Decoding the mechanisms of gait generation in salamanders by combining neurobiology, modeling and robotics

Balancing central control and sensory feedback produces adaptable and robust locomotor patterns in a spiking, neuromechanical model of the salamander spinal cord

This study introduces a novel neuromechanical model employing a detailed spiking neural network to explore the role of axial proprioceptive sensory feedback, namely stretch feedback, in salamander locomotion. Unlike previous studies that often oversimplified the dynamics of the locomotor networks, our model includes detailed simulations of the classes of neurons that are considered responsible for generating movement patterns. The locomotor circuits, modeled as a spiking neural network of adaptive leaky integrate-and-fire neurons, are coupled to a three-dimensional mechanical model of a salamander with realistic physical parameters and simulated muscles. In open-loop simulations (i.e., without sensory feedback), the model replicates locomotor patterns observed in-vitro and in-vivo for swimming and trotting gaits. Additionally, a modular descending reticulospinal drive to the central pattern generation network allows to accurately control the activation, frequency and phase relationship of the different sections of the limb and axial circuits. In closed-loop swimming simulations (i.e. including axial stretch feedback), systematic evaluations reveal that intermediate values of feedback strength increase the tail beat frequency and reduce the intersegmental phase lag, contributing to a more coordinated, faster and energy-efficient locomotion. Interestingly, the result is conserved across different feedback topologies (ascending or descending, excitatory or inhibitory), suggesting that it may be an inherent property of axial proprioception. Moreover, intermediate feedback strengths expand the stability region of the network, enhancing its tolerance to a wider range of descending drives, internal parameters' modifications and noise levels. Conversely, high values of feedback strength lead to a loss of controllability of the network and a degradation of its locomotor performance. Overall, this study highlights the beneficial role of proprioception in generating, modulating and stabilizing locomotion patterns, provided that it does not excessively override centrally-generated locomotor rhythms. This work also underscores the critical role of detailed, biologically-realistic neural networks to improve our understanding of vertebrate locomotion.

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

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

Control of movement of underwater swimmers: Animals, simulated animates and swimming robots

The control of movement in living organisms represents a fundamental task that the brain has evolved to solve. One crucial aspect is how the nervous system organizes the transformation of sensory information into motor commands. These commands lead to muscle activation and subsequent animal movement, which can exhibit complex patterns. One example of such movement is locomotion, which involves the translation of the entire body through space. Central Pattern Generators (CPGs) are neuronal circuits that provide control signals for these movements. Compared to the intricate circuits found in the brain, CPGs can be simplified into networks of neurons that generate rhythmic activation, coordinating muscle movements. Since the 1990s, researchers have developed numerous models of locomotive circuits to simulate different types of animal movement, including walking, flying, and swimming. Initially, the primary goal of these studies was to construct biomimetic robots. However, it became apparent that simplified CPGs alone were not sufficient to replicate the diverse range of adaptive locomotive movements observed in living organisms. Factors such as sensory modulation, higher-level control, and cognitive components related to learning and memory needed to be considered. This necessitated the use of more complex, high-dimensional circuits, as well as novel materials and hardware, in both modeling and robotics. With advancements in high-power computing, artificial intelligence, big data processing, smart materials, and electronics, the possibility of designing a new generation of true bio-mimetic robots has emerged. These robots have the capability to imitate not only simple locomotion but also exhibit adaptive motor behavior and decision-making. This motivation serves as the foundation for the current review, which aims to analyze existing concepts and models of movement control systems. As an illustrative example, we focus on underwater movement and explore the fundamental biological concepts, as well as the mathematical and physical models that underlie locomotion and its various modulations.

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.

Learning plastic matching of robot dynamics in closed-loop central pattern generators

Animals achieve agile locomotion performance with reduced control effort and energy efficiency by leveraging compliance in their muscles and tendons. However, it is not known how biological locomotion controllers learn to leverage the intelligence embodied in their leg mechanics. Here we present a framework to match control patterns and mechanics based on the concept of short-term elasticity and long-term plasticity. Inspired by animals, we design a robot, Morti, with passive elastic legs. The quadruped robot Morti is controlled by a bioinspired closed-loop central pattern generator that is designed to elastically mitigate short-term perturbations using sparse contact feedback. By minimizing the amount of corrective feedback on the long term, Morti learns to match the controller to its mechanics and learns to walk within 1 h. By leveraging the advantages of its mechanics, Morti improves its energy efficiency by 42% without explicit minimization in the cost function.

Spontaneous Gait Transitions of Sprawling Quadruped Locomotion by Sensory-Driven Body-Limb Coordination Mechanisms

Deciphering how quadrupeds coordinate their legs and other body parts, such as the trunk, head, and tail (i.e., body–limb coordination), can provide informative insights to improve legged robot mobility. In this study, we focused on sprawling locomotion of the salamander and aimed to understand the body–limb coordination mechanisms through mathematical modeling and simulations. The salamander is an amphibian that moves on the ground by coordinating the four legs with lateral body bending. It uses standing and traveling waves of lateral bending that depend on the velocity and stepping gait. However, the body–limb coordination mechanisms responsible for this flexible gait transition remain elusive. This paper presents a central-pattern-generator-based model to reproduce spontaneous gait transitions, including changes in bending patterns. The proposed model implements four feedback rules (feedback from limb-to-limb, limb-to-body, body-to-limb, and body-to-body) without assuming any inter-oscillator coupling. The interplay of the feedback rules establishes a self-organized body–limb coordination that enables the reproduction of the speed-dependent gait transitions of salamanders, as well as various gait patterns observed in sprawling quadruped animals. This suggests that sensory feedback plays an essential role in flexible body–limb coordination during sprawling quadruped locomotion.

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.

Control for multifunctionality: bioinspired control based on feeding in Aplysia californica

Animals exhibit remarkable feats of behavioral flexibility and multifunctional control that remain challenging for robotic systems. The neural and morphological basis of multifunctionality in animals can provide a source of bioinspiration for robotic controllers. However, many existing approaches to modeling biological neural networks rely on computationally expensive models and tend to focus solely on the nervous system, often neglecting the biomechanics of the periphery. As a consequence, while these models are excellent tools for neuroscience, they fail to predict functional behavior in real time, which is a critical capability for robotic control. To meet the need for real-time multifunctional control, we have developed a hybrid Boolean model framework capable of modeling neural bursting activity and simple biomechanics at speeds faster than real time. Using this approach, we present a multifunctional model of Aplysia californica feeding that qualitatively reproduces three key feeding behaviors (biting, swallowing, and rejection), demonstrates behavioral switching in response to external sensory cues, and incorporates both known neural connectivity and a simple bioinspired mechanical model of the feeding apparatus. We demonstrate that the model can be used for formulating testable hypotheses and discuss the implications of this approach for robotic control and neuroscience.

Walking with Salamanders: From Molecules to Biorobotics

How do four-legged animals adapt their locomotion to the environment? How do central and peripheral mechanisms interact within the spinal cord to produce adaptive locomotion and how is locomotion recovered when spinal circuits are perturbed? Salamanders are the only tetrapods that regenerate voluntary locomotion after full spinal transection. Given their evolutionary position, they provide a unique opportunity to bridge discoveries made in fish and mammalian models. Genetic dissection of salamander neural circuits is becoming feasible with new methods for precise manipulation, elimination, and visualisation of cells. These approaches can be combined with classical tools in neuroscience and with modelling and a robotic environment. We propose that salamanders provide a blueprint of the function, evolution, and regeneration of tetrapod locomotor circuits.

Modeling of the neural mechanism underlying the terrestrial turning of the salamander

In order to explore the neural mechanism underlying salamander terrestrial turning, an improved biomechanical model is proposed by modifying the forelimb structure of the existing biomechanical model. Based on the proposed improved biomechanical model, a new spinal locomotor network model is constructed which contains the interneuron networks and motoneuron pool. Control methods are also developed for the new model which increase its transient response speed, control the initial swing order of the forelimbs, and generate different walking turning gait and turning on the spot (turning without moving forward). The simulation results show that the biomechanical model controlled by the new spinal locomotor network model can generate different walking turning and turning on the spot, and can control posture and the initial swing order of the forelimbs. Moreover, the transient response speed of the proposed model is very rapid. This paper thus provides a useful tool for exploring the operational mechanism of the spinal circuitry of the salamander. In addition, the research results presented here may inspire the construction of artificial spinal control networks for bionic robots.

A new model of the spinal locomotor networks of a salamander and its properties

A salamander is an ideal animal for studying the spinal locomotor network mechanism of vertebrates from an evolutionary perspective since it represents the transition from an aquatic to a terrestrial animal. However, little is known about the spinal locomotor network of a salamander. A spinal locomotor network model is a useful tool for exploring the working mechanism of the spinal networks of salamanders. A new spinal locomotor network model for a salamander is built for a three-dimensional (3D) biomechanical model of the salamander using a novel locomotion-controlled neural network model. Based on recent experimental data on the spinal circuitry and observational results of gaits of vertebrates, we assume that different interneuron sets recruited for mediating the frequency of spinal circuits are also related to the generation of different gaits. The spinal locomotor networks of salamanders are divided into low-frequency networks for walking and high-frequency networks for swimming. Additionally, a new topological structure between the body networks and limb networks is built, which only uses the body networks to coordinate the motion of limbs. There are no direct synaptic connections among limb networks. These techniques differ from existing salamander spinal locomotor network models. A simulation is performed and analyzed to validate the properties of the new spinal locomotor networks of salamanders. The simulation results show that the new spinal locomotor networks can generate a forward walking gait, a backward walking gait, a swimming gait, and a turning gait during swimming and walking. These gaits can be switched smoothly by changing external inputs from the brainstem. These properties are consistent with those of a real salamander. However, it is still difficult for the new spinal locomotor networks to generate highly efficient turning during walking, 3D swimming, nonrhythmic movements, and so on. New experimental data are required for further validation.

Development and Training of a Neural Controller for Hind Leg Walking in a Dog Robot

Animals dynamically adapt to varying terrain and small perturbations with remarkable ease. These adaptations arise from complex interactions between the environment and biomechanical and neural components of the animal's body and nervous system. Research into mammalian locomotion has resulted in several neural and neuro-mechanical models, some of which have been tested in simulation, but few “synthetic nervous systems” have been implemented in physical hardware models of animal systems. One reason is that the implementation into a physical system is not straightforward. For example, it is difficult to make robotic actuators and sensors that model those in the animal. Therefore, even if the sensorimotor circuits were known in great detail, those parameters would not be applicable and new parameter values must be found for the network in the robotic model of the animal. This manuscript demonstrates an automatic method for setting parameter values in a synthetic nervous system composed of non-spiking leaky integrator neuron models. This method works by first using a model of the system to determine required motor neuron activations to produce stable walking. Parameters in the neural system are then tuned systematically such that it produces similar activations to the desired pattern determined using expected sensory feedback. We demonstrate that the developed method successfully produces adaptive locomotion in the rear legs of a dog-like robot actuated by artificial muscles. Furthermore, the results support the validity of current models of mammalian locomotion. This research will serve as a basis for testing more complex locomotion controllers and for testing specific sensory pathways and biomechanical designs. Additionally, the developed method can be used to automatically adapt the neural controller for different mechanical designs such that it could be used to control different robotic systems.

Stable phase-shift despite quasi-rhythmic movements: a CPG-driven dynamic model of active tactile exploration in an insect

An essential component of autonomous and flexible behavior in animals is active exploration of the environment, allowing for perception-guided planning and control of actions. An important sensory system involved is active touch. Here, we introduce a general modeling framework of Central Pattern Generators (CPGs) for movement generation in active tactile exploration behavior. The CPG consists of two network levels: (i) phase-coupled Hopf oscillators for rhythm generation, and (ii) pattern formation networks for capturing the frequency and phase characteristics of individual joint oscillations. The model captured the natural, quasi-rhythmic joint kinematics as observed in coordinated antennal movements of walking stick insects. Moreover, it successfully produced tactile exploration behavior on a three-dimensional skeletal model of the insect antennal system with physically realistic parameters. The effect of proprioceptor ablations could be simulated by changing the amplitude and offset parameters of the joint oscillators, only. As in the animal, the movement of both antennal joints was coupled with a stable phase difference, despite the quasi-rhythmicity of the joint angle time courses. We found that the phase-lead of the distal scape-pedicel (SP) joint relative to the proximal head-scape (HS) joint was essential for producing the natural tactile exploration behavior and, thus, for tactile efficiency. For realistic movement patterns, the phase-lead could vary within a limited range of 10–30° only. Tests with artificial movement patterns strongly suggest that this phase sensitivity is not a matter of the frequency composition of the natural movement pattern. Based on our modeling results, we propose that a constant phase difference is coded into the CPG of the antennal motor system and that proprioceptors are acting locally to regulate the joint movement amplitude.

A biologically based neural system coordinates the joints and legs of a tetrapod

A biologically inspired neural control system has been developed that coordinates a tetrapod trotting gait in the sagittal plane. The developed neuromechanical system is used to explore properties of connections in inter-leg and intra-leg coordination. The neural controller is built with biologically based neurons and synapses, and connections are based on data from literature where available. It is applied to a planar biomechanical model of a rat with 14 joints, each actuated by a pair of antagonistic Hill muscle models. The controller generates tension in the muscles through activation of simulated motoneurons. The hind leg and inter-leg control networks are based on pathways discovered in cat research tuned to the kinematic motions of a rat. The foreleg network was developed by extrapolating analogous pathways from the hind legs. The formulated intra-leg and inter-leg networks properly coordinate the joints and produce motions similar to those of a walking rat. Changing the strength of a single inter-leg connection is sufficient to account for differences in phase timing in different trotting rats.

Flexibility of the axial central pattern generator network for locomotion in the salamander

In tetrapods, limb and axial movements are coordinated during locomotion. It is well established that inter- and intralimb coordination show considerable variations during ongoing locomotion. Much less is known about the flexibility of the axial musculoskeletal system during locomotion and the neural mechanisms involved. Here we examined this issue in the salamander Pleurodeles waltlii, which is capable of locomotion in both aquatic and terrestrial environments. Kinematics of the trunk and electromyograms from the mid-trunk epaxial myotomes were recorded during four locomotor behaviors in freely moving animals. A similar approach was used during rhythmic struggling movements since this would give some insight into the flexibility of the axial motor system. Our results show that each of the forms of locomotion and the struggling behavior is characterized by a distinct combination of mid-trunk motor patterns and cycle durations. Using in vitro electrophysiological recordings in isolated spinal cords, we observed that the spinal networks activated with bath-applied N-methyl-d-aspartate could generate these axial motor patterns. In these isolated spinal cord preparations, the limb motor nerve activities were coordinated with each mid-trunk motor pattern. Furthermore, isolated mid-trunk spinal cords and hemicords could generate the mid-trunk motor patterns. This indicates that each side of the cord comprises a network able to generate coordinated axial motor activity. The roles of descending and sensory inputs in the behavior-related changes in axial motor coordination are discussed.

Mechanisms of coordination in distributed neural circuits: encoding coordinating information

We describe synaptic connections through which information essential for encoding efference copies reaches two coordinating neurons in each of the microcircuits that controls limbs on abdominal segments of the crayfish, Pacifastacus leniusculus. In each microcircuit, these coordinating neurons fire bursts of spikes simultaneously with motor neurons. These bursts encode timing, duration, and strength of each motor burst. Using paired microelectrode recordings, we demonstrate that one class of nonspiking neurons in each microcircuit's pattern-generating kernel--IPS--directly inhibits the ASCE coordinating neuron that copies each burst in power-stroke (PS) motor neurons. This inhibitory synapse parallels IPS's inhibition of the same PS motor neurons. Using a disynaptic pathway to control its membrane potential, we demonstrate that a second type of nonspiking interneuron in the pattern-generating kernel--IRSh--inhibits the DSC coordinating neuron that copies each burst in return-stroke (RS) motor neurons. This inhibitory synapse parallels IRS's inhibition of the microcircuit's RS motor neurons. Experimental changes in the membrane potential of one IPS or one IRSh neuron simultaneously changed the strengths of motor bursts, durations, numbers of spikes, and spike frequency in the simultaneous ASCE and DSC bursts. ASCE and DSC coordinating neurons link the segmentally distributed microcircuits into a coordinated system that oscillates with the same period and with stable phase differences. The inhibitory synapses from different pattern-generating neurons that parallel their inhibition of different sets of motor neurons enable ASCE and DSC to encode details of each oscillation that are necessary for stable, adaptive synchronization of the system.

Mechanisms of coordination in distributed neural circuits: decoding and integration of coordinating information

We describe the synaptic connections through which information required to coordinate limb movements reaches the modular microcircuits that control individual limbs on different abdominal segments of the crayfish, Pacifastacus leniusculus. In each segmental ganglion, a local commissural interneuron, ComInt 1, integrates information about other limbs and transmits it to one microcircuit. Five types of nonspiking local interneurons are components of each microcircuit's pattern-generating kernel (Smarandache-Wellmann et al., 2013). We demonstrate here, using paired microelectrode recordings, that the pathway through which information reaches this kernel is an electrical synapse between ComInt 1 and one of these five types, an IRSh interneuron. Using single-electrode voltage clamp, we show that brief changes of ComInt 1's membrane potential affect the timing of its microcircuit's motor output. Changing ComInt 1's membrane potential also changes the phase, duration, and strengths of bursts of spikes in its microcircuit's motor neurons and corresponding changes in its efferent coordinating neurons that project to other ganglia. These effects on coordinating neurons cause changes in the phases of motor output from other microcircuits in those distant ganglia. ComInt 1s function as hub neurons in the intersegmental circuit that synchronizes distributed microcircuits. The synapse between each ComInt 1 and its microcircuit's IRSh neuron completes a five synapse pathway in which analog information is encoded as a digital signal by efference-copy neurons and decoded from digital to analog form by ComInt 1. The synaptic organization of this pathway provides a cellular explanation of this nervous system's key dynamic properties.

Modular functional organisation of the axial locomotor system in salamanders

Most investigations on tetrapod locomotion have been concerned with limb movements. However, there is compelling evidence that the axial musculoskeletal system contributes to important functions during locomotion. Adult salamanders offer a remarkable opportunity to examine these functions because these amphibians use axial undulations to propel themselves in both aquatic and terrestrial environments. In this article, we review the currently available biological data on axial functions during various locomotor modes in salamanders. We also present data showing the modular organisation of the neural networks that generate axial synergies during locomotion. The functional implication of this modular organisation is discussed.

Fictive rhythmic motor patterns produced by the tail spinal cord in salamanders

Most investigations into the role of the body axis in vertebrate locomotion have focused on the trunk, although in most tetrapods, the tail also plays an active role. In salamanders, the tail contributes to propulsion during swimming and to dynamic balance and maneuverability during terrestrial locomotion. The aim of the present study was to obtain information concerning the neural mechanisms that produce tail muscle contractions during locomotion in the salamander Pleurodeles waltlii. We recorded the ventral root activities in in vitro spinal cord preparations in which locomotor-like activity was induced via bath application of N-methyl-d-aspartate (20μM) and d-serine (10μM). Recordings showed that the tail spinal cord is capable of producing propagated waves of motor activity that alternate between the left and right sides. Lesion experiments further revealed that the tail rhythmogenic network is composed of a double chain of identical hemisegmental oscillators. Finally, using spinal cord preparations bathed in a chamber partitioned into two pools, we revealed efficient short-distance coupling between the trunk and tail networks. Together, our results demonstrate the existence of a pattern generator for rhythmic tail movements in the salamander and show that the global architecture of the tail network is similar to that previously proposed for the mid-trunk locomotor network in the salamander. Our findings further support the view that salamanders can control their trunk and tail independently during stepping movements. The relevance of our results in relation to the generation of tail muscle contractions in freely moving salamanders is discussed.

Anatomical and electrophysiological plasticity of locomotor networks following spinal transection in the salamander

Recovery of locomotor behavior following spinal cord injury can occur spontaneously in some vertebrates, such as fish, urodele amphibians, and certain reptiles. This review provides an overview of the current status of our knowledge on the anatomical and electrophysiological changes occurring within the spinal cord that lead to, or are associated with the re-expression of locomotion in spinally-transected salamanders. A better understanding of these processes will help to devise strategies for restoring locomotor function in mammals, including humans.