of objects of similar mass as prey to catch (Materials and Methods and text S5). During the experiments, about 190 trials in total, the robot configurations performed highly reliably and experienced little wear (data file S3), justifying our mathematical model assumptions. Movie 2 illustrates the range of experiments and highlights the similarity in landing behavior to birds that we reported earlier (

Movie 2. Bird-inspired dynamic grasping and perching in forest environments.

All robot clips are slowed four times unless otherwise marked. All parrotlet clips are slowed 12.5 times and flipped horizontally. The speed difference may be explained by the mass difference between the parrotlet [~30 g; video in (

)] and robot (~750 g).

Across the class Aves, there exist many different toe arrangements, frequently associated with lifestyle and ecological niche (

). The two most common toe arrangements are anisodactyl [three toes in the front and one toe in the back, found in peregrine falcons among other groups (

)] and zygodactyl [two toes in the front and two toes in the back, found in parrotlets among other groups (

)] (

Fig. 4B

). Both toe topographies have opposable toes, and both enable birds to perch. However, to our knowledge, there have been no experimental studies into how these toe arrangements affect perching or grasping performance in birds (

To experimentally compare the perching performance of the two toe arrangements, we analyzed SNAG landing at different speeds with anisodactyl and zygodactyl foot designs (

Fig. 4, B and C

, and text S4). Our hypothesis was that more toes on one side will help with handling angular momentum in the opposite direction (rationale in data file 14). Thus, we would expect that the thresholds on the landing speed limits would be lower for the anisodactyl feet as compared with those of the zygodactyl feet. We tested the robot on two sections of an Oregon white oak (

Quercus garryana

) branch (64 mm in diameter). For the purposes of these tests only, we counted the landing as a success if the robot was able to bring the robot to rest (in two landings that we counted as successes, the robot fell off the perch because the balance behavior was too vigorous; data files S3 and S4). We found no difference in the thresholds on one perch section and a slight offset in the thresholds on the other (

Fig. 4B

). Although the offset on the second perch section corresponds to our hypothesis, the largest difference in thresholds is too small to be confident that there is consistent functional relevance for perching birds and robots (min/max differences: 0.04/0.23 ms

⁻¹

upper bound and 0.00/0.16 ms

⁻¹

lower bound).

Hardware design determines how the robot absorbs impact energy and whether the grasp will eject (text S9). For example, if the tension in the tendon of the leg is too high, then the legs will not fully collapse (

Fig. 4D

). However, if the tension is too low, then little flight energy is absorbed when the leg fully collapses; as a result, the robot collides with the surface at a higher speed, which could cause additional wear and damage over time. In addition, improper leg and foot design can lead to ejection, which we observed in some of our earlier SNAG prototypes (

Fig. 4E

). Upon close examination, we found that ejection can also occur in birds when they curl their claws to grasp slippery surfaces, such as Teflon (movie S1) (

). With a combination of design updates, including changing the balance of forces curling the toes, hard stops on the claw curling angle, and reducing the rebound after impact, the final SNAG design avoids this problem.

We found that active balancing behavior markedly improves perching success by widening the perching sufficiency region. To experimentally assess the effects of different balance strategies on the perching sufficiency region, we tested the robot landing with fixed leg angle, open-loop, and closed-loop algorithms (

Fig. 5, A and B

; fig. S2; and text S7 for balance model). The fixed leg angle algorithm entails commanding a constant balance angle to the leg, which requires the foot to hold relatively large pitch-back moments for a successful landing. There is some small variation in the leg angle with this algorithm due to finite motor forces, mechanism compliance, and nonzero tolerances. The closed-loop algorithm functions as follows: After a delay (while the leg collapses), the robot commands its center of mass to move toward the top of the perch using feedback from the accelerometer on its right foot (text S4). The open-loop behavior functions similar to the closed-loop algorithm, but with one modification; the algorithm commands a constant balance angle, equivalent to what would be expected in the closed-loop case if the foot maintained the same orientation as when it made contact with the perch. We found that, when SNAG used the fixed leg algorithm, the robot was not able to successfully perch with the control impact conditions (in two different landing conditions), and it fell backward after absorbing the impact energy (data file S3, trials #17 and #65). On the other hand, we would expect that the open-loop control would perform as well as the closed-loop control, so long as the foot does not slip substantially. SNAG succeeded at perching under both the open-loop and closed-loop algorithms with nearly identical kinematics. However, we did record one open-loop control trial in which the robot failed to land; although that may be due to an error found in the code that was corrected for the successful open-loop landing, the kinematics appeared similar in both cases (data files S3 and S4). When landing vertically with appropriate contact conditions, the robot was able to land successfully with both the fixed and closed-loop algorithms (

Fig. 6B

Focusing on the peregrine falcon anisodactyl toe arrangement and closed-loop balance control for the rest of the experiments, we study the effects of leg orientation and foot placement on the perching sufficiency region (text S8). At first foot-surface contact, there are three primary parameters that influence perching performance: the leg angle (θ

_leg

), the impact angle (θ

_impact

), and foot misalignment (

e_foot

) (

Fig. 3A

). If the foot misalignment is too high, then the toes will curl too far before contacting the perch, resulting in a failed landing (

Fig. 6A

). Higher leg and impact angles will result in more angular momentum over the center of the perch. If the angular momentum is too high, then the robot fails to land successfully and violates the upper angular momentum constraint in our model (

Fig. 6A

Both the magnitude and the direction of the robot’s velocity on contact shape the perching sufficiency region (

Fig. 6B

). If the robot approaches the perch at shallow velocity angles, then the robot violates the angular momentum constraints of the sufficiency region model and fails to land experimentally when the impact speed is too high or too low. Too low a speed may also cause the legs to not collapse fully, which increases the pitch-back moment and can result in failure. To account for this effect, our model places a lower bound on the acceptable linear momentum. On the other hand, if the robot drops vertically onto the perch, then gravity is sufficient to collapse the leg fully even at an initial velocity of 0 m/s. In this case, the robot gains speed as the leg collapses. If the robot lands too hard on the perch, however, then components can break. Therefore, our model also incorporates an upper bound on the linear momentum, which we did not probe experimentally.

In addition to kinematic, hardware, and behavior tradeoffs, the properties of the perch itself can change the size of the perching sufficiency region (

Fig. 6C

). We tested three diameters of an oak tree: 38 mm (1.5 inches), where the feet can wrap around most of the perch; 64 mm (2.5 inches), where the feet wrap about halfway around the perch; and 165 mm (6.5 inches), where the feet wrap less than a quarter of the way around the perch. Parrotlets can accommodate perches of similar proportions relative to their feet (

). SNAG can land on each diameter. On small-diameter perches, SNAG’s feet can fully wrap the surface, causing more tendon length to be drawn from the feet. Consequently, leg stiffness and grip force are reduced. On the other hand, larger diameter perches, which tend to have larger asperities, prevent the foot from closing. This amplifies the leg stiffness and the grip force. We also tested a medium diameter alder tree (

Alnus

) with relatively smooth bark and some moss on top. Smoother bark makes the claws more likely to eject the foot, but we found that SNAG successfully lands on this slippery perch. Further, although many tree branches are nearly horizontal in nature, there are also many that are angled in a vertical plane. Our experiments demonstrate how the independent passive energy absorption from each leg enables SNAG to accommodate these angular variations (

Fig. 6D

). However, a small amount of foot misalignment can cause the robot to fall (data files S3 and S4).

Last, SNAG is able to catch a wide variety of objects harnessing the same hardware as for perching (

Fig. 7

). Catching is, in many ways, analogous to perching. The main differences are the velocity of the grasper and the object, the textures of the object, and the forces imparted on the grasper (text S3). Our laboratory experiments show that SNAG can catch and release objects of similar size and weight to the prey of peregrine falcons (

) using peregrine falcon–inspired feet (

Fig. 7

, Materials and Methods, and data files S3 and S4). We also found that SNAG is able to catch objects during outdoor flight (

Fig. 1D