Quadrupedal gaits in hexapod animals - inter-leg coordination in free-walking adult stick insects

Interleg coordination in free-walking bug Erthesina fullo (Hemiptera: Pentatomidae)

Insects can adapt their walking patterns to complex and varied environments and retain the ability to walk even after significant changes in their physical attributes, such as amputation. Although the interleg coordination of intact insects has been widely described in previous studies, the adaptive walking patterns in free-walking insects with amputation of 1 or more legs are still unclear. The pentatomid bug Erthesina fullo exhibits a tripod gait, when walking freely on horizontal substrates, like many other insects. In this study, amputations were performed on this species to investigate changes in interleg coordination. The walking parameters were analyzed, such as the locations of touchdown and liftoff, cycle period, walking speed, and head displacement of intact and amputated insects. The results show that E. fullo displays adaptive interleg coordination in response to amputations. With 1 amputated leg, bugs changed to a 3-unit gait, whereas with 2 amputated legs they employed a wave gait. These data are helpful in exploring the motion mode control in walking insects and provide the theoretical basis for the gait control strategy of robots, when leg failure occurs.

Flexible locomotion in complex environments: the influence of species, speed and sensory feedback on panarthropod inter-leg coordination

Panarthropods (a clade containing arthropods, tardigrades and onychophorans) can adeptly move across a wide range of challenging terrains and their ability to do so given their relatively simple nervous systems makes them compelling study organisms. Studies of forward walking on flat terrain excitingly point to key features in inter-leg coordination patterns that seem to be 'universally' shared across panarthropods. However, when movement through more complex, naturalistic terrain is considered, variability in coordination patterns - from the intra-individual to inter-species level - becomes more apparent. This variability is likely to be due to the interplay between sensory feedback and local pattern-generating activity, and depends crucially on species, walking speed and behavioral goal. Here, I gather data from the literature of panarthropod walking coordination on both flat ground and across more complex terrain. This Review aims to emphasize the value of: (1) designing experiments with an eye towards studying organisms in natural environments; (2) thoughtfully integrating results from various experimental techniques, such as neurophysiological and biomechanical studies; and (3) ensuring that data is collected and made available from a wider range of species for future comparative analyses.

Behavioural function and development of body-to-limb proportions and active movement ranges in three stick insect species

Overall body proportions and relative limb length are highly characteristic for most insect taxa. In case of the legs, limb length has mostly been discussed with regard to parameters of locomotor performance and, in particular cases, as an adaptation to environmental factors or to the mating system. Here, we compare three species of stick and leaf insects (Phasmatodea) that differ strongly in the length ratio between antennae and walking legs, with the antennae of Medauroidea extradentata being much shorter than its legs, nearly equal length of antennae and legs in Carausius morosus, and considerably longer antennae than front legs in Aretaon asperrimus. We show that that relative limb length is directly related to the near-range exploration effort, with complementary function of the antennae and front legs irrespective of their length ratio. Assuming that these inter-species differences hold for both sexes and all developmental stages, we further explore how relative limb length differs between sexes and how it changes throughout postembryonic development. We show that the pattern of limb-to-body proportions is species-characteristic despite sexual dimorphism, and find that the change in sexual dimorphism is strongest during the last two moults. Finally, we show that antennal growth rate is consistently higher than that of front legs, but differs categorically between the species investigated. Whereas antennal growth rate is constant in Carausius, the antennae grow exponentially in Medauroidea and with a sudden boost during the last moult in Aretaon.

Motion Hacking – Understanding by Controlling Animals –

Insects exhibit resilient and flexible capabilities allowing them to adapt their walk in response to changes of the environment or body properties, for example the loss of a leg. While the motor control paradigm governing inter-leg coordination has been extensively studied in the past for such adaptive walking, the neural mechanism remains unknown. To overcome this situation, the project “Motion Hacking” develops a method for hacking leg movements by electrostimulating leg muscles while retaining the natural sensorimotor functions of the insect. This research aims to elucidate the flexible inter-leg coordination mechanism underlying insect walking by observing the adapting process of inter-leg coordination with the insect nervous system when leg movements are externally controlled via motion hacking.

Network Architecture Producing Swing to Stance Transitions in an Insect Walking System

The walking system of the stick insect is one of the most thoroughly described invertebrate systems. We know a lot about the role of sensory input in the control of stepping of a single leg. However, the neuronal organization and connectivity of the central neural networks underlying the rhythmic activation and coordination of leg muscles still remain elusive. It is assumed that these networks can couple in the absence of phasic sensory input due to the observation of spontaneous recurrent patterns (SRPs) of coordinated motor activity equivalent to fictive stepping-phase transitions. Here we sought to quantify the phase of motor activity within SRPs in the isolated and interconnected meso- and meta-thoracic ganglia. We show that SRPs occur not only in the meso-, but also in the metathoracic ganglia of the stick insect, discovering a qualitative difference between them. We construct a network based on neurophysiological data capable of reproducing the measured SRP phases to investigate this difference. By comparing network output to the biological measurements we confirm the plausibility of the architecture and provide a hypothesis to account for these qualitative differences. The neural architecture we present couples individual central pattern generators to reproduce the fictive stepping-phase transitions observed in deafferented stick insect preparations after pharmacological activation, providing insights into the neural architecture underlying coordinated locomotion.

Kinematic Modeling at the Ant Scale: Propagation of Model Parameter Uncertainties

Quadrupeds and hexapods are known by their ability to adapt their locomotive patterns to their functions in the environment. Computational modeling of animal movement can help to better understand the emergence of locomotive patterns and their body dynamics. Although considerable progress has been made in this subject in recent years, the strengths and limitations of kinematic simulations at the scale of small moving animals are not well understood. In response to this, this work evaluated the effects of modeling uncertainties on kinematic simulations at small scale. In order to do so, a multibody model of a Messor barbarus ant was developed. The model was built from 3D scans coming from X-ray micro-computed tomography. Joint geometrical parameters were estimated from the articular surfaces of the exoskeleton. Kinematic data of a free walking ant was acquired using high-speed synchronized video cameras. Spatial coordinates of 49 virtual markers were used to run inverse kinematics simulations using the OpenSim software. The sensitivity of the model’s predictions to joint geometrical parameters and marker position uncertainties was evaluated by means of two Monte Carlo simulations. The developed model was four times more sensitive to perturbations on marker position than those of the joint geometrical parameters. These results are of interest for locomotion studies of small quadrupeds, octopods, and other multi-legged animals.

Adaptive Interlimb Coordination Mechanism for Hexapod Locomotion Based on Active Load Sensing

Insects can flexibly coordinate their limbs to adapt to various locomotor conditions, e.g., complex environments, changes in locomotion speed, and leg amputation. An interesting aspect of insect locomotion is that the gait patterns are not necessarily stereotypical but are often highly variable, e.g., searching behavior to obtain stable footholds in complex environments. Several previous studies have focused on the mechanism for the emergence of variable limb coordination patterns. However, the proposed mechanisms are complicated and the essential mechanism underlying insect locomotion remains elusive. To address this issue, we proposed a simple mathematical model for the mechanism of variable interlimb coordination in insect locomotion. The key idea of the proposed model is “decentralized active load sensing,” wherein each limb actively moves and detects the reaction force from the ground to judge whether it plays a pivotal role in maintaining the steady support polygon. Based on active load sensing, each limb stays in the stance phase when the limb is necessary for body support. To evaluate the proposed model, we conducted simulation experiments using a hexapod robot. The results showed that the proposed simple mechanism allows the hexapod robot to exhibit typical gait patterns in response to the locomotion speed. Furthermore, the proposed mechanism improves the adaptability of the hexapod robot for leg amputations and lack of footholds by changing each limb's walking and searching behavior in a decentralized manner based on the physical interaction between the body and the environment.

Locomotion Control With Frequency and Motor Pattern Adaptations

Existing adaptive locomotion control mechanisms for legged robots are usually aimed at one specific type of adaptation and rarely combined with others. Adaptive mechanisms thus stay at a conceptual level without their coupling effect with other mechanisms being investigated. However, we hypothesize that the combination of adaptation mechanisms can be exploited for enhanced and more efficient locomotion control as in biological systems. Therefore, in this work, we present a central pattern generator (CPG) based locomotion controller integrating both a frequency and motor pattern adaptation mechanisms. We use the state-of-the-art Dual Integral Learner for frequency adaptation, which can automatically and quickly adapt the CPG frequency, enabling the entire motor pattern or output signal of the CPG to be followed at a proper high frequency with low tracking error. Consequently, the legged robot can move with high energy efficiency and perform the generated locomotion with high precision. The versatile state-of-the-art CPG-RBF network is used as a motor pattern adaptation mechanism. Using this network, the motor patterns or joint trajectories can be adapted to fit the robot's morphology and perform sensorimotor integration enabling online motor pattern adaptation based on sensory feedback. The results show that the two adaptation mechanisms can be combined for adaptive locomotion control of a hexapod robot in a complex environment. Using the CPG-RBF network for motor pattern adaptation, the hexapod learned basic straight forward walking, steering, and step climbing. In general, the frequency and motor pattern mechanisms complement each other well and their combination can be seen as an essential step toward further studies on adaptive locomotion control.

Allometry in desert ant locomotion (Cataglyphis albicans and Cataglyphis bicolor) - does body size matter?

Desert ants show a large range of adaptations to their habitats. They can reach extremely high running speeds, for example, to shorten heat stress during foraging trips. It has recently been examined how fast walking speeds are achieved in different desert ant species. It is intriguing in this context that some species exhibit distinct intraspecific size differences. We therefore performed a complete locomotion analysis over the entire size spectrum of the species Cataglyphis bicolor, and we compared this intraspecific dataset with that of the allometrically similar species Cataglyphis albicans. Emphasis was on the allometry of locomotion: we considered the body size of each animal and analysed the data in terms of relative walking speed. Body size was observed to affect walking parameters, gait patterns and phase relationships in terms of absolute walking speed. Unexpectedly, on a relative scale, all ants tended to show the same overall locomotion strategy at low walking speeds, and significant differences occurred only between C. albicans and C. bicolor at high walking speeds. Our analysis revealed that C. bicolor ants use the same overall strategy across all body sizes, with small ants reaching the highest walking speeds (up to 80 body lengths s-1) by increasing their stride length and incorporating aerial phases. By comparison, C. albicans reached high walking speeds mainly by a high synchrony of leg movement, lower swing phase duration and higher stride frequency ranging up to 40 Hz.

Motorized Treadmill and Optical Recording System for Gait Analysis of Grasshoppers

(1) Background: Insects, which serve as model systems for many disciplines with their unique advantages, have not been extensively studied in gait research because of the lack of appropriate tools and insect models to properly study the insect gaits. (2) Methods: In this study, we present a gait analysis of grasshoppers with a closed-loop custom-designed motorized insect treadmill with an optical recording system for quantitative gait analysis. We used the eastern lubber grasshopper, a flightless and large-bodied species, as our insect model. Gait kinematics were recorded and analyzed by making three grasshoppers walk on the treadmill with various speeds from 0.1 to 1.5 m/s. (3) Results: Stance duty factor was measured as 70–95% and decreased as walking speed increased. As the walking speed increased, the number of contact legs decreased, and diagonal arrangement of contact was observed at walking speed of 1.1 cm/s. (4) Conclusions: This pilot study of gait analysis of grasshoppers using the custom-designed motorized insect treadmill with the optical recording system demonstrates the feasibility of quantitative, repeatable, and real-time insect gait analysis.

Tardigrades exhibit robust interlimb coordination across walking speeds and terrains

Tardigrades must negotiate heterogeneous, fluctuating environments and accordingly utilize locomotive strategies capable of dealing with variable terrain. We analyze the kinematics and interleg coordination of freely walking tardigrades (species: Hypsibius exemplaris). We find that tardigrade walking replicates several key features of walking in insects despite disparities in size, skeleton, and habitat. To test the effect of environmental changes on tardigrade locomotor control circuits we measure kinematics and interleg coordination during walking on two substrates of different stiffnesses. We find that the phase offset between contralateral leg pairs is flexible, while ipsilateral coordination is preserved across environmental conditions. This mirrors similar results in insects and crustaceans. We propose that these functional similarities in walking coordination between tardigrades and arthropods is either due to a generalized locomotor control circuit common to panarthropods or to independent convergence onto an optimal strategy for robust multilegged control in small animals with simple circuitry. Our results highlight the value of tardigrades as a comparative system toward understanding the mechanisms-neural and/or mechanical-underlying coordination in panarthropod locomotion.

Universal Features in Panarthropod Inter-Limb Coordination during Forward Walking

Terrestrial animals must often negotiate heterogeneous, varying environments. Accordingly, their locomotive strategies must adapt to a wide range of terrain, as well as to a range of speeds to accomplish different behavioral goals. Studies in Drosophila have found that inter-leg coordination patterns (ICPs) vary smoothly with walking speed, rather than switching between distinct gaits as in vertebrates (e.g., horses transitioning between trotting and galloping). Such a continuum of stepping patterns implies that separate neural controllers are not necessary for each observed ICP. Furthermore, the spectrum of Drosophila stepping patterns includes all canonical coordination patterns observed during forward walking in insects. This raises the exciting possibility that the controller in Drosophila is common to all insects, and perhaps more generally to panarthropod walkers. Here, we survey and collate data on leg kinematics and inter-leg coordination relationships during forward walking in a range of arthropod species, as well as include data from a recent behavioral investigation into the tardigrade Hypsibius exemplaris. Using this comparative dataset, we point to several functional and morphological features that are shared among panarthropods. The goal of the framework presented in this review is to emphasize the importance of comparative functional and morphological analyses in understanding the origins and diversification of walking in Panarthropoda. Introduction.

Evaluation of force feedback in walking using joint torques as "naturalistic" stimuli

Control of adaptive walking requires the integration of sensory signals of muscle force and load. We have studied how mechanoreceptors (tibial campaniform sensilla) encode “naturalistic” stimuli derived from joint torques of stick insects walking on a horizontal substrate. Previous studies showed that forces applied to the legs using the mean torque profiles of a proximal joint were highly effective in eliciting motor activities. However, substantial variations in torque direction and magnitude occurred at the more distal femorotibial joint, which can generate braking or propulsive forces and provide lateral stability. To determine how these forces are encoded, we used torque waveforms of individual steps that had maximum values in stance in the directions of flexion or extension. Analysis of kinematic data showed that the torques in different directions tended to occur in different ranges of joint angles. Variations within stance were not accompanied by comparable changes in joint angle but often reflected vertical ground reaction forces and leg support of body load. Application of torque waveforms elicited sensory discharges with variations in firing frequency similar to those seen in freely walking insects. All sensilla directionally encoded the dynamics of force increases and showed hysteresis to transient force decreases. Smaller receptors exhibited more tonic firing. Our findings suggest that dynamic sensitivity in force feedback can modulate ongoing muscle activities to stabilize distal joints when large forces are generated at proximal joints. Furthermore, use of “naturalistic” stimuli can reproduce characteristics seen in freely moving animals that are absent in conventional restrained preparations.

NEW & NOTEWORTHY Sensory encoding of forces during walking by campaniform sensilla was characterized in stick insects using waveforms of joint torques calculated by inverse dynamics as mechanical stimuli. Tests using the mean joint torque and torques of individual steps showed the system is highly sensitive to force dynamics (dF/dt). Use of “naturalistic” stimuli can reproduce characteristics of sensory discharges seen in freely walking insects, such as load transfer among legs.

From Motor-Output to Connectivity: An In-Depth Study of in-vitro Rhythmic Patterns in the Cockroach Periplaneta americana

The cockroach is an established model in the study of locomotion control. While previous work has offered important insights into the interplay among brain commands, thoracic central pattern generators, and the sensory feedback that shapes their motor output, there remains a need for a detailed description of the central pattern generators' motor output and their underlying connectivity scheme. To this end, we monitored pilocarpine-induced activity of levator and depressor motoneurons in two types of novel in-vitro cockroach preparations: isolated thoracic ganglia and a whole-chain preparation comprising the thoracic ganglia and the subesophageal ganglion. Our data analyses focused on the motoneuron firing patterns and the coordination among motoneuron types in the network. The burstiness and rhythmicity of the motoneurons were monitored, and phase relations, coherence, coupling strength, and frequency-dependent variability were analyzed. These parameters were all measured and compared among network units both within each preparation and among the preparations. Here, we report differences among the isolated ganglia, including asymmetries in phase and coupling strength, which indicate that they are wired to serve different functions. We also describe the intrinsic default gait and a frequency-dependent coordination. The depressor motoneurons showed mostly similar characteristics throughout the network regardless of interganglia connectivity; whereas the characteristics of the levator motoneurons activity were mostly ganglion-dependent, and influenced by the presence of interganglia connectivity. Asymmetries were also found between the anterior and posterior homolog parts of the thoracic network, as well as between ascending and descending connections. Our analyses further discover a frequency-dependent inversion of the interganglia coordination from alternations between ipsilateral homolog oscillators to simultaneous activity. We present a detailed scheme of the network couplings, formulate coupling rules, and review a previously suggested model of connectivity in light of our new findings. Our data support the notion that the inter-hemiganglia coordination derives from the levator networks and their coupling with local depressor interneurons. Our findings also support a dominant role of the metathoracic ganglion and its ascending output in governing the anterior ganglia motor output during locomotion in the behaving animal.

Effect of Thoracic Connective Lesion on Inter-Leg Coordination in Freely Walking Stick Insects

Multi-legged locomotion requires appropriate coordination of all legs with coincident ground contact. Whereas behaviourally derived coordination rules can adequately describe many aspects of inter-leg coordination, the neural mechanisms underlying these rules are still not entirely clear. The fact that inter-leg coordination is strongly affected by cut thoracic connectives in tethered walking insects, shows that neural information exchange among legs is important. As yet, recent studies have shown that load transfer among legs can contribute to inter-leg coordination through mechanical coupling alone, i.e., without neural information exchange among legs. Since naturalistic load transfer among legs works only in freely walking animals but not in tethered animals, we tested the hypothesis that connective lesions have less strong effects if mechanical coupling through load transfer among legs is possible. To do so, we recorded protraction/retraction angles of all legs in unrestrained walking stick insects that either had one thoracic connective cut or had undergone a corresponding sham operation. In lesioned animals, either a pro-to-mesothorax or a meso-to-metathorax connective was cut. Overall, our results on temporal coordination were similar to published reports on tethered walking animals, in that the phase relationship of the legs immediately adjacent to the lesion was much less precise, although the effect on mean phase was relatively weak or absent. Lesioned animals could walk at the same speed as the control group, though with a significant sideward bias toward the intact side. Detailed comparison of lesion effects in free-walking and supported animals reveal that the strongest differences concern the spatial coordination among legs. In free walking, lesioned animals, touch-down and lift-off positions shifted significantly in almost all legs, including legs of the intact body side. We conclude that insects with disrupted neural information transfer through one connective adjust to this disruption differently if they experience naturalistic load distribution. While mechanical load transfer cannot compensate for lesion-induced effects on temporal inter-leg coordination, several compensatory changes in spatial coordination occur only if animals carry their own weight.

A Comparative Study of Adaptive Interlimb Coordination Mechanisms for Self-Organized Robot Locomotion

Walking animals demonstrate impressive self-organized locomotion and adaptation to body property changes by skillfully manipulating their complicated and redundant musculoskeletal systems. Adaptive interlimb coordination plays a crucial role in this achievement. It has been identified that interlimb coordination is generated through dynamical interactions between the neural system, musculoskeletal system, and environment. Based on this principle, two classical interlimb coordination mechanisms (continuous phase modulation and phase resetting) have been proposed independently. These mechanisms use decoupled central pattern generators (CPGs) with sensory feedback, such as ground reaction forces (GRFs), to generate robot locomotion autonomously without predefining it (i.e., self-organized locomotion). A comparative study was conducted on the two mechanisms under decoupled CPG-based control implemented on a quadruped robot in simulation. Their characteristics were compared by observing their CPG phase convergence processes at different control parameter values. Additionally, the mechanisms were investigated when the robot faced various unexpected situations, such as noisy feedback, leg motor damage, and carrying a load. The comparative study reveals that the phase modulation and resetting mechanisms demonstrate satisfactory performance when they are subjected to symmetric and asymmetric GRF distributions, respectively. This work also suggests a strategy for the appropriate selection of adaptive interlimb coordination mechanisms under different conditions and for the optimal setting of their control parameter values to enhance their control performance.

Dynamics of locomotion in the seed harvesting ant Messor barbarus: effect of individual body mass and transported load mass

Ants are well-known for their amazing load carriage performances. Yet, the biomechanics of locomotion during load transport in these insects has so far been poorly investigated. Here, we present a study of the biomechanics of unloaded and loaded locomotion in the polymorphic seed-harvesting ant Messor barbarus (Linnaeus, 1767). This species is characterized by a strong intra-colonial size polymorphism with allometric relationships between the different body parts of the workers. In particular, big ants have much larger heads relative to their size than small ants. Their center of mass is thus shifted forward and even more so when they are carrying a load in their mandibles. We investigated the dynamics of the ant center of mass during unloaded and loaded locomotion. We found that during both unloaded and loaded locomotion, the kinetic energy and gravitational potential energy of the ant center of mass are in phase, which is in agreement with what has been described by other authors as a grounded-running gait. During unloaded locomotion, small and big ants do not display the same posture. However, they expend the same amount of mechanical energy to raise and accelerate their center of mass per unit of distance and per unit of body mass. While carrying a load, compared to the unloaded situation, ants seem to modify their locomotion gradually with increasing load mass. Therefore, loaded and unloaded locomotion do not involve discrete types of gait. Moreover, small ants carrying small loads expend less mechanical energy per unit of distance and per unit of body mass and their locomotion thus seem more mechanically efficient.

Leg amputation modifies coordinated activation of the middle leg muscles in the cricket Gryllus bimaculatus

Insects alter their walking pattern in order to respond to demands of an ever-changing environment, such as varying ground surface textures. They also exhibit resilient and flexible ability to retain the capacity to walk even after substantial changes in their body properties, e.g. leg amputation. While the motor control paradigm governing the inter-leg coordination in such adaptive walking has been extensively described in past studies, the mechanism remains unknown. Here, we examined this question by using the cricket (Gryllus bimaculatus), which shows a tetrapod/tripod gait on a flat surfaces, like many other insects. We performed leg amputation experiments to investigate modifications of leg movements and coordination of muscle activities. We simultaneously recorded (1) the leg movements, locomotion velocity, and body rotation and (2) the leg movements and leg muscles activities before and after leg amputation. Crickets displayed adaptive coordination of leg movement patterns in response to amputations. The activation timings of levator muscles in both middle legs tended to synchronize in phase when both legs were amputated at the coxatrochanteral joint. This supports the hypothesis that an intrinsic contralateral connection within the mesothoracic ganglion exists, and that mechanosensory feedback from the legs override this connection, resulting in the anti-phase movement of a normal gait.

The roles of ascending sensory signals and top-down central control in the entrainment of a locomotor CPG

Previous authors have proposed two basic hypotheses about the factors that form the basis of locomotor rhythms in walking insects: sensory feedback only or sensory feedback together with rhythmic activity of small neural circuits called central pattern generators (CPGs). Here we focus on the latter. Following this concept, to generate functional outputs, locomotor control must feature both rhythm generation by CPGs at the level of individual joints and coordination of their rhythmic activities, so that all muscles are activated in an appropriate pattern. This work provides an in-depth analysis of an aspect of this coordination process based on an existing network model of stick insect locomotion. Specifically, we consider how the control system for a single joint in the stick insect leg may produce rhythmic output when subjected to ascending sensory signals from other joints in the leg. In this work, the core rhythm generating CPG component of the joint under study is represented by a classical half-center oscillator constrained by a basic set of experimental observations. While the dynamical features of this CPG, including phase transitions by escape and release, are well understood, we provide novel insights about how these transition mechanisms yield entrainment to the incoming sensory signal, how entrainment can be lost under variation of signal strength and period or other perturbations, how entrainment can be restored by modulation of tonic top-down drive levels, and how these factors impact the duty cycle of the motor output.

Attachment performance of stick insects (Phasmatodea) on convex substrates

Phasmatodea (stick and leaf insects) are herbivorous insects well camouflaged on plant substrates as a result of cryptic masquerade. Also, their close association with plants has allowed them to adapt to different substrate geometries and surface topographies of the plants they imitate. Stick insects are gaining increasing attention in attachment- and locomotion-focused research. However, most studies experimentally investigating stick insect attachment have been performed either on single attachment pads or on flat surfaces. In contrast, curved surfaces, especially twigs or stems of plants, are dominant substrates for phytophagous insects, but not much is known about the influence of curvature on their attachment. In this study, by combining analysis of tarsal usage with mechanical traction and pull-off force measurements, we investigated the attachment performance on curved substrates with different diameters in two species of stick insects with different tarsal lengths. We provide the first quantitative data for forces generated by stick insects on convex curved substrates and show that the curvature significantly influences attachment ability in both species. Within the studied range of substrate curvatures, traction force decreases and pull-off force increases with increasing curvature. Shorter tarsi demonstrate reduced forces; however, tarsus length only has an influence for diameters thinner than the tarsal length. The attachment force generally depends on the number of tarsi/tarsomeres in contact, tarsus/leg orientation and body posture on the surface. Pull-off force is also influenced by the tibiotarsal angle, with higher pull-off force for lower angles, while traction force is mainly influenced by load, i.e. adduction force.

General Distributed Neural Control and Sensory Adaptation for Self-Organized Locomotion and Fast Adaptation to Damage of Walking Robots

Walking animals such as invertebrates can effectively perform self-organized and robust locomotion. They can also quickly adapt their gait to deal with injury or damage. Such a complex achievement is mainly performed via coordination between the legs, commonly known as interlimb coordination. Several components underlying the interlimb coordination process (like distributed neural control circuits, local sensory feedback, and body-environment interactions during movement) have been recently identified and applied to the control systems of walking robots. However, while the sensory pathways of biological systems are plastic and can be continuously readjusted (referred to as sensory adaptation), those implemented on robots are typically static. They first need to be manually adjusted or optimized offline to obtain stable locomotion. In this study, we introduce a fast learning mechanism for online sensory adaptation. It can continuously adjust the strength of sensory pathways, thereby introducing flexible plasticity into the connections between sensory feedback and neural control circuits. We combine the sensory adaptation mechanism with distributed neural control circuits to acquire the adaptive and robust interlimb coordination of walking robots. This novel approach is also general and flexible. It can automatically adapt to different walking robots and allow them to perform stable self-organized locomotion as well as quickly deal with damage within a few walking steps. The adaptation of plasticity after damage or injury is considered here as lesion-induced plasticity. We validated our adaptive interlimb coordination approach with continuous online sensory adaptation on simulated 4-, 6-, 8-, and 20-legged robots. This study not only proposes an adaptive neural control system for artificial walking systems but also offers a possibility of invertebrate nervous systems with flexible plasticity for locomotion and adaptation to injury.

Rules for the Leg Coordination of Dung Beetle Ball Rolling Behaviour

Dung beetles can perform a number of versatile behaviours, including walking and dung ball rolling. While different walking and running gaits of dung beetles have been described in previous literature, little is known about their ball rolling gaits. From behavioural experiments and video recordings of the beetle Scarabaeus (Kheper) lamarcki, we analysed and identified four underlying rules for leg coordination during ball rolling. The rules describe the alternation of the front legs and protraction waves of the middle and hind legs. We found that while rolling a ball backwards, the front legs are decoupled or loosely coupled from the other legs, resulting in a non-standard gait, in contrast to previously described tripod and gallop walking gaits in dung beetles. This provides insight into the principles of leg coordination in dung beetle ball rolling behaviour and its underlying rules. The proposed rules can be used as a basis for further investigation into ball rolling behaviours on more complex terrain (e.g., uneven terrain and slopes). Additionally, the rules can also be used to guide the development of control mechanisms for bio-inspired ball rolling robots.

Synchrony and symmetry-breaking in active flagellar coordination

Living creatures exhibit a remarkable diversity of locomotion mechanisms, evolving structures specialized for interacting with their environment. In the vast majority of cases, locomotor behaviours such as flying, crawling and running are orchestrated by nervous systems. Surprisingly, microorganisms can enact analogous movement gaits for swimming using multiple, fast-moving cellular protrusions called cilia and flagella. Here, I demonstrate intermittency, reversible rhythmogenesis and gait mechanosensitivity in algal flagella, to reveal the active nature of locomotor patterning. In addition to maintaining free-swimming gaits, I show that the algal flagellar apparatus functions as a central pattern generator that encodes the beating of each flagellum in a network in a distinguishable manner. The latter provides a novel symmetry-breaking mechanism for cell reorientation. These findings imply that the capacity to generate and coordinate complex locomotor patterns does not require neural circuitry but rather the minimal ingredients are present in simple unicellular organisms. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

Walking kinematics in the polymorphic seed harvester ant Messor barbarus: influence of body size and load carriage

Ants are famous in the animal kingdom for their amazing load-carrying performance. Yet, the mechanisms that allow these insects to maintain their stability when carrying heavy loads have been poorly investigated. Here, we present a study of the kinematics of unloaded and loaded locomotion in the polymorphic seed-harvesting ant Messor barbarus In this species, large ants have larger heads relative to their size than small ants. Hence, their center of mass is shifted forward, and even more so when they are carrying a load in their mandibles. We tested the hypothesis that this could lead to large ants being less statically stable than small ants, thus explaining their lower load-carrying ability. We found that large ants were indeed less statically stable than small ants when walking unloaded, but they were nonetheless able to adjust their stepping pattern to partly compensate for this instability. When ants were walking loaded on the other hand, there was no evidence of different locomotor behaviors in individuals of different sizes. Loaded ants, whatever their size, move too slowly to maintain their balance through dynamic stability. Rather, they seem to do so by clinging to the ground with their hind legs during part of a stride. We show through a straightforward model that allometric relationships have a minor role in explaining the differences in load-carrying ability between large ants and small ants, and that a simple scale effect is sufficient to explain these differences.

Complementary effect of attachment devices in stick insects (Phasmatodea)

Stick insects are well adapted in their locomotion to various surfaces and topographies of natural substrates. Single pad measurements characterised the pretarsal arolia of these insects as shear-sensitive adhesive pads and the tarsal euplantulae as load-sensitive friction pads. Different attachment microstructures on the euplantulae reveal an adaptation of smooth euplantulae to smooth surfaces and nubby eupantulae to a broader range of surface roughness. However, how different attachment pads and claws work in concert and how strong the contribution of different structures is to the overall attachment performance remains unclear. We therefore assessed combinatory effects in the attachment system of two stick insect species with different types of euplantular microstructures by analysing their usage in various posture situations and the performance on different levels of substrate roughness. For comparison, we provide attachment force data of the whole attachment system. The combination of claws, arolia and euplantulae provides mechanical interlocking on rough surfaces, adhesion and friction on smooth surfaces in different directions, and facilitates attachment on different inclines and on a broad range of surface roughness, with the least performance in the range 0.3-1.0 µm. On smooth surfaces, stick insects use arolia always, but employ euplantulae if the body weight can generate load on them (upright, wall). On structured surfaces, claws enable mechanical interlocking at roughnesses higher than 12 µm. On less-structured surfaces, the attachment strength depends on the use of pads and, corroborating earlier studies, favours smooth pads on smooth surfaces, but nubby euplantulae on micro-rough surfaces.

Integrative Biomimetics of Autonomous Hexapedal Locomotion

Despite substantial advances in many different fields of neurorobotics in general, and biomimetic robots in particular, a key challenge is the integration of concepts: to collate and combine research on disparate and conceptually disjunct research areas in the neurosciences and engineering sciences. We claim that the development of suitable robotic integration platforms is of particular relevance to make such integration of concepts work in practice. Here, we provide an example for a hexapod robotic integration platform for autonomous locomotion. In a sequence of six focus sections dealing with aspects of intelligent, embodied motor control in insects and multipedal robots-ranging from compliant actuation, distributed proprioception and control of multiple legs, the formation of internal representations to the use of an internal body model-we introduce the walking robot HECTOR as a research platform for integrative biomimetics of hexapedal locomotion. Owing to its 18 highly sensorized, compliant actuators, light-weight exoskeleton, distributed and expandable hardware architecture, and an appropriate dynamic simulation framework, HECTOR offers many opportunities to integrate research effort across biomimetics research on actuation, sensory-motor feedback, inter-leg coordination, and cognitive abilities such as motion planning and learning of its own body size.

Unravelling intra- and intersegmental neuronal connectivity between central pattern generating networks in a multi-legged locomotor system

Animal walking results from a complex interplay of central pattern generating networks (CPGs), local sensory signals expressing position, velocity and forces generated in the legs, and coordinating signals between neighboring legs. In particular, the CPGs control the activity of motoneuron (MN) pools which drive the muscles of the individual legs and are thereby responsible for the generation of rhythmic leg movements. The rhythmic activity of the CPGs as well as their connectivity can be modified by the aforementioned sensory signals. However, the precise nature of the interaction between the CPGs and these sensory signals has remained generally largely unknown. Experimental methods aiming at finding out details of these interactions often apply cholinergic agonists such as pilocarpine in order to induce rhythmic activity in the CPGs. Using this general approach, we removed the influence of sensory signals and investigated the putative connections between CPGs controlling the upward/downward movement in the different legs of the stick insect. The experimental data, i.e. the measured MN activities, underwent connectivity analysis using Dynamic Causal Modelling (DCM). This method can uncover the underlying coupling structure and strength between pairs of segmental CPGs. For the analysis we set up different coupling schemes (models) for DCM and compared them using Bayesian Model Selection (BMS). Models with contralateral connections in each segment and ipsilateral connections on both sides, as well as the coupling from the meta- to the ipsilateral prothoracic ganglion were preferred by BMS to all other types of models tested. Moreover, the intrasegmental coupling strength in the mesothoracic ganglion was the strongest and most stable in all three ganglia.

A kinematic model of stick-insect walking

Animal, and insect walking (locomotion) in particular, have attracted much attention from scientists over many years up to now. The investigations included behavioral, electrophysiological experiments, as well as modeling studies. Despite the large amount of material collected, there are left many unanswered questions as to how walking and related activities are generated, maintained, and controlled. It is obvious that for them to take place, precise coordination within muscle groups of one leg and between the legs is required: intra- and interleg coordination. The nature, the details, and the interactions of these coordination mechanisms are not entirely clear. To help uncover them, we made use of modeling techniques, and succeeded in developing a six-leg model of stick-insect walking. Our main goal was to prove that the same model can mimic a variety of walking-related behavioral modes, as well as the most common coordination patterns of walking just by changing the values of a few input or internal variables. As a result, the model can reproduce the basic coordination patterns of walking: tetrapod and tripod and the transition between them. It can also mimic stop and restart, change from forward-to-backward walking and back. Finally, it can exhibit so-called search movements of the front legs both while walking or standing still. The mechanisms of the model that enable it to produce the aforementioned behavioral modes can hint at and prove helpful in uncovering further details of the biological mechanisms underlying walking.

Kinematic patterns while walking on a slope at different speeds

During walking, the elevation angles of the thigh, shank, and foot (i.e., the angle between the segment and the vertical) covary along a characteristic loop constrained on a plane. Here, we investigate how the shape of the loop and the orientation of the plane, which reflect the intersegmental coordination, change with the slope of the terrain and the speed of progression. Ten subjects walked on an inclined treadmill at different slopes (between -9° and +9°) and speeds (from 0.56 to 2.22 m/s). A principal component analysis was performed on the covariance matrix of the thigh, shank, and foot elevation angles. At each slope and speed, the variance accounted for by the two principal components was >99%, indicating that the planar covariation is maintained. The two principal components can be associated to the limb orientation (PC1*) and the limb length (PC2*). At low walking speeds, changes in the intersegmental coordination across slopes are characterized mainly by a change in the orientation of the covariation plane and in PC2* and to a lesser extent, by a change in PC1*. As speed increases, changes in the intersegmental coordination across slopes are more related to a change in PC1 *, with limited changes in the orientation of the plane and in PC 2*. Our results show that the kinematic patterns highly depend on both slope and speed. NEW & NOTEWORTHY In this paper, changes in the lower-limb intersegmental coordination during walking with slope and speed are linked to changes in the trajectory of the body center of mass. Modifications in the kinematic pattern with slope depend on speed: at slow speeds, the net vertical displacement of the body during each step is related to changes in limb length and orientation. When speed increases, the vertical displacement is mostly related to a change in limb orientation.

Leg-local neural mechanisms for searching and learning enhance robotic locomotion

Adapting motor output based on environmental forces is critical for successful locomotion in the real world. Arthropods use at least two neural mechanisms to adjust muscle activation while walking based on detected forces. Mechanism 1 uses negative feedback of leg depressor force to ensure that each stance leg supports an appropriate amount of the body's weight. Mechanism 2 encourages searching for ground contact if the leg supports no body weight. We expand the neural controller for MantisBot, a robot based upon a praying mantis, to include these mechanisms by incorporating leg-local memory and command neurons, as observed in arthropods. We present results from MantisBot transitioning between searching and stepping, mimicking data from animals as reported in the literature.

The role of phase shifts of sensory inputs in walking revealed by means of phase reduction

Detailed neural network models of animal locomotion are important means to understand the underlying mechanisms that control the coordinated movement of individual limbs. Daun-Gruhn and Tóth, Journal of Computational Neuroscience 31(2), 43-60 (2011) constructed an inter-segmental network model of stick insect locomotion consisting of three interconnected central pattern generators (CPGs) that are associated with the protraction-retraction movements of the front, middle and hind leg. This model could reproduce the basic locomotion coordination patterns, such as tri- and tetrapod, and the transitions between them. However, the analysis of such a system is a formidable task because of its large number of variables and parameters. In this study, we employed phase reduction and averaging theory to this large network model in order to reduce it to a system of coupled phase oscillators. This enabled us to analyze the complex behavior of the system in a reduced parameter space. In this paper, we show that the reduced model reproduces the results of the original model. By analyzing the interaction of just two coupled phase oscillators, we found that the neighboring CPGs could operate within distinct regimes, depending on the phase shift between the sensory inputs from the extremities and the phases of the individual CPGs. We demonstrate that this dependence is essential to produce different coordination patterns and the transition between them. Additionally, applying averaging theory to the system of all three phase oscillators, we calculate the stable fixed points - they correspond to stable tripod or tetrapod coordination patterns and identify two ways of transition between them.

Simple analytical model reveals the functional role of embodied sensorimotor interaction in hexapod gaits

Insects have various gaits with specific characteristics and can change their gaits smoothly in accordance with their speed. These gaits emerge from the embodied sensorimotor interactions that occur between the insect’s neural control and body dynamic systems through sensory feedback. Sensory feedback plays a critical role in coordinated movements such as locomotion, particularly in stick insects. While many previously developed insect models can generate different insect gaits, the functional role of embodied sensorimotor interactions in the interlimb coordination of insects remains unclear because of their complexity. In this study, we propose a simple physical model that is amenable to mathematical analysis to explain the functional role of these interactions clearly. We focus on a foot contact sensory feedback called phase resetting, which regulates leg retraction timing based on touchdown information. First, we used a hexapod robot to determine whether the distributed decoupled oscillators used for legs with the sensory feedback generate insect-like gaits through embodied sensorimotor interactions. The robot generated two different gaits and one had similar characteristics to insect gaits. Next, we proposed the simple model as a minimal model that allowed us to analyze and explain the gait mechanism through the embodied sensorimotor interactions. The simple model consists of a rigid body with massless springs acting as legs, where the legs are controlled using oscillator phases with phase resetting, and the governed equations are reduced such that they can be explained using only the oscillator phases with some approximations. This simplicity leads to analytical solutions for the hexapod gaits via perturbation analysis, despite the complexity of the embodied sensorimotor interactions. This is the first study to provide an analytical model for insect gaits under these interaction conditions. Our results clarified how this specific foot contact sensory feedback contributes to generation of insect-like ipsilateral interlimb coordination during hexapod locomotion.

Six-legged walking in insects: how CPGs, peripheral feedback, and descending signals generate coordinated and adaptive motor rhythms

Walking is a rhythmic locomotor behavior of legged animals, and its underlying mechanisms have been the subject of neurobiological research for more than 100 years. In this article, we review relevant historical aspects and contemporary studies in this field of research with a particular focus on the role of central pattern generating networks (CPGs) and their contribution to the generation of six-legged walking in insects. Aspects of importance are the generation of single-leg stepping, the generation of interleg coordination, and how descending signals influence walking. We first review how CPGs interact with sensory signals from the leg in the generation of leg stepping. Next, we summarize how these interactions are modified in the generation of motor flexibility for forward and backward walking, curve walking, and speed changes. We then review the present state of knowledge with regard to the role of CPGs in intersegmental coordination and how CPGs might be involved in mediating descending influences from the brain for the initiation, maintenance, modification, and cessation of the motor output for walking. Throughout, we aim to specifically address gaps in knowledge, and we describe potential future avenues and approaches, conceptual and methodological, with the latter emphasizing in particular options arising from the advent of neurogenetic approaches to this field of research and its combination with traditional approaches.

Adaptive Control Strategies for Interlimb Coordination in Legged Robots: A Review

Walking animals produce adaptive interlimb coordination during locomotion in accordance with their situation. Interlimb coordination is generated through the dynamic interactions of the neural system, the musculoskeletal system, and the environment, although the underlying mechanisms remain unclear. Recently, investigations of the adaptation mechanisms of living beings have attracted attention, and bio-inspired control systems based on neurophysiological findings regarding sensorimotor interactions are being developed for legged robots. In this review, we introduce adaptive interlimb coordination for legged robots induced by various factors (locomotion speed, environmental situation, body properties, and task). In addition, we show characteristic properties of adaptive interlimb coordination, such as gait hysteresis and different time-scale adaptations. We also discuss the underlying mechanisms and control strategies to achieve adaptive interlimb coordination and the design principle for the control system of legged robots.

Intra- and intersegmental influences among central pattern generating networks in the walking system of the stick insect

To efficiently move around, animals need to coordinate their limbs. Proper, context-dependent coupling among the neural networks underlying leg movement is necessary for generating intersegmental coordination. In the slow-walking stick insect, local sensory information is very important for shaping coordination. However, central coupling mechanisms among segmental central pattern generators (CPGs) may also contribute to this. Here, we analyzed the interactions between contralateral networks that drive the depressor trochanteris muscle of the legs in both isolated and interconnected deafferented thoracic ganglia of the stick insect on application of pilocarpine, a muscarinic acetylcholine receptor agonist. Our results show that depressor CPG activity is only weakly coupled between all segments. Intrasegmental phase relationships differ between the three isolated ganglia, and they are modified and stabilized when ganglia are interconnected. However, the coordination patterns that emerge do not resemble those observed during walking. Our findings are in line with recent studies and highlight the influence of sensory input on coordination in slowly walking insects. Finally, as a direct interaction between depressor CPG networks and contralateral motoneurons could not be observed, we hypothesize that coupling is based on interactions at the level of CPG interneurons.NEW & NOTEWORTHY Maintaining functional interleg coordination is vitally important as animals locomote through changing environments. The relative importance of central mechanisms vs. sensory feedback in this process is not well understood. We analyzed coordination among the neural networks generating leg movements in stick insect preparations lacking phasic sensory feedback. Under these conditions, the networks governing different legs were only weakly coupled. In stick insect, central connections alone are thus insufficient to produce the leg coordination observed behaviorally.

Fiber-type distribution in insect leg muscles parallels similarities and differences in the functional role of insect walking legs

Previous studies have demonstrated that myofibrillar ATPase (mATPase) enzyme activity in muscle fibers determines their contraction properties. We analyzed mATPase activities in muscles of the front, middle and hind legs of the orthopteran stick insect (Carausius morosus) to test the hypothesis that differences in muscle fiber types and distributions reflected differences in their behavioral functions. Our data show that all muscles are composed of at least three fiber types, fast, intermediate and slow, and demonstrate that: (1) in the femoral muscles (extensor and flexor tibiae) of all legs, the number of fast fibers decreases from proximal to distal, with a concomitant increase in the number of slow fibers. (2) The swing phase muscles protractor coxae and levator trochanteris, have smaller percentages of slow fibers compared to the antagonist stance muscles retractor coxae and depressor trochanteris. (3) The percentage of slow fibers in the retractor coxae and depressor trochanteris increases significantly from front to hind legs. These results suggest that fiber-type distribution in leg muscles of insects is not identical across leg muscles but tuned towards the specific function of a given muscle in the locomotor system.

A Minimal Model Describing Hexapedal Interlimb Coordination: The Tegotae-Based Approach

Insects exhibit adaptive and versatile locomotion despite their minimal neural computing. Such locomotor patterns are generated via coordination between leg movements, i.e., an interlimb coordination, which is largely controlled in a distributed manner by neural circuits located in thoracic ganglia. However, the mechanism responsible for the interlimb coordination still remains elusive. Understanding this mechanism will help us to elucidate the fundamental control principle of animals' agile locomotion and to realize robots with legs that are truly adaptive and could not be developed solely by conventional control theories. This study aims at providing a “minimal" model of the interlimb coordination mechanism underlying hexapedal locomotion, in the hope that a single control principle could satisfactorily reproduce various aspects of insect locomotion. To this end, we introduce a novel concept we named “Tegotae,” a Japanese concept describing the extent to which a perceived reaction matches an expectation. By using the Tegotae-based approach, we show that a surprisingly systematic design of local sensory feedback mechanisms essential for the interlimb coordination can be realized. We also use a hexapod robot we developed to show that our mathematical model of the interlimb coordination mechanism satisfactorily reproduces various insects' gait patterns.

Arthrobots

This article describes a class of robots-"arthrobots"-inspired, in part, by the musculoskeletal system of arthropods (spiders and insects, inter alia). Arthrobots combine mechanical compliance, lightweight and simple construction, and inexpensive yet scalable design. An exoskeleton, constructed from thin organic polymeric tubes, provides lightweight structural support. Pneumatic joints modeled after the hydrostatic joints of spiders provide actuation and inherent mechanical compliance to external forces. An inflatable elastomeric tube (a "balloon") enables active extension of a limb; an opposing elastic tendon enables passive retraction. A variety of robots constructed from these structural elements demonstrate (i) crawling with one or two limbs, (ii) walking with four or six limbs (including an insect-like triangular gait), (iii) walking with eight limbs, or (iv) floating and rowing on the surface of water. Arthrobots are simple to fabricate and are able to operate safely in contact with humans.

Effects of functional decoupling of a leg in a model of stick insect walking incorporating three ipsilateral legs

Legged locomotion is a fundamental form of activity of insects during which the legs perform coordinated movements. Sensory signals conveying position, velocity and load of a leg are sent between the thoracic ganglia where the local control networks of the leg muscles are situated. They affect the actual state of the local control networks, hence the stepping of the legs. Sensory coordination in stepping has been intensively studied but important details of its neuronal mechanisms are still unclear. One possibility to tackle this problem is to study what happens to the coordination if a leg is, reversibly or irreversibly, deprived of its normal function. There are numerous behavioral studies on this topic but they could not fully uncover the underlying neuronal mechanisms. Another promising approach to make further progress here can be the use of appropriate models that help elucidate those coordinating mechanisms. We constructed a model of three ipsilateral legs of a stick insect that can mimic coordinated stepping of these legs. We used this model to investigate the possible effects of decoupling a leg. We found that decoupling of the front or the hind leg did not disrupt the coordinated walking of the two remaining legs. However, decoupling of the middle leg yielded mixed results. Both disruption and continuation of coordinated stepping of the front and hind leg occurred. These results agree with the majority of corresponding experimental findings. The model suggests a number of possible mechanisms of decoupling that might bring about the changes.

Rigidity and Flexibility: The Central Basis of Inter-Leg Coordination in the Locust

Many motor behaviors, and specifically locomotion, are the product of an intricate interplay between neuronal oscillators known as central pattern generators (CPGs), descending central commands, and sensory feedback loops. The relative contribution of each of these components to the final behavior determines the trade-off between fixed movements and those that are carefully adapted to the environment. Here we sought to decipher the endogenous, default, motor output of the CPG network controlling the locust legs, in the absence of any sensory or descending influences. We induced rhythmic activity in the leg CPGs in isolated nervous system preparations, using different application procedures of the muscarinic agonist pilocarpine. We found that the three thoracic ganglia, each controlling a pair of legs, have different inherent bilateral coupling. Furthermore, we found that the pharmacological activation of one ganglion is sufficient to induce activity in the other, untreated, ganglia. Each ganglion was thus capable to impart its own bilateral inherent pattern onto the other ganglia via a tight synchrony among the ipsilateral CPGs. By cutting a connective and severing the lateral-longitudinal connections, we were able to uncouple the oscillators’ activity. While the bilateral connections demonstrated a high modularity, the ipsilateral CPGs maintained a strict synchronized activity. These findings suggest that the central infrastructure behind locust walking features both rigid elements, which presumably support the generation of stereotypic orchestrated leg movements, and flexible elements, which might provide the central basis for adaptations to the environment and to higher motor commands.

Design of Spiking Central Pattern Generators for Multiple Locomotion Gaits in Hexapod Robots by Christiansen Grammar Evolution

This paper presents a method to design Spiking Central Pattern Generators (SCPGs) to achieve locomotion at different frequencies on legged robots. It is validated through embedding its designs into a Field-Programmable Gate Array (FPGA) and implemented on a real hexapod robot. The SCPGs are automatically designed by means of a Christiansen Grammar Evolution (CGE)-based methodology. The CGE performs a solution for the configuration (synaptic weights and connections) for each neuron in the SCPG. This is carried out through the indirect representation of candidate solutions that evolve to replicate a specific spike train according to a locomotion pattern (gait) by measuring the similarity between the spike trains and the SPIKE distance to lead the search to a correct configuration. By using this evolutionary approach, several SCPG design specifications can be explicitly added into the SPIKE distance-based fitness function, such as looking for Spiking Neural Networks (SNNs) with minimal connectivity or a Central Pattern Generator (CPG) able to generate different locomotion gaits only by changing the initial input stimuli. The SCPG designs have been successfully implemented on a Spartan 6 FPGA board and a real time validation on a 12 Degrees Of Freedom (DOFs) hexapod robot is presented.

How to find home backwards? Locomotion and inter-leg coordination during rearward walking of Cataglyphis fortis desert ants

For insects, flexibility in the performance of terrestrial locomotion is a vital part of facing the challenges of their often unpredictable environment. Arthropods such as scorpions and crustaceans can switch readily from forward to backward locomotion, but in insects this behaviour seems to be less common and, therefore, is only poorly understood. Here we present an example of spontaneous and persistent backward walking in Cataglyphis desert ants that allows us to investigate rearward locomotion within a natural context. When ants find a food item that is too large to be lifted up and to be carried in a normal forward-faced orientation, they will drag the load walking backwards to their home nest. A detailed examination of this behaviour reveals a surprising flexibility of the locomotor output. Compared with forward walks with regular tripod coordination, no main coordination pattern can be assigned to rearward walks. However, we often observed leg-pair-specific stepping patterns. The front legs frequently step with small stride lengths, while the middle and the hind legs are characterized by less numerous but larger strides. But still, these specializations show no rigidly fixed leg coupling, nor are they strictly embedded within a temporal context; therefore, they do not result in a repetitive coordination pattern. The individual legs act as separate units, most likely to better maintain stability during backward dragging.

Quadrupedal Robot Locomotion: A Biologically Inspired Approach and Its Hardware Implementation

A bioinspired locomotion system for a quadruped robot is presented. Locomotion is achieved by a spiking neural network (SNN) that acts as a Central Pattern Generator (CPG) producing different locomotion patterns represented by their raster plots. To generate these patterns, the SNN is configured with specific parameters (synaptic weights and topologies), which were estimated by a metaheuristic method based on Christiansen Grammar Evolution (CGE). The system has been implemented and validated on two robot platforms; firstly, we tested our system on a quadruped robot and, secondly, on a hexapod one. In this last one, we simulated the case where two legs of the hexapod were amputated and its locomotion mechanism has been changed. For the quadruped robot, the control is performed by the spiking neural network implemented on an Arduino board with 35% of resource usage. In the hexapod robot, we used Spartan 6 FPGA board with only 3% of resource usage. Numerical results show the effectiveness of the proposed system in both cases.

Recovery of locomotion after injury in Drosophila melanogaster depends on proprioception

Locomotion is necessary for survival in most animal species. However, injuries to the appendages mediating locomotion are common. We assess the recovery of walking in Drosophila melanogaster following leg amputation. Whereas flies pre-amputation explore open arenas in a symmetric fashion on average, foreleg amputation induces a strong turning bias away from the side of the amputation. However, we find that unbiased walking behavior returns over time in wild-type flies, while recovery is significantly impaired in proprioceptive mutants. To identify the biomechanical basis of this locomotor impairment and recovery, we then examine individual leg motion (gait) at a fine scale. A minimal mathematical model that links neurodynamics to body mechanics during walking shows that redistributing leg forces between the right and left side enables the observed recovery. Altogether, our study suggests that proprioceptive input from the intact limbs plays a crucial role in the behavioral plasticity associated with locomotor recovery after injury.

Speed-dependent interplay between local pattern-generating activity and sensory signals during walking in Drosophila

In insects, the coordinated motor output required for walking is based on the interaction between local pattern-generating networks providing basic rhythmicity and leg sensory signals which modulate this output on a cycle-to-cycle basis. How this interplay changes speed-dependently and thereby gives rise to the different coordination patterns observed at different speeds is understood insufficiently. Here, we used amputation to reduce sensory signals in single legs and decouple them mechanically during walking in Drosophila. This allowed for the dissociation between locally-generated motor output in the stump and coordinating influences from intact legs. Leg stumps were still rhythmically active during walking. While the oscillatory frequency in intact legs was dependent on walking speed, stumps showed a high and relatively constant oscillation frequency at all walking speeds. At low walking speeds we found no strict cycle-to-cycle coupling between stumps and intact legs. In contrast, at high walking speeds stump oscillations were strongly coupled to the movement of intact legs on a 1-to-1 basis. While during slow walking there was no preferred phase between stumps and intact legs, we nevertheless found a preferred time interval between touch-down or lift-off events in intact legs and levation or depression of stumps. Based on these findings, we hypothesize that, as in other insects, walking speed in Drosophila is predominantly controlled by indirect mechanisms and that direct modulation of basic pattern-generating circuits plays a subsidiary role. Furthermore, inter-leg coordination strength seems to be speed-dependent and greater coordination is evident at higher walking speeds.