Mechanics of peristaltic locomotion and role of anchoring

Optical mapping of ground reaction force dynamics in freely behaving Drosophila melanogaster larvae

During locomotion, soft-bodied terrestrial animals solve complex control problems at substrate interfaces, but our understanding of how they achieve this without rigid components remains incomplete. Here, we develop new all-optical methods based on optical interference in a deformable substrate to measure ground reaction forces (GRFs) with micrometre and nanonewton precision in behaving Drosophila larvae. Combining this with a kinematic analysis of substrate-interfacing features, we shed new light onto the biomechanical control of larval locomotion. Crawling in larvae measuring ~1 mm in length involves an intricate pattern of cuticle sequestration and planting, producing GRFs of 1-7 µN. We show that larvae insert and expand denticulated, feet-like structures into substrates as they move, a process not previously observed in soft-bodied animals. These 'protopodia' form dynamic anchors to compensate counteracting forces. Our work provides a framework for future biomechanics research in soft-bodied animals and promises to inspire improved soft-robot design.

Pose analysis in free-swimming adult zebrafish, Danio rerio : "fishy" origins of movement design

Movement requires maneuvers that generate thrust to either make turns or move the body forward in physical space. The computational space for perpetually controlling the relative position of every point on the body surface can be vast. We hypothesize the evolution of efficient design for movement that minimizes active (neural) control by leveraging the passive (reactive) forces between the body and the surrounding medium at play. To test our hypothesis, we investigate the presence of stereotypical postures during free-swimming in adult zebrafish, Danio rerio . We perform markerless tracking using DeepLabCut, a deep learning pose estimation toolkit, to track geometric relationships between body parts. To identify putative clusters of postural configurations obtained from twelve freely behaving zebrafish, we use unsupervised multivariate time-series analysis (B-SOiD machine learning software). When applied to single individuals, this method reveals a best-fit for 36 to 50 clusters in contrast 86 clusters for data pooled from all 12 animals. The centroids of each cluster obtained over 14,000 sequential frames recorded for a single fish represent an apriori classification into relatively stable "target body postures" and inter-pose "transitional postures" that lead to and away from a target pose. We use multidimensional scaling of mean parameter values for each cluster to map cluster-centroids within two dimensions of postural space. From a post-priori visual analysis, we condense neighboring postural variants into 15 superclusters or core body configurations. We develop a nomenclature specifying the anteroposterior level/s (upper, mid and lower) and degree of bending. Our results suggest that constraining bends to mainly three levels in adult zebrafish preempts the neck, fore- and hindlimb design for maneuverability in land vertebrates.

Self-propulsion via slipping: Frictional swimming in multilegged locomotors

Locomotion is typically studied either in continuous media where bodies and legs experience forces generated by the flowing medium or on solid substrates dominated by friction. In the former, centralized whole-body coordination is believed to facilitate appropriate slipping through the medium for propulsion. In the latter, slip is often assumed minimal and thus avoided via decentralized control schemes. We find in laboratory experiments that terrestrial locomotion of a meter-scale multisegmented/legged robophysical model resembles undulatory fluid swimming. Experiments varying waves of leg stepping and body bending reveal how these parameters result in effective terrestrial locomotion despite seemingly ineffective isotropic frictional contacts. Dissipation dominates over inertial effects in this macroscopic-scaled regime, resulting in essentially geometric locomotion on land akin to microscopic-scale swimming in fluids. Theoretical analysis demonstrates that the high-dimensional multisegmented/legged dynamics can be simplified to a centralized low-dimensional model, which reveals an effective resistive force theory with an acquired viscous drag anisotropy. We extend our low-dimensional, geometric analysis to illustrate how body undulation can aid performance in non-flat obstacle-rich terrains and also use the scheme to quantitatively model how body undulation affects performance of biological centipede locomotion (the desert centipede Scolopendra polymorpha) moving at relatively high speeds (∼0.5 body lengths/sec). Our results could facilitate control of multilegged robots in complex terradynamic scenarios.

Untethered unidirectionally crawling gels driven by asymmetry in contact forces

Reversible thermoresponsive hydrogels, which swell and shrink (deswell) in the temperature range of 30° to 60°C, provide an attractive material class for operating untethered soft robots in human physiological and ambient conditions. Crawling has been demonstrated previously with thermoresponsive hydrogels but required patterned or constrained gels or substrates to break symmetry for unidirectional motion. Here, we demonstrate a locomotion mechanism for unidirectionally crawling gels driven by spontaneous asymmetries in contact forces during swelling and deswelling of segmented active thermoresponsive poly( N -isopropylacrylamide) (pNIPAM) and passive polyacrylamide (pAAM) bilayers with suspended linkers. Actuation studies demonstrate the consistent unidirectional movement of these gel crawlers across multiple thermal cycles on flat, unpatterned substrates. We explain the mechanism using finite element simulations and by varying experimental parameters such as the linker stiffness and the number of bilayer segments. We elucidate design criteria and validate experiments using image analysis and finite element models. We anticipate that this mechanism could potentially be applied to other shape-changing locomotors.

Optimal locomotion for limbless crawlers

Limbless crawling is ubiquitous in biology, from cells to organisms. We develop and analyze a model for the dynamics of one-dimensional elastic crawlers, subject to active stress and deformation-dependent friction with the substrate. We find that the optimal active stress distribution that maximizes the crawler's center-of-mass displacement given a fixed amount of energy input is a traveling wave. This theoretical optimum corresponds to peristalsislike extension-contraction waves observed in biological organisms, possibly explaining the prevalence of peristalsis as a convergent gait across species. Our theory elucidates key observations in biological systems connecting the anchoring phase of a crawler to the retrograde and prograde distinction seen in peristaltic waves among various organisms. Using our optimal gait solution, we derive a scaling relation between the crawling speed and body mass, explaining experiments on earthworms with three orders of magnitude body mass variations. Our results offer insights and tools for optimal bioinspired crawling robots design with finite battery capacity.

Planarian nociception: Lessons from a scrunching flatworm

In addition to being studied for their exceptional regeneration abilities, planarians (i.e., flatworms) have also been extensively used in the context of pharmacological experiments during the past century. Many researchers used planarians as a model system for the study of drug abuse because they display high similarities with the nervous system of vertebrates at cellular and molecular levels (e.g., neuronal morphology, neurotransmitter ligands, and receptor function). This research field recently led to the discovery of causal relationships between the expression of Transient Receptor Potential ion channels in planarians and their behavioral responses to noxious stimuli such as heat, cold or pharmacological analogs such as TRP agonists, among others. It has also been shown that some antinociceptive drugs modulate these behaviors. However, among the few authors that tried to implement a full behavior analysis, none reached a consensual use of the terms used to describe planarian gaits yet, nor did they establish a comprehensive description of a potential planarian nociceptive system. The aim of this review is therefore to aggregate the ancient and the most recent evidence for a true nociceptive behavior in planarians. It also highlights the convenience and relevance of this invertebrate model for nociceptive tests and suggests further lines of research. In regards to past pharmacological studies, this review finally discusses the opportunities given by the model to extensively screen for novel antinociceptive drugs.

Imaging dynamic three-dimensional traction stresses

Traction stress between contact objects is ubiquitous and crucial for various physical, biological, and engineering processes such as momentum transfer, tactile perception, and mechanical reliability. Newly developed techniques including electronic skin or traction force microscopy enable traction stress measurement. However, measuring the three-dimensional distribution during a dynamic process remains challenging. Here, we demonstrated a method based on stereo vision to measure three-dimensional traction stress with high spatial and temporal resolution. It showed the ability to image the two-stage adhesion failure of bionic microarrays and display the contribution of elastic resistance and adhesive traction to rolling friction at different contact regions. It also revealed the distributed sucking and sealing effect of the concavity pedal waves that propelled a snail crawling in the horizontal, vertical, and upside-down directions. We expected that the method would advance the understanding of various interfacial phenomena and greatly benefit related applications across physics, biology, and robotics.

Gait switching with phase reversal of locomotory waves in the centipedeScolopocryptops rubiginosus

Crawling using locomotory waves is a common method of locomotion for limbless and many-legged invertebrates and stimulates the biomimetic engineering of flexible locomotion. It is generally believed that the direction of locomotory waves is fixed for a given species. However, we found that a centipede,Scolopocryptops rubiginosus, flexibly generated its gait to allow for locomotory waves that varied in direction, depending on (i) locomotion speed and (ii) the physical conditions of terrain. We also found a new type of centipede's swimming gait unlike eel-like way known so far which is using posteriorly traveling waves of horizontal body undulation. The gait patterns of the centipede were examined in various conditions and analyzed how the waves switched in detailed. We showed that gait patterns were associated with control of stride length rather than stride frequency. Discussion was made on a possible scenario of the gait transition in the centipede compatible with our observations. This finding may give a hint at bio-inspired control of flexible gait switching in response to irregular terrain.

Yoshimura-origami Based Earthworm-like Robot With 3-dimensional Locomotion Capability

Earthworm-like robots have received great attention due to their prominent locomotion abilities in various environments. In this research, by exploiting the extraordinary three-dimensional (3D) deformability of the Yoshimura-origami structure, the state of the art of earthworm-like robots is significantly advanced by enhancing the locomotion capability from 2D to 3D. Specifically, by introducing into the virtual creases, kinematics of the non-rigid-foldable Yoshimura-ori structure is systematically analyzed. In addition to exhibiting large axial deformation, the Yoshimura-ori structure could also bend toward different directions, which, therefore, significantly expands the reachable workspace and makes it possible for the robot to perform turning and rising motions. Based on prototypes made of PETE film, mechanical properties of the Yoshimura-ori structure are also evaluated experimentally, which provides useful guidelines for robot design. With the Yoshimura-ori structure as the skeleton of the robot, a hybrid actuation mechanism consisting of SMA springs, pneumatic balloons, and electromagnets is then proposed and embedded into the robot: the SMA springs are used to bend the origami segments for turning and rising motion, the pneumatic balloons are employed for extending and contracting the origami segments, and the electromagnets serve as anchoring devices. Learning from the earthworm’s locomotion mechanism--retrograde peristalsis wave, locomotion gaits are designed for controlling the robot. Experimental tests indicate that the robot could achieve effective rectilinear, turning, and rising locomotion, thus demonstrating the unique 3D locomotion capability.

Peristalsis by pulses of activity

Peristalsis by actively generated waves of muscle contraction is one of the most fundamental ways of producing motion in living systems. We show that peristalsis can be modeled by a train of rectangular-shaped solitary waves of localized activity propagating through otherwise passive matter. Our analysis is based on the Fermi-Pasta-Ulam (FPU) type discrete model accounting for active stresses and we reveal the existence in this problem of a critical regime which we argue to be physiologically advantageous.

Fundamental understanding of millipede morphology and locomotion dynamics

A detailed model for the locomotory mechanics used by millipedes is provided here through systematic experimentation on the animal and validation of observations through a biomimetic robotic platform. Millipedes possess a powerful gait that is necessary for generating large thrust force required for proficient burrowing. Millipedes implement a metachronal gait through movement of many legs that generates a traveling wave. This traveling wave is modulated by the animal to control the magnitude of thrust force in the direction of motion for burrowing, climbing, or walking. The quasi-static model presented for the millipede locomotion mechanism matches experimental observations on live millipedes and results obtained from a biomimetic robotic platform. The model addresses questions related to the unique morphology of millipedes with respect to their locomotory performance. A complete understanding of the physiology of millipedes and mechanisms that provide modulation of the traveling wave locomotion using a metachronal gait to increase their forward thrust is provided. Further, morphological features needed to optimize various locomotory and burrowing functions are discussed. Combined, these results open opportunity for development of biologically inspired locomotory methods for miniaturized robotic platforms traversing terrains and substrates that present large resistances.

Rapid two-anchor crawling from a milliscale prismatic-push-pull (3P) robot

Many crawling organisms such as caterpillars and worms use a method of movement in which two or more anchor points alternately push and pull the body forward at a constant frequency. In this paper we present a milliscale push-pull robot which is capable of operating across a wide range of actuation frequencies thus enabling us to expand our understanding of two-anchor locomotion beyond the low-speed regime. We designed and fabricated a milliscale robot which uses anisotropic friction at two oscillating contact points to propel itself forward in a push-pull fashion. In experiments we varied the oscillation frequency,f, over a wide range (10-250 Hz) and observe a non-linear relationship between robot speed over this full frequency range. At low frequency (f< 100 Hz) forward speed increased linearly with frequency. However, at an intermediate push-pull frequency (f> 100 Hz) speed was relatively constant with increasing frequency. Lastly, at higher frequency (f> 170 Hz) the linear speed-frequency relationship returned. The speed-frequency relationship at low actuation frequencies is consistent with previously described two-anchor models and experiments in biology and robotics, however the higher frequency behavior is inconsistent with two-anchor frictional behavior. To understand the locomotion behavior of our system we first develop a deterministic two-anchor model in which contact forces are determined exactly from static or dynamic friction. Our experiments deviate from the model predictions, and through 3D kinematics measurements we confirm that ground contact is intermittent in robot locomotion at higher frequencies. By including probabilistic foot slipping behavior in the two-anchor friction model we are able to describe the three-regimes of robot locomotion.

An Analysis of Peristaltic Locomotion for Maximizing Velocity or Minimizing Cost of Transport of Earthworm-Like Robots

Earthworm-like peristaltic locomotion has been implemented in >50 robots, with many potential applications in otherwise inaccessible terrain. Design guidelines for peristaltic locomotion have come from observations of biology, but robots have empirically explored different structures, actuators, and control waveform shapes than those observed in biological organisms. In this study, we suggest a template analysis based on simplified segments undergoing beam deformations. This analysis enables calculation of the minimum power required by the structure for locomotion and maximum speed of locomotion. Thus, design relationships are shown that apply to peristaltic robots and potentially to earthworms. Specifically, although speed is maximized by moving as many segments as possible, cost of transport (COT) is optimized by moving fewer segments. Furthermore, either soft or relatively stiff segments are possible, but the anisotropy of the stiffnesses is important. Experimentally, we show on our earthworm robot that this method predicts which control waveforms (equivalent to different gaits) correspond to least input power or to maximum velocity. We extend our analysis to 150 segments (similar to that of earthworms) to show that reducing COT is an alternate explanation for why earthworms have so few moving segments. The mathematical relationships developed here between structural properties, actuation power, and waveform shape will enable the design of future robots with more segments and limited onboard power.

Controlling Long-Distance Photoactuation with Protein Additives

Long-distance wireless actuation indicates precise remote control over materials, sensors, and devices that are widely utilized in biomedical, defence, disaster relief, deep ocean, and outer space applications to replace human work. Unlike radio frequency (RF) control, which has low tolerance toward electromagnetic interference (EMI), light control represents a promising method to overcome EMI. Nonetheless, long-distance light-controlled wireless actuation able to compete with RF control has not been achieved until now due to the lack of highly light-sensitive actuator designs. Here, it is demonstrate that amyloid-like protein aggregates can organize photomodule single-layer reduced graphene oxide (rGO) into a well-defined multilayer stack to display long-distance photoactuation. The amyloid-like proteinaceous component docks the rGO layers together to form a hybrid film, which can reliably adhere onto various material surfaces with robust interfacial adhesion. The sensitive photothermal effect and a fast bending in 1 s to switch a circuit are achieved after forming the film on a plastic substrate and irradiating the bilayer film with a blue laser from 100 m away. A photoactuation distance of 50 km can be further extrapolated based on a commercial high-power laser. This study reveals the great potential of amyloid-like aggregates in remote light control of robots and devices.

Gait-optimized locomotion of wave-driven soft sheets

Inspired by the robust locomotion of limbless animals in a range of environments, the development of soft robots capable of moving by localized swelling, bending, and other forms of differential growth has become a target for soft matter research over the last decade. Engineered soft robots exhibit a wide range of morphologies, but theoretical investigations of soft robot locomotion have largely been limited to slender bodied or one-dimensional examples. Here, we demonstrate design principles regarding the locomotion of two-dimensional soft materials driven by morphoelastic waves along a dry substrate. Focusing on the essential common aspects of many natural and man-made soft actuators, a continuum model is developed which links the deformation of a thin elastic sheet to surface-bound excitation waves. Through a combination of analytic and numerical methods, we investigate the relationship between induced active stress and self-propulsion performance of self-propelling sheets driven by FitzHugh-Nagumo type chemical waves. Examining the role of both sheet geometry and terrain geography on locomotion, our results can provide guidance for the design of more efficient soft crawling devices.

Central pattern generating networks in insect locomotion

Central pattern generators (CPGs) are neural circuits that based on their connectivity can generate rhythmic and patterned output in the absence of rhythmic external inputs. This property makes CPGs crucial elements in the generation of many kinds of rhythmic motor behaviors in insects, such as flying, walking, swimming, or crawling. Arguably representing the most diverse group of animals, insects utilize at least one of these types of locomotion during one stage of their ontogenesis. Insects have been extensively used to study the neural basis of rhythmic motor behaviors, and particularly the structure and operation of CPGs involved in locomotion. Here, we review insect locomotion with regard to flying, walking, and crawling, and we discuss the contribution of central pattern generation to these three forms of locomotion. In each case, we compare and contrast the topology and structure of the CPGs, and we point out how these factors are involved in the generation of the respective motor pattern. We focus on the importance of sensory information for establishing a functional motor output and we indicate behavior-specific adaptations. Furthermore, we report on the mechanisms underlying coordination between different body parts. Last but not least, by reviewing the state-of-the-art knowledge concerning the role of CPGs in insect locomotion, we endeavor to create a common ground, upon which future research in the field of motor control in insects can build.

Do bumblebees have signatures? Demonstrating the existence of a speed-curvature power law in Bombus terrestris locomotion patterns

We report the discovery that Bombus terrestris audax (Buff-tailed bumblebee) locomotor trajectories adhere to a speed-curvature power law relationship which has previously been found in humans, non-human primates and Drosophila larval trajectories. No previous study has reported such a finding in adult insect locomotion. We used behavioural tracking to study walking Bombus terrestris in an arena under different training environments. Trajectories analysed from this tracking show the speed-curvature power law holds robustly at the population level, displaying an exponent close to two-thirds. This exponent corroborates previous findings in human movement patterns, but differs from the three-quarter exponent reported for Drosophila larval locomotion. There are conflicting hypotheses for the principal origin of these speed-curvature laws, ranging from the role of central planning to kinematic and muscular skeletal constraints. Our findings substantiate the latter idea that dynamic power-law effects are robust, differing only through kinematic constraints due to locomotive method. Our research supports the notion that these laws are present in a greater range of species than previously thought, even in the bumblebee. Such power laws may provide optimal behavioural templates for organisms, delivering a potential analytical tool to study deviations from this template. Our results suggest that curvature and angular speed are constrained geometrically, and independently of the muscles and nerves of the performing body.

Burrowing dynamics of aquatic worms in soft sediments

We investigate the dynamics of Lumbriculus variegatus in water-saturated sediment beds to understand limbless locomotion in the benthic zone found at the bottom of lakes and oceans. These slender aquatic worms are observed to perform elongation-contraction and transverse undulatory strokes in both water-saturated sediments and water. Greater drag anisotropy in the sediment medium is observed to boost the burrowing speed of the worm compared to swimming in water with the same stroke using drag-assisted propulsion. We capture the observed speeds by combining the calculated forms based on resistive-force theory of undulatory motion in viscous fluids and a dynamic anchor model of peristaltic motion in the sediments. Peristalsis is found to be effective for burrowing in noncohesive sediments which fill in rapidly behind the moving body inside the sediment bed. Whereas the undulatory stroke is found to be effective in water and in shallow sediment layers where anchoring is not possible to achieve peristaltic motion. We show that such dual strokes occur as well in the earthworm Eisenia fetida which inhabits moist sediments that are prone to flooding. Our analysis in terms of the rheology of the medium shows that the dual strokes are exploited by organisms to negotiate sediment beds that may be packed heterogeneously and can be used by active intruders to move effectively from a fluid through the loose bed surface layer which fluidizes easily to the well-consolidated bed below.

Active poroelastic two-phase model for the motion of physarum microplasmodia

The onset of self-organized motion is studied in a poroelastic two-phase model with free boundaries for Physarum microplasmodia (MP). In the model, an active gel phase is assumed to be interpenetrated by a passive fluid phase on small length scales. A feedback loop between calcium kinetics, mechanical deformations, and induced fluid flow gives rise to pattern formation and the establishment of an axis of polarity. Altogether, we find that the calcium kinetics that breaks the conservation of the total calcium concentration in the model and a nonlinear friction between MP and substrate are both necessary ingredients to obtain an oscillatory movement with net motion of the MP. By numerical simulations in one spatial dimension, we find two different types of oscillations with net motion as well as modes with time-periodic or irregular switching of the axis of polarity. The more frequent type of net motion is characterized by mechano-chemical waves traveling from the front towards the rear. The second type is characterized by mechano-chemical waves that appear alternating from the front and the back. While both types exhibit oscillatory forward and backward movement with net motion in each cycle, the trajectory and gel flow pattern of the second type are also similar to recent experimental measurements of peristaltic MP motion. We found moving MPs in extended regions of experimentally accessible parameters, such as length, period and substrate friction strength. Simulations of the model show that the net speed increases with the length, provided that MPs are longer than a critical length of ≈ 120 μm. Both predictions are in line with recent experimental observations.

Turning in Worm-Like Robots: The Geometry of Slip Elimination Suggests Nonperiodic Waves

Inspired by earthworms, soft robots have demonstrated locomotion using segments with coupled length-wise elongation and radial contraction. However, peristaltic turning has primarily been studied empirically. Surface-dependent slip, which results in frictional forces that deform the body segments, makes accurate models challenging and limited to a specific robot and environment. Here, instead of modeling specific surfaces and segments, we take a geometric approach to analyzing the constraints that result from elimination of slip for the general case of peristaltic locomotion. Thus, our abstract two-dimensional model applies to many different mechanical designs (e.g., fluidic actuation, origami, woven mesh). Specifically, we show how turning is limited by segment range of motion, which means that more than one wave will be required to completely reorient the body in an environment where slip is not possible. As a result, to eliminate slip, segments must undergo nonperiodic shape changes. By representing segments as isosceles trapezoids with reasonable ranges of motion, we can determine control waves that in simulation do not require slip. These waves follow from an initial "reach" (i.e., kinematic movement range) of the second segment. A strategy for choosing the second segment reach is proposed based on evaluating long-term turn stability. To demonstrate the value of the approach, we applied the nonperiodic waveform (NPW) to our earthworm-inspired soft robot, Compliant Modular Mesh Worm with Steering (CMMWorm-S). With the NPW, the robot slips less when compared with a naive periodic waveform, where each segment of the robot has the same kinematic reach of each wave, as indicated by the difference between predicted and actual body position over multiple waves. Using an NPW for turning, we observe a decrease in prediction error compared with a naive periodic waveform by 66%. Thus, while our model ignores many factors (inertial dynamics, radial deformation, surface forces), the resulting turn strategies can improve kinematic motion prediction for planning. The theoretical constraints on NPWs that eliminate slip during turning will help robot designers make application-specific design choices about body stiffness, frictional properties, body length, and degrees of freedom.

Long-term exposure to higher temperature increases the thermal sensitivity of grazer metabolism and movement

Ecological studies of global warming impacts have many constraints. Organisms are often exposed to higher temperatures for short periods of time, probably underestimating their ability to acclimate or adapt relative to slower but real rates of warming. Many studies also focus on a limited number of traits and miss the multifaceted effects that warming may have on organisms, from physiology to behaviour. Organisms exhibit different movement traits, some of which are primarily driven by metabolic processes and others by decision-making, which should influence the extent to which temperature affects them. We collected snails from streams that have been differentially heated by geothermal activity for decades to determine how long-term exposure to different temperatures affected their metabolism and movement. Additionally, we collected snails from a cold stream (5°C) and measured their metabolism and movement at higher temperatures (short-term exposure). We used respirometry to measure metabolic rates and automated in situ image-based tracking to quantify several movement traits from 5 to 21°C. Long-term exposure to higher temperatures resulted in a greater thermal sensitivity of metabolic rate compared to snails exposed for short durations, highlighting the need for caution when conducting acute temperature exposures in global warming research. Average speed, which is largely driven by metabolism, also increased more with temperature for long-term exposure compared to short-term exposure. Movement traits we interpret as more decision-based, such as time spent moving and trajectory shape, were less affected by temperature. Step length increased and step angle decreased at higher temperatures for both long- and short-term exposure, resulting in overall straighter trajectories. The power-law exponent of the step length distributions and fractal dimension of trajectories were independent of temperature, however, suggesting that snails retained the same movement strategy. The observed changes in snail movement at higher temperatures should lead to higher encounter rates and more efficient searching, providing a behavioural mechanism for stronger plant-herbivore interactions in warmer environments. Our research is among the first to show that temperature has contrasting effects on different movement traits, which may be determined by the metabolic contribution to those behaviours.

An earthworm-inspired friction-controlled soft robot capable of bidirectional locomotion

We present the design, fabrication, modeling and feedback control of an earthworm-inspired soft robot capable of bidirectional locomotion on both horizontal and inclined flat platforms. In this approach, the locomotion patterns are controlled by actively varying the coefficients of friction between the contacting surfaces of the robot and the supporting platform, thus emulating the limbless locomotion of earthworms at a conceptual level. Earthworms are characterized by segmented body structures, known as metameres, composed of longitudinal and circular muscles which during locomotion are contracted and relaxed periodically in order to generate a peristaltic wave that propagates backwards with respect to the worm's traveling direction; simultaneously, microscopic bristle-like structures (setae) on each metamere coordinately protrude or retract to provide varying traction with the ground, thus enabling the worm to burrow or crawl. The proposed soft robot replicates the muscle functionalities and setae mechanisms of earthworms employing pneumatically-driven actuators and 3D-printed casings. Using the notion of controllable subspace, we show that friction plays an indispensable role in the generation and control of locomotion in robots of this type. Based on this analysis, we introduce a simulation-based method for synthesizing and implementing feedback control schemes that enable the robot to generate forward and backward locomotion. From the set of feasible control strategies studied in simulation, we adopt a friction-modulation-based feedback control algorithm which is implementable in real time and compatible with the hardware limitations of the robotic system. Through experiments, the robot is demonstrated to be capable of bidirectional crawling on surfaces with different textures and inclinations.

Quantifying the mechanics of locomotion of the schistosome pathogen with respect to changes in its physical environment

Schistosomiasis is a chronic and morbid disease of poverty affecting approximately 200 million people worldwide. Mature schistosome flatworms wander in the host's hepatic portal and mesenteric venous system where they encounter a range of blood flow conditions and geometrical confinement. However, the mechanisms that support schistosome locomotion and underlie the pathogen's adaptation to its physical environment are largely unknown. By combining microfabrication and traction force microscopy, we developed various in vitro assays to quantify the mechanics of locomotion of adult male Schistosoma mansoni in different physiologically relevant conditions. We show that in unconfined settings, the parasite undergoes two-anchor marching mediated by the coordinated action of its oral and ventral suckers. This mode of locomotion is maintained when the worm faces an external flow, to which it responds by adjusting the strength of its suckers. In geometrically confined conditions, S. mansoni switches to a different crawling modality by generating retrograde peristaltic waves along its body, a mechanism shared with terrestrial and marine worms. However, while the surface of most worms has backward-pointing bristles that rectify peristaltic waves and facilitate forward locomotion, S. mansoni has isotropically oriented tubercles. This requires tight coordination between muscle contraction and substrate friction but gives S. mansoni the ability to reverse its direction of locomotion without turning its body, which is likely advantageous to manoeuvre in narrow-bore vessels. We show that the parasite can also coordinate the action of its suckers with its peristaltic body contractions to increase crawling speed. Throughout this study, we report on a number of biomechanical parameters to quantify the motility of adult schistosomes (e.g. sucker grabbing strength, the rate of detachment under flow, peristaltic wave properties and traction stresses). The new series of in vitro assays make it possible to quantify key phenotypical aspects of S. mansoni motility that could guide the discovery of new drugs to treat schistosomiasis.

Serpentine locomotion through elastic energy release

A model for serpentine locomotion is derived from a novel perspective based on concepts from configurational mechanics. The motion is realized through the release of the elastic energy of a deformable rod, sliding inside a frictionless channel, which represents a snake moving against lateral restraints. A new formulation is presented, correcting previous results and including situations never analysed so far, as in the cases when the serpent's body lies only partially inside the restraining channel or when the body has a muscle relaxation localized in a small zone. Micromechanical considerations show that propulsion is the result of reactions tangential to the frictionless constraint and acting on the snake's body, a counter-intuitive feature in mechanics. It is also experimentally demonstrated that the propulsive force driving serpentine motion can be directly measured on a designed apparatus in which flexible bars sweep a frictionless channel. Experiments fully confirm the theoretical modelling, so that the presented results open the way to exploration of effects, such as variability in the bending stiffness or channel geometry or friction, on the propulsive force of snake models made up of elastic rods.

The Optimal Locomotion of a Self-Propelled Worm Actuated by Two Square Waves

Worm-like locomotion at small scales induced by propagating a series of extensive or contraction waves has exhibited enormous possibilities in reproducing artificial mobile soft robotics. However, the optimal relation between locomotion performance and some important parameters, such as the distance between two adjacent waves, wave width, and body length, is still not clear. To solve this problem, this paper studies the optimal problem of a worm’s motion induced by two peristalsis waves in a viscous medium. Inspired by a worm’s motion, we consider that its body consists of two segments which can perform the respective shape change. Next, a quasi-static model describing the worm-like locomotion is used to investigate the relationship between its average velocity over the period and these parameters. Through the analysis of the relationship among these parameters, we find that there exist four different cases which should be addressed. Correspondingly, the average velocity in each case can be approximately derived. After that, optimization is carried out on each case to maximize the average velocity according to the Kuhn–Tucker Conditions. As a result, the optimal conditions of all of the cases are obtained. Finally, numerical and experimental verifications are carried out to demonstrate the correctness of the obtained results.

Origami-based earthworm-like locomotion robots

Inspired by the morphology characteristics of the earthworms and the excellent deformability of origami structures, this research creates a novel earthworm-like locomotion robot through exploiting the origami techniques. In this innovation, appropriate actuation mechanisms are incorporated with origami ball structures into the earthworm-like robot 'body', and the earthworm's locomotion mechanism is mimicked to develop a gait generator as the robot 'centralized controller'. The origami ball, which is a periodic repetition of waterbomb units, could output significant bidirectional (axial and radial) deformations in an antagonistic way similar to the earthworm's body segment. Such bidirectional deformability can be strategically programmed by designing the number of constituent units. Experiments also indicate that the origami ball possesses two outstanding mechanical properties that are beneficial to robot development: one is the structural multistability in the axil direction that could contribute to the robot control implementation; and the other is the structural compliance in the radial direction that would increase the robot robustness and applicability. To validate the origami-based innovation, this research designs and constructs three robot segments based on different axial actuators: DC-motor, shape-memory-alloy springs, and pneumatic balloon. Performance evaluations reveal their merits and limitations, and to prove the concept, the DC-motor actuation is selected for building a six-segment robot prototype. Learning from earthworms' fundamental locomotion mechanism-retrograde peristalsis wave, seven gaits are automatically generated; controlled by which, the robot could achieve effective locomotion with qualitatively different modes and a wide range of average speeds. The outcomes of this research could lead to the development of origami locomotion robots with low fabrication costs, high customizability, light weight, good scalability, and excellent re-configurability.

Soft Modular Robotic Cubes: Toward Replicating Morphogenetic Movements of the Embryo

In this paper we present a new type of simple, pneumatically actuated, soft modular robotic system that can reproduce fundamental cell behaviors observed during morphogenesis; the initial shaping stage of the living embryo. The fabrication method uses soft lithography for producing composite elastomeric hollow cubes and permanent magnets as passive docking mechanism. Actuation is achieved by controlling the internal pressurization of cubes with external micro air pumps. Our experiments show how simple soft robotic modules can serve to reproduce to great extend the overall mechanics of collective cell migration, delamination, invagination, involution, epiboly and even simple forms of self-reconfiguration. Instead of relying in complex rigid onboard docking hardware, we exploit the coordinated inflation/deflation of modules as a simple mechanism to detach/attach modules and even rearrange the spatial position of components. Our results suggest new avenues for producing inexpensive, yet functioning, synthetic morphogenetic systems and provide new tangible models of cell behavior.

Coordination of contractility, adhesion and flow in migrating Physarum amoebae

This work examines the relationship between spatio-temporal coordination of intracellular flow and traction stress and the speed of amoeboid locomotion of microplasmodia of Physarum polycephalum. We simultaneously perform particle image velocimetry and traction stress microscopy to measure the velocity of cytoplasmic flow and the stresses applied to the substrate by migrating Physarum microamoebae. In parallel, we develop a mathematical model of a motile cell which includes forces from the viscous cytosol, a poro-elastic, contractile cytoskeleton and adhesive interactions with the substrate. Our experiments show that flow and traction stress exhibit back-to-front-directed waves with a distinct phase difference. The model demonstrates that the direction and speed of locomotion are determined by this coordination between contraction, flow and adhesion. Using the model, we identify forms of coordination that generate model predictions consistent with experiments. We demonstrate that this coordination produces near optimal migration speed and is insensitive to heterogeneity in substrate adhesiveness. While it is generally thought that amoeboid motility is robust to changes in extracellular geometry and the nature of extracellular adhesion, our results demonstrate that coordination of adhesive forces is essential to producing robust migration.

Scrunching: a novel escape gait in planarians

The ability to escape a predator or other life-threatening situations is central to animal survival. Different species have evolved unique strategies under anatomical and environmental constraints. In this study, we describe a novel musculature-driven escape gait in planarians, 'scrunching', which is quantitatively different from other planarian gaits, such as gliding and peristalsis. We show that scrunching is a conserved gait among different flatworm species, underlying its importance as an escape mechanism. We further demonstrate that it can be induced by a variety of physical stimuli, including amputation, high temperature, electric shock and low pH. We discuss the functional basis for scrunching as the preferential gait when gliding is impaired due to a disruption of mucus production. Finally, we show that the key mechanical features of scrunching are adequately captured by a simple biomechanical model that is solely based on experimental data from traction force microscopy and tissue rheology without fit parameters. Together, our results form a complete description of this novel form of planarian locomotion. Because scrunching has distinct dynamics, this gait can serve as a robust behavioral readout for studies of motor neuron and muscular functions in planarians and in particular the restoration of these functions during regeneration.

Periodic traction in migrating large amoeba of Physarum polycephalum

The slime mould Physarum polycephalum is a giant multinucleated cell exhibiting well-known Ca(2+)-dependent actomyosin contractions of its vein network driving the so-called cytoplasmic shuttle streaming. Its actomyosin network forms both a filamentous cortical layer and large fibrils. In order to understand the role of each structure in the locomotory activity, we performed birefringence observations and traction force microscopy on excised fragments of Physarum. After several hours, these microplasmodia adopt three main morphologies: flat motile amoeba, chain types with round contractile heads connected by tubes and motile hybrid types. Each type exhibits oscillations with a period of about 1.5 min of cell area, traction forces and fibril activity (retardance) when fibrils are present. The amoeboid types show only peripheral forces while the chain types present a never-reported force pattern with contractile rings far from the cell boundary under the spherical heads. Forces are mostly transmitted where the actomyosin cortical layer anchors to the substratum, but fibrils maintain highly invaginated structures and contribute to forces by increasing the length of the anchorage line. Microplasmodia are motile only when there is an asymmetry in the shape and/or the force distribution.

A robotic crawler exploiting directional frictional interactions: experiments, numerics and derivation of a reduced model

We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.

Common mechanics of mode switching in locomotion of limbless and legged animals

Crawling using muscular waves is observed in many species, including planaria, leeches, nemertea, aplysia, snails, chitons, earthworms and maggots. Contraction or extension waves propagate along the antero-posterior axis of the body as the crawler pushes the ground substratum backward. However, the observation that locomotory waves can be directed forward or backward has attracted much attention over the past hundred years. Legged organisms such as centipedes and millipedes exhibit parallel phenomena; leg tips form density waves that propagate backward or forward. Mechanical considerations reveal that leg-density waves play a similar role to locomotory waves in limbless species, and that locomotory waves are used by a mechanism common to both legged and limbless species to achieve crawling. Here, we report that both mode switching of the wave direction and friction control were achieved when backward motion was induced in the laboratory. We show that the many variations of switching in different animals can essentially be classified in two types according to mechanical considerations. We propose that during their evolution, limbless crawlers first moved in a manner similar to walking before legs were obtained. Therefore, legged crawlers might have learned the mechanical mode of movement involved in walking long before obtaining legs.

Crawling motility through the analysis of model locomotors: two case studies

We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.