Grand challenges for burrowing soft robots

Robotic burrowing holds promise for applications in agriculture, resource extraction, and infrastructure development, but current approaches are ineffective, inefficient, or cause significant environmental disruption. In contrast, natural burrowers penetrate substrates with minimal disturbance, providing biomechanical principles that could inspire more efficient and sustainable mechanisms. A notable feature of many natural burrowers is their reliance on soft body compositions, raising the question of whether softness contributes to their burrowing success. This review explores the role of soft materials in biological burrowing and their implications for robotic design. We examine the mechanisms that soft-bodied organisms and soft robots employ for submerging and subterranean locomotion, focusing on how softness enhances efficiency and adaptability in granular media. We analyze the gaps between the capabilities of natural burrowers and soft robotic burrowers, identify grand challenges, and propose opportunities to enhance robotic burrowing performance. By bridging biological principles with engineering innovation, this review aims to inform the development of next-generation burrowing robots capable of operating with the efficiency and efficacy seen in nature.

Time-dependent propulsion of fully inertial active stochastic particles: theory and simulations

Up to now, studies on fully inertial (adding mass and moment of inertia) active Brownian particles (IABPs) have only considered a constant propulsion force. This work overcomes this by studying IABPs but with a time-dependent propulsion and analytically characterizes this system by finding its mean-square displacement and effective diffusion for any periodic time-dependent propulsion speed. To exemplify the periodic general expressions, three particular self-propulsion signals are addressed, expressly, a cosine, a square-wave, and a zig-zag propulsion force. Langevin dynamics simulations are also employed to validate the analytical findings.

Granular Temperature Controls Local Rheology of Vibrated Granular Flows

We use numerical simulations to demonstrate a local rheology for dense granular flows under shear and vibration. Granular temperature has been suggested as a rheological control but has been difficult to isolate. Here, we consider a granular assembly that is subjected to simple shear and harmonic vibration at the boundary, which provides a controlled source of granular temperature. We find that friction is reduced due to local velocity fluctuations of grains. All data obey a local rheology that relates the material friction coefficient, the granular temperature, and the dimensionless shear rate. We also observe that reduction in material friction due to granular temperature is associated with reduction in fabric anisotropy. We demonstrate that the temperature can be modeled by a heat equation with dissipation with appropriate boundary conditions, which provides complete closure of the system and allows a fully local continuum description of sheared, vibrated granular flows. This success suggests local rheology based on temperature combined with a diffusion equation for granular temperature may provide a general strategy to model dense granular flows.

The environment to the rescue: can physics help predict predator-prey interactions?

Understanding the factors that determine the occurrence and strength of ecological interactions under specific abiotic and biotic conditions is fundamental since many aspects of ecological community stability and ecosystem functioning depend on patterns of interactions among species. Current approaches to mapping food webs are mostly based on traits, expert knowledge, experiments, and/or statistical inference. However, they do not offer clear mechanisms explaining how trophic interactions are affected by the interplay between organism characteristics and aspects of the physical environment, such as temperature, light intensity or viscosity. Hence, they cannot yet predict accurately how local food webs will respond to anthropogenic pressures, notably to climate change and species invasions. Herein, we propose a framework that synthesises recent developments in food-web theory, integrating body size and metabolism with the physical properties of ecosystems. We advocate for combination of the movement paradigm with a modular definition of the predation sequence, because movement is central to predator-prey interactions, and a generic, modular model is needed to describe all the possible variation in predator-prey interactions. Pending sufficient empirical and theoretical knowledge, our framework will help predict the food-web impacts of well-studied physical factors, such as temperature and oxygen availability, as well as less commonly considered variables such as wind, turbidity or electrical conductivity. An improved predictive capability will facilitate a better understanding of ecosystem responses to a changing world.

Animal-Morphing Bio-Inspired Mechatronic Systems: Research Framework in Robot Design to Enhance Interplanetary Exploration on the Moon

Over the past 50 years, the space race has potentially grown due to the development of sophisticated mechatronic systems. One of the most important is the bio-inspired mobile-planetary robots, actually for which there is no reported one that currently works physically on the Moon. Nonetheless, significant progress has been made to design biomimetic systems based on animal morphology adapted to sand (granular material) to test them in analog planetary environments, such as regolith simulants. Biomimetics and bio-inspired attributes contribute significantly to advancements across various industries by incorporating features from biological organisms, including autonomy, intelligence, adaptability, energy efficiency, self-repair, robustness, lightweight construction, and digging capabilities-all crucial for space systems. This study includes a scoping review, as of July 2024, focused on the design of animal-inspired robotic hardware for planetary exploration, supported by a bibliometric analysis of 482 papers indexed in Scopus. It also involves the classification and comparison of limbed and limbless animal-inspired robotic systems adapted for movement in soil and sand (locomotion methods such as grabbing-pushing, wriggling, undulating, and rolling) where the most published robots are inspired by worms, moles, snakes, lizards, crabs, and spiders. As a result of this research, this work presents a pioneering methodology for designing bio-inspired robots, justifying the application of biological morphologies for subsurface or surface lunar exploration. By highlighting the technical features of actuators, sensors, and mechanisms, this approach demonstrates the potential for advancing space robotics, by designing biomechatronic systems that mimic animal characteristics.

Robotic feet modeled after ungulates improve locomotion on soft wet grounds

Locomotion on soft yielding grounds is more complicated and energetically demanding than on hard ground. Wet soft ground (such as mud or snow) is a particularly difficult substance because it dissipates energy when stepping and resists extrusion of the foot. Sinkage in mud forces walkers to make higher steps, thus, to spend more energy. Yet wet yielding terrains are part of the habitat of numerous even-toed ungulates (large mammals with split hooves). We hypothesized that split hooves provide an advantage on wet grounds and investigated the behavior of moose legs on a test rig. We found that split hooves of a moose reduce suction force at extrusion but could not find conclusive evidence that the hoof reduces sinkage. We then continued by designing artificial feet equipped with split-hoof-inspired protuberances and testing them under different conditions. These bio-inspired feet demonstrate an anisotropic behavior enabling reduction of sinkage depth up to 46.3%, suction force by 47.6%, and energy cost of stepping on mud by up to 70.4%. Finally, we mounted these artificial feet on a Go1 quadruped robot moving in mud and observed 38.7% reduction of the mechanical cost of transport and 55.0% increase of speed. Those results help us understand the physics of mud locomotion of animals and design better robots moving on wet terrains. We did not find any disadvantages of the split-hooves-inspired design on hard ground, which suggests that redesigning the feet of quadruped robots improves their overall versatility and efficiency on natural terrains.

Are toe fringes important for lizard burying in highly mobile sand?

Toe fringes are a key innovation for sand dwelling lizards, and the relationship between toe fringe function and substrate properties is helpful in understanding the adaptation of lizards to sand dune environments. We tested the sand burial performance of Phrynocephalus mystaceus on different sand substrates with toe fringe manipulation, with the aim of assessing whether the function of the toe fringes shifts under different substrate properties, especially in highly mobile substrates. The sand burial performance of P. mystaceus was influenced by substrate properties in relation to the toe fringe states of the lizard. After removal of the bilateral toe fringes, the sand burial ability score of P. mystaceus was significantly higher on sand substrates below 100 mesh than on native sand substrates. As the angle of stability of the substrate properties decreased, the sand burial performance of the lizard was even better after the bilateral toe fringes were removed. The results of the LASSO model and the path analysis model showed that the stability angle provided the opposite effect on sand burial performance in different toe fringe states. These results further suggest that the sand burial function of toe fringes may not be suitable for highly mobile sand substrates. It remains to be tested further whether the function of toe fringes is more important for running on sand.

Recent Progress in the Physical Principles of Dynamic Ground Self-Righting

Animals and robots must self-right on the ground after overturning. Biology research has described various strategies and motor patterns in many species. Robotics research has devised many strategies. However, we do not well understand the physical principles of how the need to generate mechanical energy to overcome the potential energy barrier governs behavioral strategies and 3D body rotations given the morphology. Here, I review progress on this which I led studying cockroaches self-righting on level, flat, solid, low-friction ground, by integrating biology experiments, robotic modeling, and physics modeling. Animal experiments using three species (Madagascar hissing, American, and discoid cockroaches) found that ground self-righting is strenuous and often requires multiple attempts to succeed. Two species (American and discoid cockroaches) often self-right dynamically, using kinetic energy to overcome the barrier. All three species use and often stochastically transition across diverse strategies. In these strategies, propelling motions are often accompanied by perturbing motions. All three species often display complex yet stereotyped body rotation. They all roll more in successful attempts than in failed ones, which lowers the barrier, as revealed by a simplistic 3D potential energy landscape of a rigid body self-righting. Experiments of an initial robot self-righting via rotation about a fixed axis revealed that the longer and faster appendages push, the more mechanical energy can be gained to overcome the barrier. However, the cockroaches rarely achieve this. To further understand the physical principles of strenuous ground self-righting, we focused on the discoid cockroach's leg-assisted winged self-righting. In this strategy, wings propel against the ground to pitch the body up but are unable to overcome the highest pitch barrier. Meanwhile, legs flail in the air to perturb the body sideways to self-right via rolling. Experiments using a refined robot and an evolving 3D potential energy landscape revealed that, although wing propelling cannot generate sufficient kinetic energy to overcome the highest pitch barrier, it reduces the barrier to allow small kinetic energy from the perturbing legs to probabilistically overcome the barrier to self-right via rolling. Thus, only by combining propelling and perturbing can self-righting be achieved when it is so strenuous; this physical constraint leads to the stereotyped body rotation. Finally, multi-body dynamics simulation and template modeling revealed that the animal's substantial randomness in wing and leg motions helps it, by chance, to find good coordination, which accumulates more mechanical energy to overcome the barrier, thus increasing the likelihood of self-righting.

Active Adaptive Strategies of Mallard Feet in Response to Changes in Wetness and Compactness of the Sand Terrain

Mallards (Anas platyrhynchos) exhibit exceptional locomotive abilities in diverse terrains, such as beaches, swamps, and tidal flats. This capability is primarily attributed to their unique webbed toe structure and cooperative locomotion posture of their feet. Therefore, this study aims to further delve into the active adaptive strategies of mallard feet in response to diverse external environmental conditions. Six adult male mallards were selected for this research. Their locomotion on sandy surfaces with differing wetness levels and varying degrees of compaction were captured using a high-speed camera, and analysis of instantaneous and continuous changes in the primary joint angles of the mallards' feet, including the toe-webbed opening and closing angles, the tarsometatarsal-phalangeal joint (TMTPJ), and the intertarsal joint (ITJ). It was found that on loose sandy surfaces, increasing wetness expanded the ground contact area of the mallards' feet. This led to greater flexion at the TMTPJ joint during mid-stance, accompanied by decreased flexion of the ITJ during touch-down and mid-stance. Conversely, on compacted sand, increasing wetness resulted in a reduced foot effect area and lessened ITJ flexion at both touch-down and mid-stance. Furthermore, on looser sand, the ground contact area of the mallards' feet decreased, with an increase in ITJ buckling at touch-down. During the swing phase, sand wetness and compactness effected minimally on the feet of the mallards. On dry and loose sand ground, mallards will contract their second and fourth toes with webbing upon ground contact, covering and compacting the sand beneath, while increasing ITJ flexion to mitigate sinking. This adaptation reduces the energy expended on sand and enhances body stability. In wet and compacted sand conditions, mallards expand their second and fourth toes upon ground contact and reduce ITJ flexion. Therefore, this coordinated foot and ITJ locomotion offers mallards a natural advantage when moving on various environmental media.

Penetration of a spinning sphere impacting a granular medium

We investigate experimentally the influence of rotation on the penetration depth of a spherical projectile impacting a granular medium. We show that a rotational motion significantly increases the penetration depth achieved. Moreover, we model our experimental results by modifying the frictional term of the equation describing the penetration dynamics of an object in a granular medium. In particular, we find that the frictional drag decreases linearly with the velocity ratio between rotational (spin motion) and translational (falling motion) velocities. The good agreement between our model and our experimental measurements offers perspectives for estimating the depth that spinning projectiles reach after impacting onto a granular ground, such as happens with seeds dropped from aircraft or with landing probes.

Why animals can outrun robots

Animals are much better at running than robots. The difference in performance arises in the important dimensions of agility, range, and robustness. To understand the underlying causes for this performance gap, we compare natural and artificial technologies in the five subsystems critical for running: power, frame, actuation, sensing, and control. With few exceptions, engineering technologies meet or exceed the performance of their biological counterparts. We conclude that biology's advantage over engineering arises from better integration of subsystems, and we identify four fundamental obstacles that roboticists must overcome. Toward this goal, we highlight promising research directions that have outsized potential to help future running robots achieve animal-level performance.

Viability leads to the emergence of gait transitions in learning agile quadrupedal locomotion on challenging terrains

Quadruped animals are capable of seamless transitions between different gaits. While energy efficiency appears to be one of the reasons for changing gaits, other determinant factors likely play a role too, including terrain properties. In this article, we propose that viability, i.e., the avoidance of falls, represents an important criterion for gait transitions. We investigate the emergence of gait transitions through the interaction between supraspinal drive (brain), the central pattern generator in the spinal cord, the body, and exteroceptive sensing by leveraging deep reinforcement learning and robotics tools. Consistent with quadruped animal data, we show that the walk-trot gait transition for quadruped robots on flat terrain improves both viability and energy efficiency. Furthermore, we investigate the effects of discrete terrain (i.e., crossing successive gaps) on imposing gait transitions, and find the emergence of trot-pronk transitions to avoid non-viable states. Viability is the only improved factor after gait transitions on both flat and discrete gap terrains, suggesting that viability could be a primary and universal objective of gait transitions, while other criteria are secondary objectives and/or a consequence of viability. Moreover, our experiments demonstrate state-of-the-art quadruped robot agility in challenging scenarios.

Biomimetic lizard robot for adapting to Martian surface terrain

The exploration of the planet Mars still is a top priority in planetary science. The Mars surface is extensively covered with soil-like material. Current wheeled rovers on Mars have been occasionally experiencing immobilization instances in unexpectedly weak terrains. The development of Mars rovers adaptable to these terrains is instrumental in improving exploration efficiency. Inspired by locomotion of the desert lizard, this paper illustrates a biomimetic quadruped robot with structures of flexible active spine and toes. By accounting for spine lateral flexion and its coordination with four leg movements, three gaits of tripod, trot and turning are designed. The motions corresponding to the three gaits are conceptually and numerically analyzed. On the granular terrains analog to Martian surface, the gasping forces by the active toes are estimated. Then traversing tests for the robot to move on Martian soil surface analog with the three gaits were investigated. Moreover, the traversing characteristics for Martian rocky and slope surface analog are analyzed. Results show that the robot can traverse Martian soil surface analog with maximum forward speed 28.13 m s-1turning speed 1.94° s-1and obstacle height 74.85 mm. The maximum angle for climbing Martian soil slope analog is 28°, corresponding slippery rate 76.8%. It is predicted that this robot can adapt to Martian granular rough terrain with gentle slopes.

Kinematics and muscle activity of pectoral fins in rainbow trout (Oncorhynchus mykiss) station holding in turbulent flow

Pectoral fins play a crucial role in fish locomotion. Despite fishes living in complex fluid environments that exist in rivers and tidal flows, the role of the pectoral fins in navigating turbulent flows is not well understood. This study investigated the kinematics and muscle activity of pectoral fins in rainbow trout as they held station in the unsteady flows behind a D-section cylinder. We observed two distinct pectoral fin behaviors, one during braking and the other during Kármán gaiting. These behaviors were correlated to whole-body movements in response to the hydrodynamic conditions of specific regions in the cylinder wake. Sustained fin extensions during braking, where the fin was held out to maintain its position away from the body and against the flow, were associated with the cessation of forward body velocity, where the fish avoided the suction region directly downstream of the cylinder. Transient fin extensions and retractions during Kármán gaiting controlled body movements in the cross-stream direction. These two fin behaviors had different patterns of muscle activity. All braking events required recruitment from both the abductor and adductor musculature to actively extend a pectoral fin. In contrast, over 50% of fin extension movements during Kármán gaiting proceed in the absence of muscle activity. We reveal that in unsteady fluid environments, pectoral fin movements are the result of a complex combination of passive and active mechanisms that deviate substantially from canonical labriform locomotion, the implications of which await further work on the integration of sensory and motor systems.

Effect of Bionic Crab Shell Attitude Parameters on Lift and Drag in a Flow Field

Underwater bionic-legged robots encounter significant challenges in attitude, velocity, and positional control due to lift and drag in water current environments, making it difficult to balance operational efficiency with motion stability. This study delves into the hydrodynamic properties of a bionic crab robot's shell, drawing inspiration from the sea crab's motion postures. It further refines the robot's underwater locomotion strategy based on these insights. Initially, the research involved collecting attitude data from crabs during underwater movement through biological observation. Subsequently, hydrodynamic simulations and experimental validations of the bionic shell were conducted, examining the impact of attitude parameters on hydrodynamic performance. The findings reveal that the transverse angle predominantly influences lift and drag. Experiments in a test pool with a crab-like robot, altering transverse angles, demonstrated that increased transverse angles enhance the robot's underwater walking efficiency, stability, and overall performance.

Modeling of slip rate-dependent traversability for path planning of wheeled mobile robot in sandy terrain

A planetary exploration rover has been employed for scientific endeavors or as a precursor for upcoming manned missions. Predicting rover traversability from its wheel slip ensures safe and efficient autonomous operations of rovers on deformable planetary surfaces; path planning algorithms that reduce slips by considering wheel-soil interaction or terrain data can minimize the risk of the rover becoming immobilized. Understanding wheel-soil interaction in transient states is vital for developing a more precise slip ratio prediction model, while path planning in the past assumes that slips generated at the path is a series of slip ratio in steady state. In this paper, we focus on the transient slip, or slip rate the time derivative of slip ratio, to explicitly address it into the cost function of path planning algorithm. We elaborated a regression model that takes slip rate and traction force as inputs and outputs slip ratio, which is employed in the cost function to minimize the rover slip in path planning phase. Experiments using a single wheel testbed revealed that even with the same wheel traction force, the slip ratio varies with different slip rates; we confirmed that the smaller the absolute value of the slip rate, the larger the slip ratio for the same traction force. The statistical analysis of the regression model confirms that the model can estimate the slip ratio within an accuracy of 85% in average. The path planning simulation with the regression model confirmed a reduction of 58% slip experienced by the rover when driving through rough terrain environments. The dynamics simulation results insisted that the proposed method can reduce the slip rate in rough terrain environments.

Finite size effects during the penetration of objects in a granular medium

In many industrial or geotechnical applications, objects move through a granular medium and an important issue is the prediction of the force that develops during the motion of the intruder. In this paper, we experimentally study the vertical penetration of intruders into granular media and analyze both the average force and the fluctuations during motion. We investigate configurations where the size of the intruder becomes close to a few grain sizes, a regime that has not been studied before. Finite size effects are observed, showing that both the mean force and the fluctuations significantly increase when decreasing the ratio of the intruder size to the particle size, and scaling laws are identified to characterize this effect. The role of a conical tip in front of the cylinder to facilitate the penetration is also studied, showing that it is more efficient when the aspect ratio between the intruder size and the grain size is low.

Rate-dependent adhesion together with limb collaborations facilitate grasshoppers reliable attachment under highly dynamic conditions

Dynamic attachment is indispensable for animals to cope with unexpected disturbances. Minor attention has been paid to the dynamic performance of insects' adhesive pads. Through experiments pulling whole grasshoppers off a glass rod at varying speeds, surprising findings emerged. The feet did not always maintain contact but released and then reconnected to the substrate rapidly during leg extension, potentially reducing the shock damage to pads. As the pulling speeds increased from 1 to 400 mm/s, the maximum forces of single front tarsus insects and entire tarsi insects were nearly proportional to the 1/3 power of pulling speeds by 0.11 and 0.29 times, respectively. The force of some individuals could be even 800 times greater than their weight, which is unexpectedly high for smooth insect pads. This work not only helps us to understand the attachment intelligence of animals but is also informative for artificial attachment in extreme situations.

Environmental force sensing helps robots traverse cluttered large obstacles

Robots can traverse sparse obstacles by sensing environmental geometry and avoiding contact with obstacles. However, for search and rescue in rubble, environmental monitoring through dense vegetation, and planetary exploration over Martian and lunar rocks, robots must traverse cluttered obstacles as large as themselves by physically interacting with them. Previous work discovered that the forest floor-dwelling discoid cockroach and a sensor-less minimalistic robot can traverse cluttered grass-like beam obstacles of various stiffness by transitioning across different locomotor modes. Yet the animal was better at traversal than the sensor-less robot, likely by sensing forces during obstacle interaction to control its locomotor transitions. Inspired by this, here we demonstrated in simulation that environmental force sensing helps robots traverse cluttered large obstacles. First, we developed a multi-body dynamics simulation and a physics model of the minimalistic robot interacting with beams to estimate beam stiffness from the sensed contact forces. Then, we developed a force feedback strategy for the robot to use the sensed beam stiffness to choose the locomotor mode with a lower mechanical energy cost. With feedforward pushing, the robot was stuck in front of stiff beams if it has a limited force capacity; without force limit, it traversed but suffered a high energy cost. Using obstacle avoidance, the robot traversed beams by avoiding beam contact regardless of beam stiffness, resulting in a high energy cost for flimsy beams. With force feedback, the robot determined beam stiffness, then traversed flimsy beams by pushing them over and stiff beams by rolling through the gap between them with a low energy cost. Stiffness estimation based on force sensing was accurate across varied body oscillation amplitude and frequency and position sensing uncertainty. Mechanical energy cost of traversal increased with sensorimotor delay. Future work should demonstrate cluttered large obstacle traversal using force feedback in a physical robot.

Capillary washboarding during slow drainage of a frictional fluid

Numerous natural and industrial processes involve the mixed displacement of liquids, gases and granular materials through confining structures. However, understanding such three-phase flows remains a formidable challenge, despite their tremendous economic and environmental impact. To unveil the complex interplay of capillary and granular stresses in such flows, we consider here a model configuration where a frictional fluid (an immersed sedimented granular layer) is slowly drained out of a horizontal capillary. Analyzing how liquid/air menisci displace particles from such granular beds, we reveal various drainage patterns, notably the periodic formation of dunes, analogous to road washboard instability. Considering the competitive role of friction and capillarity, a 2D theoretical approach supported by numerical simulations of a meniscus bulldozing a front of particles provides quantitative criteria for the emergence of those dunes. A key element is the strong increase of the frictional forces, as the bulldozed particles accumulate and bend the meniscus horizontally. Interestingly, this frictional enhancement with the attack angle is also crucial in small-legged animals' locomotion over granular media.

Maneuverable and Efficient Locomotion of a Myriapod Robot with Variable Body-Axis Flexibility via Instability and Bifurcation

Legged robots have remarkable terrestrial mobility, but are susceptible to falling and leg malfunction during locomotion. The use of a large number of legs, as in centipedes, can overcome these problems, but it makes the body long and leads to many legs being constrained to contact with the ground to support the long body, which impedes maneuverability. A mechanism for maneuverable locomotion using a large number legs is thus desirable. However, controlling a long body with a large number of legs requires huge computational and energy costs. Inspired by agile locomotion in biological systems, this study proposes a control strategy for maneuverable and efficient locomotion of a myriapod robot based on dynamic instability. Specifically, our previous study made the body axis of a 12-legged robot flexible and showed that changing the body-axis flexibility produces pitchfork bifurcation. The bifurcation not only induces the dynamic instability of a straight walk but also a transition to a curved walk, whose curvature is controllable by the body-axis flexibility. This study incorporated a variable stiffness mechanism into the body axis and developed a simple control strategy based on the bifurcation characteristics. With this strategy, maneuverable and autonomous locomotion was achieved, as demonstrated by multiple robot experiments. Our approach does not directly control the movement of the body axis; instead, it controls body-axis flexibility, which significantly reduces computational and energy costs. This study provides a new design principle for maneuverable and efficient locomotion of myriapod robots.

Granular flow experiment using artificial gravity generator at International Space Station

Studying the gravity-dependent characteristics of regolith, fine-grained granular media covering extra-terrestrial bodies is essential for the reliable design and analysis of landers and rovers for space exploration. In this study, we propose an experimental approach to examine a granular flow under stable artificial gravity conditions for a long duration generated by a centrifuge at the International Space Station. We also perform a discrete element simulation of the granular flow in both artificial and natural gravity environments. The simulation results verify that the granular flows in artificial and natural gravity are consistent. Further, regression analysis of the experimental results reveals that the mass flow rate of granular flow quantitatively follows a well-known physics-based law with some deviations under low-gravity conditions, implying that the bulk density of the granular media decreases with gravity. This insight also indicates that the bulk density considered in simulation studies of space probes under low-gravity conditions needs to be tuned for their reliable design and analysis.

Efficient reciprocating burrowing with anisotropic origami feet

Origami folding is an ancient art which holds promise for creating compliant and adaptable mechanisms, but has yet to be extensively studied for granular environments. At the same time, biological systems exploit anisotropic body forces for locomotion, such as the frictional anisotropy of a snake's skin. In this work, we explore how foldable origami feet can be used to passively induce anisotropic force response in granular media, through varying their resistive plane. We present a reciprocating burrower which transfers pure symmetric linear motion into directed burrowing motion using a pair of deployable origami feet on either end. We also present an application of the reduced order model granular Resistive Force Theory to inform the design of deformable structures, and compare results with those from experiments and Discrete Element Method simulations. Through a single actuator, and without the use of advanced controllers or sensors, these origami feet enable burrowing locomotion. In this paper, we achieve burrowing translation ratios-net forward motion to overall linear actuation-over 46% by changing foot design without altering overall foot size. Specifically, anisotropic folding foot parameters should be tuned for optimal performance given a linear actuator's stroke length.

Substrate-mediated leg interactions play a key role in insect stability on granular slopes

Locomotion on granular inclines is a subject of high relevance in ecological physics as well as in biomimmetics and robotics. Enhancing stability on granular materials represents a huge challenge due to the fluidization transition when inclination approaches the avalanche angle. Our motivating example is the predator-prey system made of the antlion, its pit, and its prey. Recent studies have demonstrated that stability on granular inclines strongly depends on the pressure exerted on the substrate. In this work we show that for multilegged locomotion, along with pressure, the distance between the leg contacts on the substrate also plays a major role in the determination of the stability threshold. Through a set of model experiments using artificial sliders, we determine a critical distance below which stability is importantly affected by the interactions between the perturbed regions generated by each contact point. A simple model based on the Coulomb method of wedges allows us to estimate a stability criterion based on pressure, interleg distance, and substrate characteristics. Our work suggests that mass to leg-length allometric relationships, as the ones observed in ants, may be an important key in determining the locomotion success of multilegged locomotion on granular inclines.

Maneuvering on non-Newtonian fluidic terrain: a survey of animal and bio-inspired robot locomotion techniques on soft yielding grounds

Frictionally yielding media are a particular type of non-Newtonian fluids that significantly deform under stress and do not recover their original shape. For example, mud, snow, soil, leaf litters, or sand are such substrates because they flow when stress is applied but do not bounce back when released. Some robots have been designed to move on those substrates. However, compared to moving on solid ground, significantly fewer prototypes have been developed and only a few prototypes have been demonstrated outside of the research laboratory. This paper surveys the existing biology and robotics literature to analyze principles of physics facilitating motion on yielding substrates. We categorize animal and robot locomotion based on the mechanical principles and then further on the nature of the contact: discrete contact, continuous contact above the material, or through the medium. Then, we extract different hardware solutions and motion strategies enabling different robots and animals to progress. The result reveals which design principles are more widely used and which may represent research gaps for robotics. We also discuss that higher level of abstraction helps transferring the solutions to the robotics domain also when the robot is not explicitly meant to be bio-inspired. The contribution of this paper is a review of the biology and robotics literature for identifying locomotion principles that can be applied for future robot design in yielding environments, as well as a catalog of existing solutions either in nature or man-made, to enable locomotion on yielding grounds.

Complex Three-Dimensional Terrains Traversal of Insect-Scale Soft Robot

This article proposes a piezoelectric-driven insect-scale soft robot with ring-like curved legs, enabling it to traverse complex three-dimensional (3D) terrain only by body-terrain mechanical action. Relying on the repeated deformation of the main body's n and u shapes, the robot's leg-ground mechanical action produces an "elastic gait" to move. Regarding the detailed design, first, a theoretical curve of the front leg with a fixed angle of attack of 75° is designed by finite element simulation and comparative experiments. It ensures no increase in drag and no decrease in the lift when climbing steps. Second, a ring-like leg structure with 100% closed degree is proposed to ensure a smooth pass through small-sized uneven terrain without getting stuck. Then, the design of the overall asymmetrical structure of the robot can improve the conversion ratio of vibration to forward force. The shape of curved legs is controlled by pulling the flexible leg structure with two metal wires working as spokes. The semirigid leg structure made of fully flexible materials has shape stability and structural robustness. Compared with the plane-legged robot, the curved-legged robot can smoothly traverse different rugged 3D terrains and cross the terrain covering obstacles 0.36 times body height (BH) at a speed of >4 body lengths per second. Moreover, the curved-legged robot shows 100% and 64% chances of climbing steps with 1.2- and 1.9-times BH, respectively.

Multilegged matter transport: A framework for locomotion on noisy landscapes

Whereas the transport of matter by wheeled vehicles or legged robots can be guaranteed in engineered landscapes such as roads or rails, locomotion prediction in complex environments such as collapsed buildings or crop fields remains challenging. Inspired by the principles of information transmission, which allow signals to be reliably transmitted over "noisy" channels, we developed a "matter-transport" framework that demonstrates that noninertial locomotion can be provably generated over noisy rugose landscapes (heterogeneities on the scale of locomotor dimensions). Experiments confirm that sufficient spatial redundancy in the form of serially connected legged robots leads to reliable transport on such terrain without requiring sensing and control. Further analogies from communication theory coupled with advances in gaits (coding) and sensor-based feedback control (error detection and correction) can lead to agile locomotion in complex terradynamic regimes.

Learning quadrupedal locomotion on deformable terrain

Simulation-based reinforcement learning approaches are leading the next innovations in legged robot control. However, the resulting control policies are still not applicable on soft and deformable terrains, especially at high speed. The primary reason is that reinforcement learning approaches, in general, are not effective beyond the data distribution: The agent cannot perform well in environments that it has not experienced. To this end, we introduce a versatile and computationally efficient granular media model for reinforcement learning. Our model can be parameterized to represent diverse types of terrain from very soft beach sand to hard asphalt. In addition, we introduce an adaptive control architecture that can implicitly identify the terrain properties as the robot feels the terrain. The identified parameters are then used to boost the locomotion performance of the legged robot. We applied our techniques to the Raibo robot, a dynamic quadrupedal robot developed in-house. The trained networks demonstrated high-speed locomotion capabilities on deformable terrains: The robot was able to run on soft beach sand at 3.03 meters per second although the feet were completely buried in the sand during the stance phase. We also demonstrate its ability to generalize to different terrains by presenting running experiments on vinyl tile flooring, athletic track, grass, and a soft air mattress.

Historical evolution and new trends for soil-intruder interaction modeling

Soil is a crucial resource for life on Earth. Every activity, whether natural or man-made, that interacts with the sub or deep soil can affect the land at large scales (e.g. geological risks). Understanding such interactions can help identify more sustainable and less invasive soil penetration, exploration, and monitoring solutions. Over the years, multiple approaches have been used in modeling soil mechanics to reveal soil behavior. This paper reviews the different modeling techniques used to simulate the interaction between a penetrating tool and the soil, following their use over time. Opening with analytical methods, we discuss the limitations that have partially been overcome by the finite element method (FEM). FEM models are capable of simulating more complex conditions and geometries. However, they require the continuum mechanics assumption. Hence, FEM analysis cannot simulate the discrete processes occurring during soil deformation (i.e. the separation and mixing of soil layers, the appearance of cracks, or the flow of soil particles). The discrete element method (DEM) has thus been adopted as a more promising modeling technique. Alongside models, experimental approaches have also been used to describe soil-intruder interactions, complementing or validating simulation results. Recently, bioinspired approaches have been considered promising to improve sustainability and reduce the invasiveness of classical penetration strategies. This review highlights how DEM-based models can help in studying the interaction mechanisms between bioinspired root-like artificial penetrometers and the soil. Bioinspired designs and the merging of multiple analysis approaches can offer new perspectives. These may be pivotal in the design of highly optimized soil robotic explorers capable of adapting their morphology and penetration strategies based on their surrounding conditions.

Field Traction Performance Test Analysis of Bionic Paddy Wheel and Vaned Wheel

In order to improve the traction performance of a wheel of a micro-tiller on the soil surface of a paddy field, we extracted the surface curve of a cow's hoof and used the cow's hoof as a bionic prototype to design a bionic paddy wheel. In order to verify the passability of the bionic paddy wheel in paddy soil, a wheel-soil test bench was built in the experimental field with a moisture content of 36%. The test results show that under the condition of the same load on the wheel, the changing laws of torque, drawbar pull, and slip ratio of the bionic paddy wheel and the conventional vaned wheel are similar. The torque and drawbar pull of the bionic paddy wheel are higher than those of the conventional vaned wheel at the same slip ratio. The maximum torque and hook traction provided by the bionic paddy wheel and the conventional vaned wheel both increase with the increase of the load on the wheel. Under the same load on the wheel, the bionic paddy wheel is at least 22% higher than the conventional vaned wheel. Compared with the conventional vaned wheel, the bionic paddy wheel can provide a higher driving force and hook traction, which can improve the working efficiency of the vehicle in the paddy field.

Mole crab-inspired vertical self-burrowing

We present EMBUR-EMerita BUrrowing Robot-the first legged robot inspired by the Pacific mole crab, Emerita analoga, capable of burrowing vertically downward. We choose Emerita analoga as a model organism for its rapid downward burrowing behaviors, as it is four times as fast as the most rapid bivalve mollusk. Vertical burrowing in granular media is a challenging endeavor due to the tendency for the media to create upwards resistive forces on an intruder, even during purely horizontal motions. Our robot is capable of vertically burrowing its body in granular substrate primarily through excavation using two leg pairs, which are functionally analogous to groupings of leg pairs of the mole crab. We implement a novel leg mechanism with a sweeping trajectory, using compliant fabric to enable an anisotropic force response. The maximum resistive force during the power stroke is 6.4 times that of the return stroke. We compare robot body pitch and spatial trajectories with results from biomechanical studies of the mole crabs. We characterize the sensitivity of the robot to initial depth, body pitch and leg pose, and propose bounds on initial conditions which predict various burrowing failure modes. Parametric studies utilizing Granular Resistive Force Theory inform our understanding of robot behavior in response to leg phasing and orientation. Not only does this robotic platform represent the first robophysical model of vertical mole crab-inspired burrowing, it is also one of the first legged, primarily excavative small-scale burrowing agents.

Wireless Miniature Magnetic Phase-Change Soft Actuators

Wireless miniature soft actuators are promising for various potential high-impact applications in medical, robotic grippers, and artificial muscles. However, these miniature soft actuators are currently constrained by a small output force and low work capacity. To address such challenges, a miniature magnetic phase-change soft composite actuator is reported. This soft actuator exhibits an expanding deformation and enables up to a 70 N output force and 175.2 J g-1 work capacity under remote magnetic radio frequency heating, which are 106 -107 times that of traditional magnetic soft actuators. To demonstrate its capabilities, a wireless soft robotic device is first designed that can withstand 0.24 m s-1 fluid flows in an artery phantom. By integrating it with a thermally-responsive shape-memory polymer and bistable metamaterial sleeve, a wireless reversible bistable stent is designed toward future potential angioplasty applications. Moreover, it can additionally locomote inside and jump out of granular media. At last, the phase-change actuator can realize programmable bending deformations when a specifically designed magnetization profile is encoded, enhancing its shape-programming capability. Such a miniature soft actuator provides an approach to enhance the mechanical output and versatility of magnetic soft robots and devices, extending their medical and other potential applications.

Field-mediated locomotor dynamics on highly deformable surfaces

Studies of active matter-systems consisting of individuals or ensembles of internally driven and damped locomotors-are of interest to physicists studying nonequilibrium dynamics, biologists interested in individuals and swarm locomotion, and engineers designing robot controllers. While principles governing active systems on hard ground or within fluids are well studied, another class of systems exists at deformable interfaces. Such environments can display mixes of fluid-like and elastic features, leading to locomotor dynamics that are strongly influenced by the geometry of the surface, which, in itself, can be a dynamical entity. To gain insight into principles by which locomotors are influenced via a deformation field alone (and can influence other locomotors), we study robot locomotion on an elastic membrane, which we propose as a model of active systems on highly deformable interfaces. As our active agent, we use a differential driven wheeled robotic vehicle which drives straight on flat homogeneous surfaces, but reorients in response to environmental curvature. We monitor the curvature field-mediated dynamics of a single vehicle interacting with a fixed deformation as well as multiple vehicles interacting with each other via local deformations. Single vehicles display precessing orbits in centrally deformed environments, while multiple vehicles influence each other by local deformation fields. The active nature of the system facilitates a differential geometry-inspired mathematical mapping from the vehicle dynamics to those of test particles in a fictitious "spacetime," allowing further understanding of the dynamics and how to control agent interactions to facilitate or avoid multivehicle membrane-induced cohesion.

Coordinating tiny limbs and long bodies: Geometric mechanics of lizard terrestrial swimming

Although typically possessing four limbs and short bodies, lizards have evolved diverse morphologies, including elongate trunks with tiny limbs. Such forms are hypothesized to aid locomotion in cluttered/fossorial environments but propulsion mechanisms (e.g., the use of body and/or limbs to interact with substrates) and potential body/limb coordination remain unstudied. Here, we use biological experiments, a geometric theory of locomotion, and robophysical models to investigate body-limb coordination in diverse lizards. Locomotor field studies in short-limbed, elongate lizards (Brachymeles and Lerista) and laboratory studies of fully limbed lizards (Uma scoparia and Sceloporus olivaceus) and a snake (Chionactis occipitalis) reveal that body-wave dynamics can be described by a combination of standing and traveling waves; the ratio of the amplitudes of these components is inversely related to the degree of limb reduction and body elongation. The geometric theory (which replaces laborious calculation with diagrams) helps explain our observations, predicting that the advantage of traveling-wave body undulations (compared with a standing wave) emerges when the dominant thrust-generation mechanism arises from the body rather than the limbs and reveals that such soil-dwelling lizards propel via "terrestrial swimming" like sand-swimming lizards and snakes. We test our hypothesis by inducing the use of traveling waves in stereotyped lizards via modulating the ground-penetration resistance. Study of a limbed/undulatory robophysical model demonstrates that a traveling wave is beneficial when propulsion is generated by body-environment interaction. Our models could be valuable in understanding functional constraints on the evolutionary processes of elongation and limb reduction as well as advancing robot designs.

Unified penetration depth of low-velocity intruders into granular packings

Penetration of intruders into granular packings is well described by separately considering the dry or wet case of granular environments in previous experiments and simulations; however, the unified description of such penetration depth in these two granular media remains elusive due to lacking clear explanations about its origins. Based on three-dimensional discrete element method simulations, we introduce a power-law fitting form of the final penetration depth of a spherical intruder with low velocity vertically penetrating into dry and wet granular packings, excellently expressed on a master curve as a power-law function of a dimensionless impact number that is defined as the square root of the ratio between the inertial stress of the intruder and the linear combination of the mean gravitational stress and the cohesive stress exerted on each grain in the packings, as a remarkable extension of the inertial number in dry granular flows. This scaling robustly provides physical insights inherent in the unified description of the material properties of granular packings and the impactor penetration conditions on the final penetration depth in the impact tests, providing evidence of impact properties in different disciplines and applications in science and engineering.

Successive reintrusions in a granular medium

We measure and analyze the drag force experienced by a rigid rod that penetrates vertically into a granular medium and partially withdraws before sinking again. The drag during the successive reintrusions is observed to be significantly smaller than the force experienced in the first run. Two force regimes are evidenced depending on how the reintrusion depth compares with the withdrawal distance Δ. These two regimes are characterized by a force curve of positive and negative curvature and are separated by an inflection point, which is characterized experimentally. We approach the difference between the first intrusion and the following reintrusions by considering a modification in the stress field of the granular material after the partial extraction of the rod. A theoretical model for the stress modification is proposed and allows to rationalize all the experiments realized for different withdrawal distances Δ. This framework introduces a crossover length λ above which the stress modification in the granular medium is maintained and that is shown to depend linearly on Δ. Finally, the model provides a prediction for the location of the inflection points in reasonable agreement with observations.

Mudskippers modulate their locomotor kinematics when moving on deformable and inclined substrates

Many ecological factors influence animal movement, including properties of the media that they move on or through. Animals moving in terrestrial environments encounter conditions that can be challenging for generating propulsion and maintaining stability, such as inclines and deformable substrates that can cause slipping and sinking. In response, tetrapods tend to adopt a more crouched posture and lower their center of mass on inclines and increase the surface area of contact on deformable substrates, such as sand. Many amphibious fishes encounter the same challenges when moving on land, but how these finned animals modulate their locomotion with respect to different environmental conditions and how these modifications compare with those seen within tetrapods is relatively understudied. Mudskippers (Gobiidae: Oxudercinae) are a particularly noteworthy group of amphibious fishes in this context given that they navigate a wide range of environmental conditions, from flat mud to inclined mangrove trees. They use a unique form of terrestrial locomotion called 'crutching', where their pectoral fins synchronously lift and vault the front half of the body forward before landing on their pelvic fins while the lower half of the body and tail are kept straight. However, recent work has shown that mudskippers modify some aspects of their locomotion when crutching on deformable surfaces, particularly those at an incline. For example, on inclined dry sand, mudskippers bent their bodies laterally and curled and extended their tails to potentially act as a secondary propulsor and/or anti-slip device. In order to gain a more comprehensive understanding of the functional diversity and context-dependency of mudskipper crutching, we compared their kinematics on different combinations of substrate types (solid, mud, dry sand) and inclines (0°, 10°, 20°). In addition to increasing lateral bending on deformable and inclined substrates, we found that mudskippers increased the relative contact time and contact area of their paired fins while becoming more crouched, responses comparable to those seen in tetrapods and other amphibious fishes. Mudskippers on these substrates also exhibited previously undocumented behaviors, such as extending and adpressing the distal portions of their pectoral fins more anteriorly, dorsoventrally bending their trunk, "belly-flopping" on sand, and "gripping" the mud substrate with their pectoral fin rays. Our study highlights potential compensatory mechanisms shared among vertebrates in terrestrial environments while also illustrating that locomotor flexibility and even novelty can emerge when animals are challenged with environmental variation.

Twisting for soft intelligent autonomous robot in unstructured environments

SignificanceAutonomy is crucial for soft robotics that are constructed of soft materials. It remains challenging to create autonomous soft robots that can intelligently interact with and adapt to changing environments without external controls. To do so, it often requires an analogical soft "brain" that integrates on-board sensing, control, computation, and decision-making. Here, we report an autonomous soft robot embodied with physical intelligence for decision-making via adaptive soft body-environment interactions and snap-through instability, without integrated sensing and external controls. This study harnesses physical intelligence as a new paradigm for designing autonomous soft robots that can interact intelligently with their environments, thus potentially reducing the burdens on the conventional integrated sensing, control, computations, and decision-making systems in designing intelligent soft robots.

Analysis and control of a running spring-mass model with a trunk based on virtual pendulum concept

The spring-loaded inverted pendulum model has been one of the most studied conceptual models in the locomotion community. Even though it can adequately explain the center of mass trajectories of numerous legged animals, it remains insufficient in template-based control of complex robot platforms, being unable to capture additional dynamic characteristics of locomotion exhibited in additional degrees of freedom such as trunk pitch oscillations. In fact, analysis of trunk behavior during locomotion has been one of the motivations behind studying the virtual pivot point (VPP) concept, with biological inspiration and basis for both natural and synthetic systems with non-negligible trunk dynamics. This study first presents a comprehensive analysis of the VPP concept for planar running behaviors, followed by a systematic study of the existence and characteristics of periodic solutions. In particular, we investigate how periodic solutions depend on model control parameters and compare them based on stability and energetic cost. We then develop a feedback controller that can stabilize system dynamics around its periodic solutions and evaluate performance as compared to a previously introduced controller from the literature. We demonstrate the effectiveness of both controllers and find that the proposed control scheme creates larger basins of attraction with minor degradation in convergence speed. In conclusion, this study shows that the VPP concept, in conjunction with the proposed controller, could be beneficial in designing and controlling legged robots capable of running with non-trivial upper body dynamics. Our systematic analysis of periodic solutions arising from the use of the VPP concept is also an important step towards a more formal basis for comparisons of the VPP concept with bio-locomotion.

Performance and Kinematic Differences Between Terrestrial and Aquatic Running in Anolis Sagrei

Many animals frequently transition between different media while navigating their heterogeneous environments. These media vary in compliance, moisture content, and other characteristics that affect their physical properties. As a result, animals may need to alter their kinematics to adapt to potential changes in media while maintaining performance during predator escape and foraging. Due to its fluid nature, water is highly compliant, and although usually associated with swimming, water running has evolved in a variety of animals ranging from insects to mammals. While the best studied large water runners are the bipedal basilisk lizards (Basiliscus spp.), other lizards have also been observed to run across the surface of water, namely Hemidactylus platyurus, a house gecko, and in this study, Anolis sagrei, the brown anole. Unlike the basilisk lizard, the primarily arboreal Anolis sagrei is not adapted for water running. Moreover, water running in A. sagrei, similar to that of the house gecko, was primarily quadrupedal. Here, we tested for performance and kinematic differences between aquatic and terrestrial running and if the variance in performance and kinematic variables differed between the two media. We found no difference in average and maximum velocity between running on land and water. We also found that Anolis sagrei had higher hindlimb stride frequencies, decreased duty factor, and shorter stride lengths on water, as well as more erect postures. Finally, we found that most kinematics did not differ in variance between the two media, but of those that were different, almost all were more variable during terrestrial running. Our findings show that animals may be capable of specialized modes of locomotion, even if they are not obviously adapted for them, and that they may do this by modulating their kinematics to facilitate locomotion through novel environments.

What is Stance Phase On Deformable Substrates?

The stance phase of walking is when forces are applied to the environment to support, propel, and maneuver the body. Unlike solid surfaces, deformable substrates yield under load, allowing the foot to sink to varying degrees. For bipedal birds and their dinosaurian ancestors, a shared response to walking on these substrates has been identified in the looping path the digits follow underground. Because a volume of substrate preserves a 3-D record of stance phase in the form of footprints or tracks, understanding how the bipedal stride cycle relates to this looping motion is critical for building a track-based framework for the study of walking in extinct taxa. Here we used biplanar X-ray imaging to record and analyze 161 stance phases from 81 trials of three Helmeted Guineafowl (Numida meleagris) walking on radiolucent substrates of different consistency (solid, dry granular, firm to semi-liquid muds). Across all substrates, the feet sank to a range of depths up to 78% of hip height. With increasing substrate hydration, the majority of foot motion shifted from above to below ground. Walking kinematics sampled across all stride cycles revealed six sequential gait-based events originating from both feet, conserved throughout the spectrum of substrate consistencies during normal alternating walking. On all substrates that yielded, five sub-phases of gait were drawn out in space and formed a loop of varying shape. We describe the two-footed coordination and weight distribution that likely contributed to the observed looping patterns of an individual foot. Given such complex subsurface foot motion during normal alternating walking and some atypical walking behaviors, we discuss the definition of "stance phase" on deformable substrates. We also discuss implications of the gait-based origins of subsurface looping on the interpretation of locomotory information preserved in fossil dinosaur tracks.

Nonadditive drag of tandem rods drafting in granular sediments

We examine the drag experienced by a pair of vertical rods moving in tandem through a granular bed immersed in a fluid as a function of their separation distance and speed. As in Newtonian fluids, the net drag experienced by the rods initially increases with distance from the value for a single rod before plateauing to twice the value. However, the drag acting on the two rods is remarkably different, with the leading rod experiencing roughly similar drag compared to a solitary rod, while the following rod experiences far less drag. The anomalous relationship of drag and the distance between the leading and following body is observed in both dry granular beds and while immersed in viscous Newtonian fluids across the quasistatic and the rate-dependent regimes. Through refractive index matching, we visualize the sediment flow past the two rods and show that a stagnant region develops in their reference frame between the rods for small separations. Thus, the following rod is increasingly shielded from the granular flow with decreasing separation distance, leading to a lower net drag. Care should be exercised in applying resistive force theory to multicomponent objects moving in granular sediments based on our result that drag is not additive at short separation distances.

The neuroecology of the water-to-land transition and the evolution of the vertebrate brain

The water-to-land transition in vertebrate evolution offers an unusual opportunity to consider computational affordances of a new ecology for the brain. All sensory modalities are changed, particularly a greatly enlarged visual sensorium owing to air versus water as a medium, and expanded by mobile eyes and neck. The multiplication of limbs, as evolved to exploit aspects of life on land, is a comparable computational challenge. As the total mass of living organisms on land is a hundredfold larger than the mass underwater, computational improvements promise great rewards. In water, the midbrain tectum coordinates approach/avoid decisions, contextualized by water flow and by the animal's body state and learning. On land, the relative motions of sensory surfaces and effectors must be resolved, adding on computational architectures from the dorsal pallium, such as the parietal cortex. For the large-brained and long-living denizens of land, making the right decision when the wrong one means death may be the basis of planning, which allows animals to learn from hypothetical experience before enactment. Integration of value-weighted, memorized panoramas in basal ganglia/frontal cortex circuitry, with allocentric cognitive maps of the hippocampus and its associated cortices becomes a cognitive habit-to-plan transition as substantial as the change in ecology. This article is part of the theme issue 'Systems neuroscience through the lens of evolutionary theory'.

The Smooth Transition From Many-Legged to Bipedal Locomotion—Gradual Leg Force Reduction and its Impact on Total Ground Reaction Forces, Body Dynamics and Gait Transitions

Most terrestrial animals move with a specific number of propulsive legs, which differs between clades. The reasons for these differences are often unknown and rarely queried, despite the underlying mechanisms being indispensable for understanding the evolution of multilegged locomotor systems in the animal kingdom and the development of swiftly moving robots. Moreover, when speeding up, a range of species change their number of propulsive legs. The reasons for this behaviour have proven equally elusive. In animals and robots, the number of propulsive legs also has a decisive impact on the movement dynamics of the centre of mass. Here, I use the leg force interference model to elucidate these issues by introducing gradually declining ground reaction forces in locomotor apparatuses with varying numbers of leg pairs in a first numeric approach dealing with these measures’ impact on locomotion dynamics. The effects caused by the examined changes in ground reaction forces and timing thereof follow a continuum. However, the transition from quadrupedal to a bipedal locomotor system deviates from those between multilegged systems with different numbers of leg pairs. Only in quadrupeds do reduced ground reaction forces beneath one leg pair result in increased reliability of vertical body oscillations and therefore increased energy efficiency and dynamic stability of locomotion.