Walknet, a bio-inspired controller for hexapod walking

Context-dependent coordination of movement in Tribolium castaneum larvae

Insect pests such as the red flour beetle (Tribolium castaneum) destroy up to 20% of stored grain products worldwide, making them a significant threat to food security. Their success hinges upon adapting their movements to unpredictable, heterogeneous environments like flour. Tribolium is well developed as a genetic model system; however, little is known about its natural locomotion and how its nervous system coordinates adaptive movement. Here, we employed videographic whole-animal and leg tracking to assess how Tribolium larvae locomote over different substrates and analyse their gait kinematics across speeds. Unlike many hexapods, larvae employed a bilaterally symmetric, posterior-to-anterior wave gait during fast locomotion. At slower speeds, coordination within thoracic segments was disrupted, although intersegmental coordination remained intact. Moreover, larvae used terminal abdominal structures (pygopods) to support challenging movements, such as climbing overhangs. Pygopod placement coincided with leg swing initiation, suggesting a stabilising role as adaptive anchoring devices. Surgically lesioning the connective between thoracic and abdominal ganglia impaired pygopod engagement and led to escalating impairments in flat-terrain locomotion, climbing and tunnelling. These results suggest that effective movement in Tribolium larvae requires thoracic-abdominal coordination, and that larval gait and limb recruitment is context dependent. Our work provides the first kinematic analysis of Tribolium larval locomotion and gives insights into its neural control, creating a foundation for future motor control research in a genetically tractable beetle that jeopardises global food security.

Sensorimotor delays constrain robust locomotion in a 3D kinematic model of fly walking

Walking animals must maintain stability in the presence of external perturbations, despite significant temporal delays in neural signaling and muscle actuation. Here, we develop a 3D kinematic model with a layered control architecture to investigate how sensorimotor delays constrain robustness of walking behavior in the fruit fly, Drosophila. Motivated by the anatomical architecture of insect locomotor control circuits, our model consists of three component layers: a neural network that generates realistic 3D joint kinematics for each leg, an optimal controller that executes the joint kinematics while accounting for delays, and an inter-leg coordinator. The model generates realistic simulated walking that resembles real fly walking kinematics and sustains walking even when subjected to unexpected perturbations, generalizing beyond its training data. However, we found that the model's robustness to perturbations deteriorates when sensorimotor delay parameters exceed the physiological range. These results suggest that fly sensorimotor control circuits operate close to the temporal limit at which they can detect and respond to external perturbations. More broadly, we show how a modular, layered model architecture can be used to investigate physiological constraints on animal behavior.

I2Bot: an open-source tool for multi-modal and embodied simulation of insect navigation

Achieving a comprehensive understanding of animal intelligence demands an integrative approach that acknowledges the interplay between an organism's brain, body and environment. Insects, despite their limited computational resources, demonstrate remarkable abilities in navigation. Existing computational models often fall short in faithfully replicating the morphology of real insects and their interactions with the environment, hindering validation and practical application in robotics. To address these gaps, we present I2Bot, a novel simulation tool based on the morphological characteristics of real insects. This tool empowers robotic models with dynamic sensory capabilities, realistic modelling of insect morphology, physical dynamics and sensory capacity. By integrating gait controllers and computational models into I2Bot, we have implemented classical embodied navigation behaviours and revealed some fundamental navigation principles. By open-sourcing I2Bot, we aim to accelerate the understanding of insect intelligence and foster advances in the development of autonomous robotic systems.

NeuroMechFly v2: simulating embodied sensorimotor control in adult Drosophila

Discovering principles underlying the control of animal behavior requires a tight dialogue between experiments and neuromechanical models. Such models have primarily been used to investigate motor control with less emphasis on how the brain and motor systems work together during hierarchical sensorimotor control. NeuroMechFly v2 expands Drosophila neuromechanical modeling by enabling vision, olfaction, ascending motor feedback and complex terrains that can be navigated using leg adhesion. We illustrate its capabilities by constructing biologically inspired controllers that use ascending feedback to perform path integration and head stabilization. After adding vision and olfaction, we train a controller using reinforcement learning to perform a multimodal navigation task. Finally, we illustrate more bio-realistic modeling involving complex odor plume navigation, and fly-fly following using a connectome-constrained visual network. NeuroMechFly can be used to accelerate the discovery of explanatory models of the nervous system and to develop machine learning-based controllers for autonomous artificial agents and robots.

Moving in an Uncertain World: Robust and Adaptive Control of Locomotion from Organisms to Machine Intelligence

Whether walking, running, slithering, or flying, organisms display a remarkable ability to move through complex and uncertain environments. In particular, animals have evolved to cope with a host of uncertainties-both of internal and external origin-to maintain adequate performance in an ever-changing world. In this review, we present mathematical methods in engineering to highlight emerging principles of robust and adaptive control of organismal locomotion. Specifically, by drawing on the mathematical framework of control theory, we decompose the robust and adaptive hierarchical structure of locomotor control. We show how this decomposition along the robust-adaptive axis provides testable hypotheses to classify behavioral outcomes to perturbations. With a focus on studies in non-human animals, we contextualize recent findings along the robust-adaptive axis by emphasizing two broad classes of behaviors: (1) compensation to appendage loss and (2) image stabilization and fixation. Next, we attempt to map robust and adaptive control of locomotion across some animal groups and existing bio-inspired robots. Finally, we highlight exciting future directions and interdisciplinary collaborations that are needed to unravel principles of robust and adaptive locomotion.

Bionic Multi-Legged Robots with Flexible Bodies: Design, Motion, and Control

Bionic multi-legged robots with flexible bodies embody human ingenuity in imitating, learning, and exploring the natural world. In contrast to rigid-body robots, these robots with flexible bodies exhibit superior locomotive capabilities. The flexible body of the robot not only boosts the moving speed and walking stability but also enhances adaptability across complex terrains. This article focuses on the innovative design of flexible bodies. Firstly, the structural designs, including artificial spines and single/multi-axis articulation mechanisms, are outlined systematically. Secondly, the enhancement of robotic motion by flexible bodies is reviewed, examining the impact that body degrees of freedom, stiffness, and coordinated control between the body and limbs have on robotic motion. Thirdly, existing robotic control methods, organized by control architectures, are comprehensively overviewed in this article. Finally, the application prospects of bionic multi-legged robots with flexible bodies are offered, and the challenges that may arise in their future development are listed. This article aims to serve as a reference for bionic robot research.

Geometric phase predicts locomotion performance in undulating living systems across scales

Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar traveling waves of axial body bending for movement. Delineating how self-deformation parameters lead to locomotor performance (e.g. speed, energy, turning capabilities) remains challenging. We show that a geometric framework, replacing laborious calculation with a diagrammatic scheme, is well-suited to discovery and comparison of effective patterns of wave dynamics in diverse living systems. We focus on a regime of undulatory locomotion, that of highly damped environments, which is applicable not only to small organisms in viscous fluids, but also larger animals in frictional fluids (sand) and on frictional ground. We find that the traveling wave dynamics used by mm-scale nematode worms and cm-scale desert dwelling snakes and lizards can be described by time series of weights associated with two principal modes. The approximately circular closed path trajectories of mode weights in a self-deformation space enclose near-maximal surface integral (geometric phase) for organisms spanning two decades in body length. We hypothesize that such trajectories are targets of control (which we refer to as "serpenoid templates"). Further, the geometric approach reveals how seemingly complex behaviors such as turning in worms and sidewinding snakes can be described as modulations of templates. Thus, the use of differential geometry in the locomotion of living systems generates a common description of locomotion across taxa and provides hypotheses for neuromechanical control schemes at lower levels of organization.

Integration of feedforward and feedback control in the neuromechanics of vertebrate locomotion: a review of experimental, simulation and robotic studies

Animal locomotion is the result of complex and multi-layered interactions between the nervous system, the musculo-skeletal system and the environment. Decoding the underlying mechanisms requires an integrative approach. Comparative experimental biology has allowed researchers to study the underlying components and some of their interactions across diverse animals. These studies have shown that locomotor neural circuits are distributed in the spinal cord, the midbrain and higher brain regions in vertebrates. The spinal cord plays a key role in locomotor control because it contains central pattern generators (CPGs) - systems of coupled neuronal oscillators that provide coordinated rhythmic control of muscle activation that can be viewed as feedforward controllers - and multiple reflex loops that provide feedback mechanisms. These circuits are activated and modulated by descending pathways from the brain. The relative contributions of CPGs, feedback loops and descending modulation, and how these vary between species and locomotor conditions, remain poorly understood. Robots and neuromechanical simulations can complement experimental approaches by testing specific hypotheses and performing what-if scenarios. This Review will give an overview of key knowledge gained from comparative vertebrate experiments, and insights obtained from neuromechanical simulations and robotic approaches. We suggest that the roles of CPGs, feedback loops and descending modulation vary among animals depending on body size, intrinsic mechanical stability, time required to reach locomotor maturity and speed effects. We also hypothesize that distal joints rely more on feedback control compared with proximal joints. Finally, we highlight important opportunities to address fundamental biological questions through continued collaboration between experimentalists and engineers.

The neuromechanics of animal locomotion: From biology to robotics and back

Robotics and neuroscience are sister disciplines that both aim to understand how agile, efficient, and robust locomotion can be achieved in autonomous agents. Robotics has already benefitted from neuromechanical principles discovered by investigating animals. These include the use of high-level commands to control low-level central pattern generator-like controllers, which, in turn, are informed by sensory feedback. Reciprocally, neuroscience has benefited from tools and intuitions in robotics to reveal how embodiment, physical interactions with the environment, and sensory feedback help sculpt animal behavior. We illustrate and discuss exemplar studies of this dialog between robotics and neuroscience. We also reveal how the increasing biorealism of simulations and robots is driving these two disciplines together, forging an integrative science of autonomous behavioral control with many exciting future opportunities.

A virtuous cycle between invertebrate and robotics research: perspective on a decade of Living Machines research

Many invertebrates are ideal model systems on which to base robot design principles due to their success in solving seemingly complex tasks across domains while possessing smaller nervous systems than vertebrates. Three areas are particularly relevant for robot designers: Research on flying and crawling invertebrates has inspired new materials and geometries from which robot bodies (their morphologies) can be constructed, enabling a new generation of softer, smaller, and lighter robots. Research on walking insects has informed the design of new systems for controlling robot bodies (their motion control) and adapting their motion to their environment without costly computational methods. And research combining wet and computational neuroscience with robotic validation methods has revealed the structure and function of core circuits in the insect brain responsible for the navigation and swarming capabilities (their mental faculties) displayed by foraging insects. The last decade has seen significant progress in the application of principles extracted from invertebrates, as well as the application of biomimetic robots to model and better understand how animals function. This Perspectives paper on the past 10 years of the Living Machines conference outlines some of the most exciting recent advances in each of these fields before outlining lessons gleaned and the outlook for the next decade of invertebrate robotic research.

Modularity in Nervous Systems—a Key to Efficient Adaptivity for Deep Reinforcement Learning

Modularity as observed in biological systems has proven valuable for guiding classical motor theories towards good answers about action selection and execution. New challenges arise when we turn to learning: Trying to scale current computational models, such as deep reinforcement learning (DRL), to action spaces, input dimensions, and time horizons seen in biological systems still faces severe obstacles unless vast amounts of training data are available. This leads to the question: does biological modularity also hold an important key for better answers to obtain efficient adaptivity for deep reinforcement learning? We review biological experimental work on modularity in biological motor control and link this with current examples of (deep) RL approaches. Analyzing outcomes of simulation studies, we show that these approaches benefit from forms of modularization as found in biological systems. We identify three different strands of modularity exhibited in biological control systems. Two of them—modularity in state (i) and in action (ii) spaces—appear as a consequence of local interconnectivity (as in reflexes) and are often modulated by higher levels in a control hierarchy. A third strand arises from chunking of action elements along a (iii) temporal dimension. Usually interacting in an overarching spatio-temporal hierarchy of the overall system, the three strands offer major “factors” decomposing the entire modularity structure. We conclude that modularity with its above strands can provide an effective prior for DRL approaches to speed up learning considerably and making learned controllers more robust and adaptive.

neuroWalknet, a controller for hexapod walking allowing for context dependent behavior

Decentralized control has been established as a key control principle in insect walking and has been successfully leveraged to account for a wide range of walking behaviors in the proposed neuroWalknet architecture. This controller allows for walking patterns at different velocities in both, forward and backward direction-quite similar to the behavior shown in stick insects-, for negotiation of curves, and for robustly dealing with various disturbances. While these simulations focus on the cooperation of different, decentrally controlled legs, here we consider a set of biological experiments not yet been tested by neuroWalknet, that focus on the function of the individual leg and are context dependent. These intraleg studies deal with four groups of interjoint reflexes. The reflexes are elicited by stimulation of the femoral chordotonal organ (fCO) or groups of campaniform sensilla (CS). Motor output signals are recorded from the alpha-joint, the beta-joint or the gamma-joint of the leg. Furthermore, the influence of these sensory inputs to artificially induced oscillations by application of pilocarpine has been studied. Although these biological data represent results obtained from different local reflexes in different contexts, they fit with and are embedded into the behavior shown by the global structure of neuroWalknet. In particular, a specific and intensively studied behavior, active reaction, has since long been assumed to represent a separate behavioral element, from which it is not clear why it occurs in some situations, but not in others. This question could now be explained as an emergent property of the holistic structure of neuroWalknet which has shown to be able to produce artificially elicited pilocarpine-driven oscillation that can be controlled by sensory input without the need of explicit innate CPG structures. As the simulation data result from a holistic system, further results were obtained that could be used as predictions to be tested in further biological experiments.

Multi-scopic neuro-cognitive adaptation for legged locomotion robots

Dynamic locomotion is realized through a simultaneous integration of adaptability and optimality. This article proposes a neuro-cognitive model for a multi-legged locomotion robot that can seamlessly integrate multi-modal sensing, ecological perception, and cognition through the coordination of interoceptive and exteroceptive sensory information. Importantly, cognitive models can be discussed as micro-, meso-, and macro-scopic; these concepts correspond to sensing, perception, and cognition; and short-, medium-, and long-term adaptation (in terms of ecological psychology). The proposed neuro-cognitive model integrates these intelligent functions from a multi-scopic point of view. Macroscopic-level presents an attention mechanism with short-term adaptive locomotion control conducted by a lower-level sensorimotor coordination-based model. Macrosopic-level serves environmental cognitive map featuring higher-level behavior planning. Mesoscopic level shows integration between the microscopic and macroscopic approaches, enabling the model to reconstruct a map and conduct localization using bottom-up facial environmental information and top-down map information, generating intention towards the ultimate goal at the macroscopic level. The experiments demonstrated that adaptability and optimality of multi-legged locomotion could be achieved using the proposed multi-scale neuro-cognitive model, from short to long-term adaptation, with efficient computational usage. Future research directions can be implemented not only in robotics contexts but also in the context of interdisciplinary studies incorporating cognitive science and ecological psychology.

Influence of caste and subcaste characteristics in ant locomotion (Camponotus fellah)

Worker polymorphism in ants has evolved repeatedly, with considerable differences in the morphometry of worker subcastes. Such body size differences and especially caste- and subcaste-specific characteristics might significantly influence locomotion. Therefore, we performed a comprehensive locomotion analysis along gradients in both body size and walking speed of Camponotus fellah worker subcastes, and of males, which have rarely been studied to date due to short life spans associated with mating flights. We provide a detailed description of the morphometry and size differences of C. fellah castes and subcastes and analyse locomotion in the different polymorphic groups in terms of absolute and relative walking speeds (mesosoma lengths per second). Our results reveal that body size and shape affect locomotion behaviour to different extents in the worker subcastes (minor workers, medias, major workers) and in males. Nevertheless, C. fellah ants use the same overall locomotion strategy, with males and major workers reaching considerably lower walking speeds than minors and medias. Body size thus mainly affects walking speed. Minor workers reach the highest relative velocities by high relative stride lengths in combination with large vertical and lateral COM oscillations and clearly higher stride frequencies of up to 25 Hz. Locomotion of males was characterised by clearly lower walking speeds, wider footprint positions, significant phase shifts and a notable dragging of the shorter hind legs. However, general walking parameters of males differed less from those of the female workers than expected due to division of labour in the colony.

NeuroMechFly, a neuromechanical model of adult Drosophila melanogaster

Animal behavior emerges from an interaction between neural network dynamics, musculoskeletal properties and the physical environment. Accessing and understanding the interplay between these elements requires the development of integrative and morphologically realistic neuromechanical simulations. Here we present NeuroMechFly, a data-driven model of the widely studied organism, Drosophila melanogaster. NeuroMechFly combines four independent computational modules: a physics-based simulation environment, a biomechanical exoskeleton, muscle models and neural network controllers. To enable use cases, we first define the minimum degrees of freedom of the leg from real three-dimensional kinematic measurements during walking and grooming. Then, we show how, by replaying these behaviors in the simulator, one can predict otherwise unmeasured torques and contact forces. Finally, we leverage NeuroMechFly's full neuromechanical capacity to discover neural networks and muscle parameters that drive locomotor gaits optimized for speed and stability. Thus, NeuroMechFly can increase our understanding of how behaviors emerge from interactions between complex neuromechanical systems and their physical surroundings.

Continuous Online Adaptation of Bioinspired Adaptive Neuroendocrine Control for Autonomous Walking Robots

Walking animals can continuously adapt their locomotion to deal with unpredictable changing environments. They can also take proactive steps to avoid colliding with an obstacle. In this study, we aim to realize such features for autonomous walking robots so that they can efficiently traverse complex terrains. To achieve this, we propose novel bioinspired adaptive neuroendocrine control. In contrast to conventional locomotion control methods, this approach does not require robot and environmental models, exteroceptive feedback, or multiple learning trials. It integrates three main modular neural mechanisms, relying only on proprioceptive feedback and short-term memory, namely: 1) neural central pattern generator (CPG)-based control; 2) an artificial hormone network (AHN); and 3) unsupervised input correlation-based learning (ICO). The neural CPG-based control creates insect-like gaits, while the AHN can continuously adapt robot joint movement individually with respect to the terrain during the stance phase using only the torque feedback. In parallel, the ICO generates short-term memory for proactive obstacle negotiation during the swing phase, allowing the posterior legs to step over the obstacle before hitting it. The control approach is evaluated on a bioinspired hexapod robot walking on complex unpredictable terrains (e.g., gravel, grass, and extreme random stepfield). The results show that the robot can successfully perform energy-efficient autonomous locomotion and online continuous adaptation with proactivity to overcome such terrains. Since our adaptive neural control approach does not require a robot model, it is general and can be applied to other bioinspired walking robots to achieve a similar adaptive, autonomous, and versatile function.

Locomotion in the pseudoscorpion Chelifer cancroides - forward, backward and upside down walking in an eight-legged arthropod

While insect locomotion has been intensively studied, there are comparably few studies investigating octopedal walking behaviour, and very little is known about pseudoscorpions in particular. Therefore, we performed an extensive locomotion analysis during forward, backward and upside down walking in the cosmopolitan pseudoscorpion Chelifer cancroides. During forward locomotion, we observed C. cancroides to freeze locomotion frequently for short time periods. These microstops were barely visible to the naked eye with a duration of 100-200 ms. Our locomotion analysis revealed that C. cancroides performs a statically stable and highly coordinated alternating tetrapod gait during forward and backward walking, with almost complete inversion of the tetrapod schemes, but no rigidly fixed leg coordination during upside down walks with low walking speeds up to 4 body lengths per second. Highest speeds (up to 17 body lengths per second), mainly achieved by consistent leg coordination and strong phase shifts, were observed during backward locomotion (escape behaviour), while forward walking was characterised by lower speeds and phase shifts around 10% between two loosely coupled leg groups within one tetrapod. That is, during the movement of one tetrapod group, the last and the third leg are almost synchronous in their swing phases, as are the second and the first leg. A special role of the second leg pair was demonstrated, probably mainly for stability reasons and related to the large pedipalps.

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.

Adaptive Centipede Walking via Synergetic Coupling Between Decentralized Control and Flexible Body Dynamics

Multi-legged animals such as myriapods can locomote on unstructured rough terrain using their flexible bodies and legs. This highly adaptive locomotion emerges through the dynamic interactions between an animal’s nervous system, its flexible body, and the environment. Previous studies have primarily focused on either adaptive leg control or the passive compliance of the body parts and have shown how each enhanced adaptability to complex terrains in multi-legged locomotion. However, the essential mechanism considering both the adaptive locomotor circuits and bodily flexibility remains unclear. In this study, we focused on centipedes and aimed to understand the well-balanced coupling between the two abovementioned mechanisms for rough terrain walking by building a neuromechanical model based on behavioral findings. In the behavioral experiment, we observed a centipede walking when part of the terrain was temporarily removed and thereafter restored. We found that the ground contact sense of each leg was essential for generating rhythmic leg motions and also for establishing adaptive footfall patterns between adjacent legs. Based on this finding, we proposed decentralized control mechanisms using ground contact sense and implemented them into a physical centipede model with flexible bodies and legs. In the simulations, our model self-organized the typical gait on flat terrain and adaptive walking during gap crossing, which were similar to centipedes. Furthermore, we demonstrated that the locomotor performance deteriorated on rough terrain when adaptive leg control was removed or when the body was rigid, which indicates that both the adaptive leg control and the flexible body are essential for adaptive locomotion. Thus, our model is expected to capture the possible essential mechanisms underlying adaptive centipede walking and pave the way for designing multi-legged robots with high adaptability to irregular terrain.

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.

Insect-Inspired Robots: Bridging Biological and Artificial Systems

This review article aims to address common research questions in hexapod robotics. How can we build intelligent autonomous hexapod robots that can exploit their biomechanics, morphology, and computational systems, to achieve autonomy, adaptability, and energy efficiency comparable to small living creatures, such as insects? Are insects good models for building such intelligent hexapod robots because they are the only animals with six legs? This review article is divided into three main sections to address these questions, as well as to assist roboticists in identifying relevant and future directions in the field of hexapod robotics over the next decade. After an introduction in section (1), the sections will respectively cover the following three key areas: (2) biomechanics focused on the design of smart legs; (3) locomotion control; and (4) high-level cognition control. These interconnected and interdependent areas are all crucial to improving the level of performance of hexapod robotics in terms of energy efficiency, terrain adaptability, autonomy, and operational range. We will also discuss how the next generation of bioroboticists will be able to transfer knowledge from biology to robotics and vice versa.

Decentralized control and local information for robust and adaptive decentralized Deep Reinforcement Learning

Decentralization is a central characteristic of biological motor control that allows for fast responses relying on local sensory information. In contrast, the current trend of Deep Reinforcement Learning (DRL) based approaches to motor control follows a centralized paradigm using a single, holistic controller that has to untangle the whole input information space. This motivates to ask whether decentralization as seen in biological control architectures might also be beneficial for embodied sensori-motor control systems when using DRL. To answer this question, we provide an analysis and comparison of eight control architectures for adaptive locomotion that were derived for a four-legged agent, but with their degree of decentralization varying systematically between the extremes of fully centralized and fully decentralized. Our comparison shows that learning speed is significantly enhanced in distributed architectures-while still reaching the same high performance level of centralized architectures-due to smaller search spaces and local costs providing more focused information for learning. Second, we find an increased robustness of the learning process in the decentralized cases-it is less demanding to hyperparameter selection and less prone to becoming trapped in poor local minima. Finally, when examining generalization to uneven terrains-not used during training-we find best performance for an intermediate architecture that is decentralized, but integrates only local information from both neighboring legs. Together, these findings demonstrate beneficial effects of distributing control into decentralized units and relying on local information. This appears as a promising approach towards more robust DRL and better generalization towards adaptive behavior.

Generation of Direct-, Retrograde-, and Source-Wave Gaits in Multi-Legged Locomotion in a Decentralized Manner via Embodied Sensorimotor Interaction

Multi-legged animals show several types of ipsilateral interlimb coordination. Millipedes use a direct-wave gait, in which the swing leg movements propagate from posterior to anterior. In contrast, centipedes use a retrograde-wave gait, in which the swing leg movements propagate from anterior to posterior. Interestingly, when millipedes walk in a specific way, both direct and retrograde waves of the swing leg movements appear with the waves' source, which we call the source-wave gait. However, the gait generation mechanism is still unclear because of the complex nature of the interaction between neural control and dynamic body systems. The present study used a simple model to understand the mechanism better, primarily how local sensory feedback affects multi-legged locomotion. The model comprises a multi-legged body and its locomotion control system using biologically inspired oscillators with local sensory feedback, phase resetting. Each oscillator controls each leg independently. Our simulation produced the above three types of animal gaits. These gaits are not predesigned but emerge through the interaction between the neural control and dynamic body systems through sensory feedback (embodied sensorimotor interaction) in a decentralized manner. The analytical description of these gaits' solution and stability clarifies the embodied sensorimotor interaction's functional roles in the interlimb coordination.

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.

Trends in the Control of Hexapod Robots: A Survey

The static stability of hexapods motivates their design for tasks in which stable locomotion is required, such as navigation across complex environments. This task is of high interest due to the possibility of replacing human beings in exploration, surveillance and rescue missions. For this application, the control system must adapt the actuation of the limbs according to their surroundings to ensure that the hexapod does not tumble during locomotion. The most traditional approach considers their limbs as robotic manipulators and relies on mechanical models to actuate them. However, the increasing interest in model-free models for the control of these systems has led to the design of novel solutions. Through a systematic literature review, this paper intends to overview the trends in this field of research and determine in which stage the design of autonomous and adaptable controllers for hexapods is.

Adaptive and Energy-Efficient Optimal Control in CPGs Through Tegotae-Based Feedback

To obtain biologically inspired robotic control, the architecture of central pattern generators (CPGs) has been extensively adopted to generate periodic patterns for locomotor control. This is attributed to the interesting properties of nonlinear oscillators. Although sensory feedback in CPGs is not necessary for the generation of patterns, it plays a central role in guaranteeing adaptivity to environmental conditions. Nonetheless, its inclusion significantly modifies the dynamics of the CPG architecture, which often leads to bifurcations. For instance, the force feedback can be exploited to derive information regarding the state of the system. In particular, the Tegotae approach can be adopted by coupling proprioceptive information with the state of the oscillation itself in the CPG model. This paper discusses this policy with respect to other types of feedback; it provides higher adaptivity and an optimal energy efficiency for reflex-like actuation. We believe this is the first attempt to analyse the optimal energy efficiency along with the adaptivity of the Tegotae approach.

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.

Integrating Non-spiking Interneurons in Spiking Neural Networks

Researchers working with neural networks have historically focused on either non-spiking neurons tractable for running on computers or more biologically plausible spiking neurons typically requiring special hardware. However, in nature homogeneous networks of neurons do not exist. Instead, spiking and non-spiking neurons cooperate, each bringing a different set of advantages. A well-researched biological example of such a mixed network is a sensorimotor pathway, responsible for mapping sensory inputs to behavioral changes. This type of pathway is also well-researched in robotics where it is applied to achieve closed-loop operation of legged robots by adapting amplitude, frequency, and phase of the motor output. In this paper we investigate how spiking and non-spiking neurons can be combined to create a sensorimotor neuron pathway capable of shaping network output based on analog input. We propose sub-threshold operation of an existing spiking neuron model to create a non-spiking neuron able to interpret analog information and communicate with spiking neurons. The validity of this methodology is confirmed through a simulation of a closed-loop amplitude regulating network inspired by the internal feedback loops found in insects for posturing. Additionally, we show that non-spiking neurons can effectively manipulate post-synaptic spiking neurons in an event-based architecture. The ability to work with mixed networks provides an opportunity for researchers to investigate new network architectures for adaptive controllers, potentially improving locomotion strategies of legged robots.

Sprawling Quadruped Robot Driven by Decentralized Control With Cross-Coupled Sensory Feedback Between Legs and Trunk

Quadruped animals achieve agile and highly adaptive locomotion owing to the coordination between their legs and other body parts, such as the trunk, head, and tail, that is, body–limb coordination. This study aims to understand the sensorimotor control underlying body–limb coordination. To this end, we adopted sprawling locomotion in vertebrate animals as a model behavior. This is a quadruped walking gait with lateral body bending used by many amphibians and lizards. Our previous simulation study demonstrated that cross-coupled sensory feedback between the legs and trunk helps to rapidly establish body–limb coordination and improve locomotion performance. This paper presented an experimental validation of the cross-coupled sensory feedback control using a newly developed quadruped robot. The results show similar tendencies to the simulation study. Sensory feedback provides rapid convergence to stable gait, robustness against leg failure, and morphological changes. Our study suggests that sensory feedback potentially plays an essential role in body–limb coordination and provides a robust, sensory-driven control principle for quadruped robots.

Flexible Spiking CPGs for Online Manipulation During Hexapod Walking

Neural signals for locomotion are influenced both by the neural network architecture and sensory inputs coordinating and adapting the gait to the environment. Adaptation relies on the ability to change amplitude, frequency, and phase of the signals within the sensorimotor loop in response to external stimuli. However, in order to experiment with closed-loop control, we first need a better understanding of the dynamics of the system and how adaptation works. Based on insights from biology, we developed a spiking neural network capable of continuously changing amplitude, frequency, and phase online. The resulting network is deployed on a hexapod robot in order to observe the walking behavior. The morphology and parameters of the network results in a tripod gait, demonstrating that a design without afferent feedback is sufficient to maintain a stable gait. This is comparable to results from biology showing that deafferented samples exhibit a tripod-like gait and adds to the evidence for a meaningful role of network topology in locomotion. Further, this work enables research into the role of sensory feedback and high-level control signals in the adaptation of gait types. A better understanding of the neural control of locomotion relates back to biology where it can provide evidence for theories that are currently not testable on live insects.

Decentralized control of insect walking: A simple neural network explains a wide range of behavioral and neurophysiological results

Controlling the six legs of an insect walking in an unpredictable environment is a challenging task, as many degrees of freedom have to be coordinated. Solutions proposed to deal with this task are usually based on the highly influential concept that (sensory-modulated) central pattern generators (CPG) are required to control the rhythmic movements of walking legs. Here, we investigate a different view. To this end, we introduce a sensor based controller operating on artificial neurons, being applied to a (simulated) insectoid robot required to exploit the "loop through the world" allowing for simplification of neural computation. We show that such a decentralized solution leads to adaptive behavior when facing uncertain environments which we demonstrate for a broad range of behaviors never dealt with in a single system by earlier approaches. This includes the ability to produce footfall patterns such as velocity dependent "tripod", "tetrapod", "pentapod" as well as various stable intermediate patterns as observed in stick insects and in Drosophila. These patterns are found to be stable against disturbances and when starting from various leg configurations. Our neuronal architecture easily allows for starting or interrupting a walk, all being difficult for CPG controlled solutions. Furthermore, negotiation of curves and walking on a treadmill with various treatments of individual legs is possible as well as backward walking and performing short steps. This approach can as well account for the neurophysiological results usually interpreted to support the idea that CPGs form the basis of walking, although our approach is not relying on explicit CPG-like structures. Application of CPGs may however be required for very fast walking. Our neuronal structure allows to pinpoint specific neurons known from various insect studies. Interestingly, specific common properties observed in both insects and crustaceans suggest a significance of our controller beyond the realm of insects.

Resource-efficient bio-inspired visual processing on the hexapod walking robot HECTOR

Emulating the highly resource-efficient processing of visual motion information in the brain of flying insects, a bio-inspired controller for collision avoidance and navigation was implemented on a novel, integrated System-on-Chip-based hardware module. The hardware module is used to control visually-guided navigation behavior of the stick insect-like hexapod robot HECTOR. By leveraging highly parallelized bio-inspired algorithms to extract nearness information from visual motion in dynamically reconfigurable logic, HECTOR is able to navigate to predefined goal positions without colliding with obstacles. The system drastically outperforms CPU- and graphics card-based implementations in terms of speed and resource efficiency, making it suitable to be also placed on fast moving robots, such as flying drones.

Flexible Coordination of Flexible Limbs: Decentralized Control Scheme for Inter- and Intra-Limb Coordination in Brittle Stars' Locomotion

Conventional mobile robots have difficulties adapting to unpredictable environments or performing adequately after undergoing physical damages in realtime operation, unlike animals. We address this issue by focusing on brittle stars, an echinoderm related to starfish. Most brittle stars have five flexible arms, and they can coordinate among the arms (i.e., inter-arm coordination) as well as the many bodily degrees of freedom within each arm (i.e., intra-arm coordination). They can move in unpredictable environments while promptly adapting to those, and to their own physical damages (e.g., arm amputation). Our previous work focused on the inter-arm coordination by studying trimmed-arm brittle stars. Herein, we extend our previous work and propose a decentralized control mechanism that enables coupling between the inter-arm and intra-arm coordination. We demonstrate via simulations and real-world experiments with a brittle star-like robot that the behavior of brittle stars when they are intact and undergoing shortening or amputation of arms can be replicated.

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.

High-speed locomotion in the Saharan silver ant, Cataglyphis bombycina

The diurnal thermophilic Saharan silver ant, Cataglyphis bombycina, is the fastest of the North African Cataglyphis desert ant species. These highly mobile ants endure the extreme temperatures of their sand dune environment with outstanding behavioural, physiological and morphological adaptations. Surprisingly, C. bombycina has comparatively shorter legs than its well-studied sister species Cataglyphis fortis from salt pan habitats. This holds despite the somewhat hotter surface temperatures and the more yielding sand substrate. Here, we report that C. bombycina employs a different strategy in reaching high running speeds, outperforming the fastest known runs of the longer-legged C. fortis ants. Video analysis across a broad range of locomotor speeds revealed several differences to C. fortis. Shorter leg lengths are compensated for by high stride frequencies, ranging beyond 40 Hz. This is mainly achieved by a combination of short stance phases (down to 7 ms) and fast leg swing movements (up to 1400 mm s−1). The legs of one tripod group exhibit almost perfect synchrony in the timings of their lift-offs and touch-downs, and good tripod coordination is present over the entire walking speed range (tripod coordination strength values around 0.8). This near synchrony in leg movement may facilitate locomotion across the yielding sand dune substrate.

Decentralized Control Mechanism for Determination of Moving Direction in Brittle Stars With Penta-Radially Symmetric Body

A brittle star, an echinoderm with penta-radially symmetric body, can make decisions about its moving direction and move adapting to various circumstances despite lacking a central nervous system and instead possessing a rather simple distributed nervous system. In this study, we aimed to elucidate the essential control mechanism underlying the determination of moving direction in brittle stars. Based on behavioral findings on brittle stars whose nervous systems were lesioned in various ways, we propose a phenomenological mathematical model. We demonstrate via simulations that the proposed model can well reproduce the behavioral findings. Our findings not only provide insights into the mechanism for the determination of moving direction in brittle stars, but also help understand the essential mechanism underlying autonomous behaviors of animals. Moreover, they will pave the way for developing fully autonomous robots that can make decisions by themselves and move adaptively under various circumstances.

Information-based centralization of locomotion in animals and robots

The centralization of locomotor control from weak and local coupling to strong and global is hard to assess outside of particular modeling frameworks. We developed an empirical, model-free measure of centralization that compares information between control signals and both global and local states. A second measure, co-information, quantifies the net redundancy in global and local control. We first validate that our measures predict centralization in simulations of phase-coupled oscillators. We then test how centralization changes with speed in freely running cockroaches. Surprisingly, across all speeds centralization is constant and muscle activity is more informative of the global kinematic state (the averages of all legs) than the local state of that muscle's leg. Finally we use a legged robot to show that mechanical coupling alone can change the centralization of legged locomotion. The results of these systems span a design space of centralization and co-information for biological and robotic systems.

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.

The Metastability of the Double-Tripod Gait in Locust Locomotion

Insect locomotion represents a fundamental example of neuronal oscillating circuits generating different motor patterns or gaits by controlling their phase coordination. Walking gaits are assumed to represent stable states of the system, often modeled as coupled oscillators. This view is challenged, however, by recent experimental observations, in which in vitro locust preparations consistently converged to synchronous rhythms (all legs oscillating as one), a locomotive pattern never seen in vivo. To reconcile this inconsistency, we developed a modeling framework to capture the trade-off between the two competing mechanisms: the endogenous neuronal circuitry, expressed in vitro, and the feedback mechanisms from sensory and descending inputs, active only in vivo. We show that the ubiquitously observed double-tripod walking gait emerges precisely from this balance. The outcome is a short-lived meta-stable double-tripod gait, which transitions and alternates with stable idling, thus recovering the observed intermittent bouts of locomotion, typical of many insects' locomotion behavior.

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Isolated in vitro locust preparations indicate that idling is a stable fictive gait

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This is in contrast to the dominant in vivo locomotive pattern (i.e., double tripod)

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Hence functional locomotion behavior is dependent on descending and sensory inputs

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The presented model generates intermittent double-tripod bouts as seen empirically

Transfer of Spatial Contact Information Among Limbs and the Notion of Peripersonal Space in Insects

Internal representation of far-range space in insects is well established, as it is necessary for navigation behavior. Although it is likely that insects also have an internal representation of near-range space, the behavioral evidence for the latter is much less evident. Here, we estimate the size and shape of the spatial equivalent of a near-range representation that is constituted by somatosensory sampling events. To do so, we use a large set of experimental whole-body motion capture data on unrestrained walking, climbing and searching behavior in stick insects of the species Carausius morosus to delineate ‘action volumes’ and ‘contact volumes’ for both antennae and all six legs. As these volumes are derived from recorded sampling events, they comprise a volume equivalent to a representation of coinciding somatosensory and motor activity. Accordingly, we define this volume as the peripersonal space of an insect. It is of immediate behavioral relevance, because it comprises all potential external object locations within the action range of the body. In a next step, we introduce the notion of an affordance space as that part of peripersonal space within which contact-induced spatial estimates lie within the action ranges of more than one limb. Because the action volumes of limbs overlap in this affordance space, spatial information from one limb can be used to control the movement of another limb. Thus, it gives rise to an affordance as known for contact-induced reaching movements and spatial coordination of footfall patterns in stick insects. Finally, we probe the computational properties of the experimentally derived affordance space for pairs of neighboring legs. This is done by use of artificial neural networks that map the posture of one leg into a target posture of another leg with identical foot position.

Static stability predicts the continuum of interleg coordination patterns in Drosophila

During walking, insects must coordinate the movements of their six legs for efficient locomotion. This interleg coordination is speed dependent: fast walking in insects is associated with tripod coordination patterns, whereas slow walking is associated with more variable, tetrapod-like patterns. To date, however, there has been no comprehensive explanation as to why these speed-dependent shifts in interleg coordination should occur in insects. Tripod coordination would be sufficient at low walking speeds. The fact that insects use a different interleg coordination pattern at lower speeds suggests that it is more optimal or advantageous at these speeds. Furthermore, previous studies focused on discrete tripod and tetrapod coordination patterns. Experimental data, however, suggest that changes observed in interleg coordination are part of a speed-dependent spectrum. Here, we explore these issues in relation to static stability as an important aspect for interleg coordination in Drosophila We created a model that uses basic experimentally measured parameters in fruit flies to find the interleg phase relationships that maximize stability for a given walking speed. The model predicted a continuum of interleg coordination patterns spanning the complete range of walking speeds as well as an anteriorly directed swing phase progression. Furthermore, for low walking speeds, the model predicted tetrapod-like patterns to be most stable, whereas at high walking speeds, tripod coordination emerged as most optimal. Finally, we validated the basic assumption of a continuum of interleg coordination patterns in a large set of experimental data from walking fruit flies and compared these data with the model-based predictions.

A load-based mechanism for inter-leg coordination in insects

Animals rely on an adaptive coordination of legs during walking. However, which specific mechanisms underlie coordination during natural locomotion remains largely unknown. One hypothesis is that legs can be coordinated mechanically based on a transfer of body load from one leg to another. To test this hypothesis, we simultaneously recorded leg kinematics, ground reaction forces and muscle activity in freely walking stick insects (Carausius morosus). Based on torque calculations, we show that load sensors (campaniform sensilla) at the proximal leg joints are well suited to encode the unloading of the leg in individual steps. The unloading coincides with a switch from stance to swing muscle activity, consistent with a load reflex promoting the stance-to-swing transition. Moreover, a mechanical simulation reveals that the unloading can be ascribed to the loading of a specific neighbouring leg, making it exploitable for inter-leg coordination. We propose that mechanically mediated load-based coordination is used across insects analogously to mammals.

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.

A Synthetic Nervous System Controls a Simulated Cockroach

The purpose of this work is to better understand how animals control locomotion. This knowledge can then be applied to neuromechanical design to produce more capable and adaptable robot locomotion. To test hypotheses about animal motor control, we model animals and their nervous systems with dynamical simulations, which we call synthetic nervous systems (SNS). However, one major challenge is picking parameter values that produce the intended dynamics. This paper presents a design process that solves this problem without the need for global optimization. We test this method by selecting parameter values for SimRoach2, a dynamical model of a cockroach. Each leg joint is actuated by an antagonistic pair of Hill muscles. A distributed SNS was designed based on pathways known to exist in insects, as well as hypothetical pathways that produced insect-like motion. Each joint’s controller was designed to function as a proportional-integral (PI) feedback loop and tuned with numerical optimization. Once tuned, SimRoach2 walks through a simulated environment, with several cockroach-like features. A model with such reliable low-level performance is necessary to investigate more sophisticated locomotion patterns in the future.