Walking is like slithering: A unifying, data-driven view of locomotion.

Legged movement is ubiquitous in nature and of increasing interest for robotics. Most legged animals routinely encounter foot slipping, yet detailed modeling of multiple contacts with slipping exceeds current simulation capacity. Here we present a principle that unifies multilegged walking (including that involving slipping) with slithering and Stokesian (low Reynolds number) swimming. We generated data-driven principally kinematic models of locomotion for walking in low-slip animals (Argentine ant, 4.7% slip ratio of slipping to total motion) and for high-slip robotic systems (BigANT hexapod, slip ratio 12 to 22%; Multipod robots ranging from 6 to 12 legs, slip ratio 40 to 100%). We found that principally kinematic models could explain much of the variability in body velocity and turning rate using body shape and could predict walking behaviors outside the training data. Most remarkably, walking was principally kinematic irrespective of leg number, foot slipping, and turning rate. We find that grounded walking, with or without slipping, is governed by principally kinematic equations of motion, functionally similar to frictional swimming and slithering. Geometric mechanics thus leads to a unified model for swimming, slithering, and walking. Such commonality may shed light on the evolutionary origins of animal locomotion control and offer new approaches for robotic locomotion and motion planning.

Jumping over fences: why field- and laboratory-based biomechanical studies can and should learn from each other.

Locomotor biomechanics faces a core trade-off between laboratory-based and field-based studies. Laboratory conditions offer control over confounding factors, repeatability, and reduced technological challenges, but limit the diversity of animals and environmental conditions that may influence behavior and locomotion. This article considers how study setting influences the selection of animals, behaviors and methodologies for studying animal motion. We highlight the benefits of both field- and laboratory-based studies and discuss how recent work leverages technological advances to blend these approaches. These studies have prompted other subfields of biology, namely evolutionary biology and ecology, to incorporate biomechanical metrics more relevant to survival in natural habitats. The concepts discussed in this Review provide guidance for blending methodological approaches and inform study design for both laboratory and field biomechanics. In this way, we hope to facilitate integrative studies that relate biomechanical performance to animal fitness, determine the effect of environmental factors on motion, and increase the relevance of biomechanics to other subfields of biology and robotics.

The bumpy road ahead: the role of substrate roughness on animal walking and a proposed comparative metric.

Outside laboratory conditions and human-made structures, animals rarely encounter flat surfaces. Instead, natural substrates are uneven surfaces with height variation that ranges from the microscopic scale to the macroscopic scale. For walking animals (which we define as encompassing any form of legged movement across the ground, such as walking, running, galloping, etc.), such substrate 'roughness' influences locomotion in a multitude of ways across scales, from roughness that influences how each toe or foot contacts the ground, to larger obstacles that animals must move over or navigate around. Historically, the unpredictability and variability of natural environments has limited the ability to collect data on animal walking biomechanics. However, recent technical advances, such as more sensitive and portable cameras, biologgers, laboratory tools to fabricate rough terrain, as well as the ability to efficiently store and analyze large variable datasets, have expanded the opportunity to study how animals move under naturalistic conditions. As more researchers endeavor to assess walking over rough terrain, we lack a consistent approach to quantifying roughness and contextualizing these findings. This Review summarizes existing literature that examines non-human animals walking on rough terrain and presents a metric for characterizing the relative substrate roughness compared with animal size. This framework can be applied across terrain and body scales, facilitating direct comparisons of walking over rough surfaces in animals ranging in size from ants to elephants.

Vision does not impact walking performance in Argentine ants.

Many walking insects use vision for long-distance navigation, but the influence of vision on rapid walking performance that requires close-range obstacle detection and directing the limbs towards stable footholds remains largely untested. We compared Argentine ant (Linepithema humile) workers in light versus darkness while traversing flat and uneven terrain. In darkness, ants reduced flat-ground walking speeds by only 5%. Similarly, the approach speed and time to cross a step obstacle were not significantly affected by lack of lighting. To determine whether tactile sensing might compensate for vision loss, we tracked antennal motion and observed shifts in spatiotemporal activity as a result of terrain structure but not illumination. Together, these findings suggest that vision does not impact walking performance in Argentine ant workers. Our results help contextualize eye variation across ants, including subterranean, nocturnal and eyeless species that walk in complete darkness. More broadly, our findings highlight the importance of integrating vision, proprioception and tactile sensing for robust locomotion in unstructured environments.

Comparative hindlimb myology of foot-propelled swimming birds.

Several groups of birds have convergently evolved the ability to swim using their feet despite facing trade-offs with walking. However, swimming relative to terrestrial performance varies across these groups. Highly specialized divers, such as loons and grebes, excel at swimming underwater but struggle to stand on land, whereas species that primarily swim on the water surface, such as Mallards, retain the ability to move terrestrially. The identification of skeletal features associated with a swimming style and conserved across independent groups suggests that the hindlimb of foot-propelled swimming birds has adapted to suit the physical challenges of producing propulsive forces underwater. But in addition to skeletal features, how do hindlimb muscles reflect swimming ability and mode? This paper presents the first comparative myology analysis associated with foot-based swimming. Our detailed dissections of 35 specimens representing eight species reveal trends in hindlimb muscle size and attachment location across four independent lineages of extant swimming birds. We expand upon our dissections by compiling data from historical texts and provide a key to any outdated muscle nomenclature used in these sources. Our results show that highly diving birds tuck the femur and proximal tibiotarsus next to the ribcage and under the skin covering the abdomen, streamlining the body. Several hindlimb muscles exhibit dramatic anatomical variation in diving birds, including the flexor cruris lateralis (FCL) and iliofibularis (IF), which reduce in size and shift distally along the tibiotarsus. The femorotibialis medius (FTM) extends along an expanded cnemial crest. The resulting increased moment arms of these muscles likely help stabilize the hip and knee while paddling. Additionally, distal ankle plantarflexors, including the gastrocnemius and digital flexors, are exceptionally large in diving birds in order to power foot propulsion. These patterns exist within distantly related lineages of diving birds and, to a lesser extent, in surface swimmers. Together, our findings verify conserved muscular adaptations to a foot-propelled swimming lifestyle. The association of muscle anatomy with skeletal features and biomechanical movement demands can inform functional interpretation of fossil birds and reveal selective pressures underlying avian diversification.

Foot-propelled swimming kinematics and turning strategies in common loons.

Loons (Gaviiformes) are arguably one of the most successful groups of swimming birds. As specialist foot-propelled swimmers, loons are capable of diving up to 70 m, remaining underwater for several minutes, and capturing fish. Despite the swimming prowess of loons, their undomesticated nature has prevented prior quantitative analysis. Our study used high-speed underwater cameras to film healthy common loons (Gavia immer) at the Tufts Wildlife Clinic in order to analyze their swimming and turning strategies. Loons swim by synchronously paddling their feet laterally at an average of 1.8 Hz. Combining flexion-extension of the ankle with rotation at the knee, loon swimming resembles grebe swimming and likely generates lift forces for propulsion. Loons modulate swimming speed by altering power stroke duration and use head bobbing to enhance underwater vision. We observed that loons execute tight but slow turns compared with other aquatic swimmers, potentially associated with hunting by flushing fish from refuges at short range. To execute turns, loons use several strategies. Loons increase the force produced on the outside of the turn by increasing the speed of the outboard foot, which also begins its power stroke before the inboard foot. During turns, loons bank their body away from the turn and alter the motion of the feet to maintain the turn. Our findings demonstrate that foot-propelled swimming has evolved convergently in loons and grebes, but divergently from cormorants. The swimming and turning strategies used by loons that allow them to capture fish could inspire robotic designs or novel paddling techniques.

Western and Clark's grebes use novel strategies for running on water.

Few vertebrates run on water. The largest animals to accomplish this feat are western and Clark's grebes (Aechmophorus occidentalis and Aechmophorus clarkii). These birds use water running to secure a mate during a display called rushing. Grebes weigh an order of magnitude more than the next largest water runners, basilisk lizards (Basilicus basiliscus), and therefore face a greater challenge to support their body weight. How do these birds produce the hydrodynamic forces necessary to overcome gravity and sustain rushing? We present the first quantitative study of water running by grebes. High-speed video recordings elucidate the hindlimb movements of grebes rushing in the wild. We complement these findings with laboratory experiments using physical models and a preserved grebe foot to estimate how slapping the water surface contributes to weight support. Our results indicate that grebes use three novel tactics to successfully run on water. First, rushing grebes use exceptionally high stride rates, reaching 10 Hz. Second, grebe foot size and high water impact speed allow grebes to generate up to 30-55% of the required weight support through water slap alone. Finally, flattened foot bones reduce downward drag, permitting grebes to retract each foot from the water laterally. Together, these mechanisms outline a water-running strategy qualitatively different from that of the only previously studied water runner, the basilisk lizard. The hydrodynamic specializations of rushing grebes could inform the design of biomimetic appendages. Furthermore, the mechanisms underlying this impressive display demonstrate that evolution can dramatically alter performance under sexual selection.

Exploring storm petrel pattering and sea-anchoring using deep reinforcement learning.

Developing hybrid aerial-aquatic vehicles that can interact with water surfaces while remaining aloft is valuable for various tasks, including ecological monitoring, water quality sampling, and search and rescue operations. Storm petrels are a group of pelagic seabirds that exhibit a unique locomotion pattern known as 'pattering' or 'sea-anchoring,' which is hypothesized to support forward locomotion and/or stationary posture at the water surface. In this study, we use morphological measurements of three storm petrel species and aero/hydrodynamic models to develop a computational storm petrel model and interact it with a hybrid fluid environment. Using deep reinforcement learning algorithms, we find that the storm petrel model exhibits high maneuverability and stability under a wide range of constant wind velocities after training. We also verify in the simulation that the storm petrel can use its 'pattering' or 'sea-anchoring' behavior to achieve different biomechanical sub-tasks (e.g. weight support, forward locomotion, stabilization) and adapt it under different wind speeds and optimization objectives. Specifically, we observe an adjustment in storm petrel's movement patterns as wind velocity increases and quantitively analyze its biomechanics underneath. Our results provide new insights into how storm petrels achieve efficient locomotion and dynamic stability at the air-water interface and adapt their behaviors to different wind velocities and tasks in open environments. Ultimately, our study will guide the design of next-generation biomimetic petrel-inspired robots for tasks requiring proximity to the water interface and efficiency.

Optimal planar leg geometry in robots and crabs for idealized rocky terrain.

Natural terrain is uneven so it may be beneficial to grasp onto the depressions or 'valleys' between obstacles when walking over such a surface. To examine how leg geometry influences walking across obstacles with valleys, we (1) modeled the performance of a two-linkage leg with parallel axis 'hip' and 'knee' joints to determine how relative segment lengths influence stepping across rocks of varying diameter, and (2) measured the walking limbs in two species of intertidal crabs,Hemigrapsus nudusandPachygrapsus crassipes, which live on rocky shores and granular terrains. We idealized uneven terrains as adjacent rigid hemispherical 'rocks' with valleys between them and calculated kinematic factors such as workspace, limb angles with respect to the ground, and body configurations needed to step over rocks. We first find that the simulated foot tip radius relative to the rock radius is limited by friction and material failure. To enable force closure for grasping, and assuming that friction coefficients above 0.5 are unrealistic, the foot tip radius must be at least 10 times smaller than that of the rocks. However, ratios above 15 are at risk of fracture. Second, we find the theoretical optimal leg geometry for robots is, with the distal segment 0.63 of the total length, which enables the traversal of rocks with a diameter that is 37% of the total leg length. Surprisingly, the intertidal crabs' walking limbs cluster around the same limb ratio of 0.63, showing deviations for limbs less specialized for walking. Our results can be applied broadly when designing segment lengths and foot shapes for legged robots on uneven terrain, as demonstrated here using a hexapod crab-inspired robot. Furthermore, these findings can inform our understanding of the evolutionary patterns in leg anatomy associated with adapting to rocky terrain.

Anisotropic compliance of robot legs improves recovery from swing-phase collisions.

Uneven terrain in natural environments challenges legged locomotion by inducing instability and causing limb collisions. During the swing phase, the limb releases from the ground and arcs forward to target a secure next foothold. In natural environments leg-obstacle collisions may occur during the swing phase which can result in instability, and may require contact sensing and trajectory re-planning if a collision occurs. However, collision detection and response often requires computationally- and temporally-expensive control strategies. Inspired by low stiffness limbs that can pass past obstacles in small insects and running birds, we investigated a passive method for overcoming swing-collisions. We implemented virtual compliance control in a robot leg that allowed us to systematically vary the limb stiffness and ultimately its response to collisions with obstacles in the environment. In addition to applying a standard positional control during swing motion, we developed two virtual compliance methods: (1) an isotropic compliance for which perturbations in thexandydirections generated the same stiffness response, and (2) a vertical anisotropic compliance in which a decrease of the upwardyvertical limb stiffness enabled the leg to move upwards more freely. The virtual compliance methods slightly increased variability along the limb's planned pathway, but the anisotropic compliance control improved the successful negotiation of step obstacles by over 70% compared to isotropic compliance and positional control methods. We confirmed these findings in simulation and using a self-propelling bipedal robot walking along a linear rail over bumpy terrain. While the importance of limb compliance for stance interactions have been known, our results highlight how limb compliance in the swing-phase can enhance walking performance in naturalistic environments.