Scaling of sensorimotor delays in terrestrial mammals

Why animals can outrun robots

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

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 matches 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.

Persistent and responsive collective motion with adaptive time delay

It is beneficial for collective structures to simultaneously have high persistence to environmental noise and high responsivity to nontrivial external stimuli. However, without the ability to differentiate useful information from noise, there is always a tradeoff between persistence and responsivity within the collective structures. To address this, we propose adaptive time delay inspired by the adaptive behavior observed in the school of fish. This strategy is tested using particles powered by optothermal fields coupled with an optical feedback-control system. By applying the adaptive time delay with a proper threshold, we experimentally observe the responsivity of the collective structures enhanced by approximately 1.6 times without sacrificing persistence. Furthermore, we integrate adaptive time delay with long-distance transportation and obstacle-avoidance capabilities to prototype adaptive swarm microrobots. This research demonstrates the potential of adaptive time delay to address the persistence-responsivity tradeoff and lays the foundation for intelligent swarm micro/nanorobots operating in complex environments.

The spinal cord facilitates cerebellar upper limb motor learning and control; inputs from neuromusculoskeletal simulation

Complex interactions between brain regions and the spinal cord (SC) govern body motion, which is ultimately driven by muscle activation. Motor planning or learning are mainly conducted at higher brain regions, whilst the SC acts as a brain-muscle gateway and as a motor control centre providing fast reflexes and muscle activity regulation. Thus, higher brain areas need to cope with the SC as an inherent and evolutionary older part of the body dynamics. Here, we address the question of how SC dynamics affects motor learning within the cerebellum; in particular, does the SC facilitate cerebellar motor learning or constitute a biological constraint? We provide an exploratory framework by integrating biologically plausible cerebellar and SC computational models in a musculoskeletal upper limb control loop. The cerebellar model, equipped with the main form of cerebellar plasticity, provides motor adaptation; whilst the SC model implements stretch reflex and reciprocal inhibition between antagonist muscles. The resulting spino-cerebellar model is tested performing a set of upper limb motor tasks, including external perturbation studies. A cerebellar model, lacking the implemented SC model and directly controlling the simulated muscles, was also tested in the same. The performances of the spino-cerebellar and cerebellar models were then compared, thus allowing directly addressing the SC influence on cerebellar motor adaptation and learning, and on handling external motor perturbations. Performance was assessed in both joint and muscle space, and compared with kinematic and EMG recordings from healthy participants. The differences in cerebellar synaptic adaptation between both models were also studied. We conclude that the SC facilitates cerebellar motor learning; when the SC circuits are in the loop, faster convergence in motor learning is achieved with simpler cerebellar synaptic weight distributions. The SC is also found to improve robustness against external perturbations, by better reproducing and modulating muscle cocontraction patterns.

Behavioral Motor Performance

The human sensorimotor control system has exceptional abilities to perform skillful actions. We easily switch between strenuous tasks that involve brute force, such as lifting a heavy sewing machine, and delicate movements such as threading a needle in the same machine. Using a structure with different control architectures, the motor system is capable of updating its ability to perform through our daily interaction with the fluctuating environment. However, there are issues that make this a difficult computational problem for the brain to solve. The brain needs to control a nonlinear, nonstationary neuromuscular system, with redundant and occasionally undesired degrees of freedom, in an uncertain environment using a body in which information transmission is subject to delays and noise. To gain insight into the mechanisms of motor control, here we survey movement laws and invariances that shape our everyday motion. We then examine the major solutions to each of these problems in the three parts of the sensorimotor control system, sensing, planning, and acting. We focus on how the sensory system, the control architectures, and the structure and operation of the muscles serve as complementary mechanisms to overcome deviations and disturbances to motor behavior and give rise to skillful motor performance. We conclude with possible future research directions based on suggested links between the operation of the sensorimotor system across the movement stages. © 2024 American Physiological Society. Compr Physiol 14:5179-5224, 2024.

Visual feedback influences the consistency of the locomotor pattern in Asian elephants (Elephas maximus)

Elephants are atypical of most quadrupeds in that they maintain the same lateral sequence footfall pattern across all locomotor speeds. It has been speculated that the preservation of the footfall patterns is necessary to maintain a statically stable support polygon. This should be a particularly important constraint in large, relatively slow animals. This suggests that elephants must rely on available sensory feedback mechanisms to actively control their massive pillar-like limbs for proper foot placement and sequencing. How the nervous system of elephants integrates the available sensory information for a stable gait is unknown. Here we explored the role that visual feedback plays in the control of the locomotor pattern in Asian elephants. Four Asian elephants (Elephas maximus) walked with and without a blindfold as we measured their stride time intervals. Coefficient of variation was used to assess changes in the overall variability of the stride time intervals, while approximate entropy was used to measure the stride-to-stride consistency of the time intervals. We show that visual feedback plays a role in the stride-to-stride consistency of the locomotor pattern in Asian elephants. These results suggest that elephants use visual feedback to correct and maintain proper sequencing of the limbs during locomotion.

Mechanosensory Control of Locomotion in Animals and Robots: Moving Forward

While animals swim, crawl, walk, and fly with apparent ease, building robots capable of robust locomotion remains a significant challenge. In this review, we draw attention to mechanosensation-the sensing of mechanical forces generated within and outside the body-as a key sense that enables robust locomotion in animals. We discuss differences between mechanosensation in animals and current robots with respect to (1) the encoding properties and distribution of mechanosensors and (2) the integration and regulation of mechanosensory feedback. We argue that robotics would benefit greatly from a detailed understanding of these aspects in animals. To that end, we highlight promising experimental and engineering approaches to study mechanosensation, emphasizing the mutual benefits for biologists and engineers that emerge from moving forward together.

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.

Muscle force-length dynamics during walking over obstacles indicates delayed recovery and a shift towards more 'strut-like' function in birds with proprioceptive deficit

Recent studies of in vivo muscle function in guinea fowl revealed that distal leg muscles rapidly modulate force and work to stabilize running in uneven terrain. Previous studies focused on running only, and it remains unclear how muscular mechanisms for stability differ between walking and running. Here, we investigated in vivo function of the lateral gastrocnemius (LG) during walking over obstacles. We compared muscle function in birds with intact (iLG) versus self-reinnervated LG (rLG). Self-reinnervation results in proprioceptive feedback deficit due to loss of monosynaptic stretch reflex. We tested the hypothesis that proprioceptive deficit results in decreased modulation of EMG activity in response to obstacle contact, and a delayed obstacle recovery compared with that for iLG. We found that total myoelectric intensity (Etot) of iLG increased by 68% in obstacle strides (S 0) compared with level terrain, suggesting a substantial reflex-mediated response. In contrast, Etot of rLG increased by 31% in S 0 strides compared with level walking, but also increased by 43% in the first post-obstacle (S +1) stride. In iLG, muscle force and work differed significantly from level walking only in the S 0 stride, indicating a single-stride recovery. In rLG, force increased in S 0, S +1 and S +2 compared with level walking, indicating three-stride obstacle recovery. Interestingly, rLG showed little variation in work output and shortening velocity in obstacle terrain, indicating a shift towards near-isometric strut-like function. Reinnervated birds also adopted a more crouched posture across level and obstacle terrains compared with intact birds. These findings suggest gait-specific control mechanisms in walking and running.

Muscle preflex response to perturbations in locomotion: In vitro experiments and simulations with realistic boundary conditions

Neuromuscular control loops feature substantial communication delays, but mammals run robustly even in the most adverse conditions. In vivo experiments and computer simulation results suggest that muscles' preflex-an immediate mechanical response to a perturbation-could be the critical contributor. Muscle preflexes act within a few milliseconds, an order of magnitude faster than neural reflexes. Their short-lasting action makes mechanical preflexes hard to quantify in vivo. Muscle models, on the other hand, require further improvement of their prediction accuracy during the non-standard conditions of perturbed locomotion. Our study aims to quantify the mechanical work done by muscles during the preflex phase (preflex work) and test their mechanical force modulation. We performed in vitro experiments with biological muscle fibers under physiological boundary conditions, which we determined in computer simulations of perturbed hopping. Our findings show that muscles initially resist impacts with a stereotypical stiffness response-identified as short-range stiffness-regardless of the exact perturbation condition. We then observe a velocity adaptation to the force related to the amount of perturbation similar to a damping response. The main contributor to the preflex work modulation is not the change in force due to a change in fiber stretch velocity (fiber damping characteristics) but the change in magnitude of the stretch due to the leg dynamics in the perturbed conditions. Our results confirm previous findings that muscle stiffness is activity-dependent and show that also damping characteristics are activity-dependent. These results indicate that neural control could tune the preflex properties of muscles in expectation of ground conditions leading to previously inexplicable neuromuscular adaptation speeds.

Slack-based tunable damping leads to a trade-off between robustness and efficiency in legged locomotion

Animals run robustly in diverse terrain. This locomotion robustness is puzzling because axon conduction velocity is limited to a few tens of meters per second. If reflex loops deliver sensory information with significant delays, one would expect a destabilizing effect on sensorimotor control. Hence, an alternative explanation describes a hierarchical structure of low-level adaptive mechanics and high-level sensorimotor control to help mitigate the effects of transmission delays. Motivated by the concept of an adaptive mechanism triggering an immediate response, we developed a tunable physical damper system. Our mechanism combines a tendon with adjustable slackness connected to a physical damper. The slack damper allows adjustment of damping force, onset timing, effective stroke, and energy dissipation. We characterize the slack damper mechanism mounted to a legged robot controlled in open-loop mode. The robot hops vertically and planarly over varying terrains and perturbations. During forward hopping, slack-based damping improves faster perturbation recovery (up to 170%) at higher energetic cost (27%). The tunable slack mechanism auto-engages the damper during perturbations, leading to a perturbation-trigger damping, improving robustness at a minimum energetic cost. With the results from the slack damper mechanism, we propose a new functional interpretation of animals' redundant muscle tendons as tunable dampers.

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.

Ecomorphological patterns in trigeminal canal branching among sauropsids reveal sensory shift in suchians

The vertebrate trigeminal nerve is the primary mediator of somatosensory information from nerve endings across the face, extending nerve branches through bony canals in the face and mandibles, terminating in sensory receptors. Reptiles evolved several extreme forms of cranial somatosensation in which enhanced trigeminal tissues are present in species engaging in unique mechanosensory behaviors. However, morphology varies by clade and ecology among reptiles. Few lineages approach the extreme degree of tactile somatosensation possessed by crocodylians, the only remaining members of a clade that underwent an ecological transition from the terrestrial to semiaquatic habitat, also evolving a specialized trigeminal system. It remains to be understood how trigeminal osteological correlates inform how adaptations for enhanced cranial sensation evolved in crocodylians. Here we identify an increase in sensory abilities in Early Jurassic crocodylomorphs, preceding the transitions to a semiaquatic habitat. Through quantification of trigeminal neurovascular canal branching patterns in an extant phylogenetic bracket we quantify and identify morphologies associated with sensory behaviors in representative fossil taxa, we find stepwise progression of increasing neurovascular canal density, complexity, and distribution from the primitive archosaurian to the derived crocodilian condition. Model-based inferences of sensory ecologies tested on quantified morphologies of extant taxa with known sensory behaviors indicate a parallel increase in sensory abilities among pseudosuchians. These findings establish patterns of reptile trigeminal ecomorphology, revealing evolutionary patterns of somatosensory ecology.

Spontaneous vortex formation by microswimmers with retarded attractions

Collective states of inanimate particles self-assemble through physical interactions and thermal motion. Despite some phenomenological resemblance, including signatures of criticality, the autonomous dynamics that binds motile agents into flocks, herds, or swarms allows for much richer behavior. Low-dimensional models have hinted at the crucial role played in this respect by perceived information, decision-making, and feedback, implying that the corresponding interactions are inevitably retarded. Here we present experiments on spherical Brownian microswimmers with delayed self-propulsion toward a spatially fixed target. We observe a spontaneous symmetry breaking to a transiently chiral dynamical state and concomitant critical behavior that do not rely on many-particle cooperativity. By comparison with the stochastic delay differential equation of motion of a single swimmer, we pinpoint the delay-induced effective synchronization of the swimmers with their own past as the key mechanism. Increasing numbers of swimmers self-organize into layers with pro- and retrograde orbital motion, synchronized and stabilized by steric, phoretic, and hydrodynamic interactions. Our results demonstrate how even most simple retarded interactions can foster emergent complex adaptive behavior in small active-particle ensembles.

How axon and dendrite branching are guided by time, energy, and spatial constraints

Neurons are connected by complex branching processes-axons and dendrites-that process information for organisms to respond to their environment. Classifying neurons according to differences in structure or function is a fundamental part of neuroscience. Here, by constructing biophysical theory and testing against empirical measures of branching structure, we develop a general model that establishes a correspondence between neuron structure and function as mediated by principles such as time or power minimization for information processing as well as spatial constraints for forming connections. We test our predictions for radius scale factors against those extracted from neuronal images, measured for species that range from insects to whales, including data from light and electron microscopy studies. Notably, our findings reveal that the branching of axons and peripheral nervous system neurons is mainly determined by time minimization, while dendritic branching is determined by power minimization. Our model also predicts a quarter-power scaling relationship between conduction time delay and body size.

Rethinking statistical learning as a continuous dynamic stochastic process, from the motor systems perspective

The brain integrates streams of sensory input and builds accurate predictions, while arriving at stable percepts under disparate time scales. This stochastic process bears different unfolding dynamics for different people, yet statistical learning (SL) currently averages out, as noise, individual fluctuations in data streams registered from the brain as the person learns. We here adopt a new analytical approach that instead of averaging out fluctuations in continuous electroencephalographic (EEG)-based data streams, takes these gross data as the important signals. Our new approach reassesses how individuals dynamically learn predictive information in stable and unstable environments. We find neural correlates for two types of learners in a visuomotor task: narrow-variance learners, who retain explicit knowledge of the regularity embedded in the stimuli. They seem to use an error-correction strategy steadily present in both stable and unstable environments. This strategy can be captured by current optimization-based computational frameworks. In contrast, broad-variance learners emerge only in the unstable environment. Local analyses of the moment-by-moment fluctuations, naïve to the overall outcome, reveal an initial period of memoryless learning, well characterized by a continuous gamma process starting out exponentially distributed whereby all future events are equally probable, with high signal (mean) to noise (variance) ratio. The empirically derived continuous Gamma process smoothly converges to predictive Gaussian signatures comparable to those observed for the error-corrective mode that is captured by current optimization-driven computational models. We coin this initially seemingly purposeless stage exploratory. Globally, we examine a posteriori the fluctuations in distributions' shapes over the empirically estimated stochastic signatures. We then confirm that the exploratory mode of those learners, free of expectation, random and memoryless, but with high signal, precedes the acquisition of the error-correction mode boasting smooth transition from exponential to symmetric distributions' shapes. This early naïve phase of the learning process has been overlooked by current models driven by expected, predictive information and error-based learning. Our work demonstrates that (statistical) learning is a highly dynamic and stochastic process, unfolding at different time scales, and evolving distinct learning strategies on demand.

A Tunable, Simplified Model for Biological Latch Mediated Spring Actuated Systems

We develop a model of latch-mediated spring actuated (LaMSA) systems relevant to comparative biomechanics and bioinspired design. The model contains five components: two motors (muscles), a spring, a latch, and a load mass. One motor loads the spring to store elastic energy and the second motor subsequently removes the latch, which releases the spring and causes movement of the load mass. We develop freely available software to accompany the model, which provides an extensible framework for simulating LaMSA systems. Output from the simulation includes information from the loading and release phases of motion, which can be used to calculate kinematic performance metrics that are important for biomechanical function. In parallel, we simulate a comparable, directly actuated system that uses the same motor and mass combinations as the LaMSA simulations. By rapidly iterating through biologically relevant input parameters to the model, simulated kinematic performance differences between LaMSA and directly actuated systems can be used to explore the evolutionary dynamics of biological LaMSA systems and uncover design principles for bioinspired LaMSA systems. As proof of principle of this concept, we compare a LaMSA simulation to a directly actuated simulation that includes either a Hill-type force-velocity trade-off or muscle activation dynamics, or both. For the biologically-relevant range of parameters explored, we find that the muscle force-velocity trade-off and muscle activation have similar effects on directly actuated performance. Including both of these dynamic muscle properties increases the accelerated mass range where a LaMSA system outperforms a directly actuated one.

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.

Characterizing the performance of human leg external force control

Our legs act as our primary contact with the surrounding environment, generating external forces that enable agile motion. To be agile, the nervous system has to control both the magnitude of the force that the feet apply to the ground and the point of application of this force. The purpose of this study was to characterize the performance of the healthy human neuromechanical system in controlling the force-magnitude and position of an externally applied force. To accomplish this, we built an apparatus that immobilized participants but allowed them to exert variable but controlled external forces with a single leg onto a ground embedded force plate. We provided real-time visual feedback of either the leg force-magnitude or force-position that participants were exerting against the force platform and instructed participants to best match their real-time signal to prescribed target step functions. We tested target step functions of a range of sizes and quantified the responsiveness and accuracy of the control. For the control of force-magnitude and for intermediate step sizes of 0.45 bodyweights, we found a bandwidth of 1.8 ± 0.5 Hz, a steady-state error of 2.6 ± 0.9%, and a steady-state variability of 2.7 ± 0.9%. We found similar control performance in terms of responsiveness and accuracy across step sizes and between force-magnitude and position control. Increases in responsiveness correlated with reductions in other measures of control performance, such as a greater magnitude of overshooting. We modelled the observed control performance and found that a second-order model was a good predictor of external leg force control. We discuss how benchmarking force control performance in young healthy humans aids in understanding differences in agility between humans, between humans and other animals, and between humans and engineered systems.

Comparison of Threshold and Tolerance Nociceptive Withdrawal Reflexes in Horses

Simple Summary

Nociception is the physiological basis of the complex experience of pain. An established model for its quantification in equine studies is based on the nociceptive withdrawal reflex evoked by electrical stimulation of a sensory nerve. The reflex is recorded via electromyography and it is common to determine the threshold at which a nociceptive-specific reflex activity can be observed. In the present study, the classical methodology was expanded for a deeper understanding of the physiology of nociceptive reflexes in horses. First, for each individual horse, a threshold was determined as the minimal stimulation intensity able to evoke a nociceptive withdrawal reflex. Second, the stimulation intensity was stepwise increased up to tolerance, which was defined as the stimulus that is able to elicit the maximal tolerable behavioral reaction. The characteristics of the reflex activity on the electromyographic records were compared for threshold and tolerance stimulation intensities. At tolerance, the reflex became faster and wider than at threshold, indicating that either a spinal summation mechanism or the recruitment of faster sensory fibers occurs in response to high-intensity noxious stimuli. A novel endpoint (i.e., tolerance) can now be considered when applying the nociceptive withdrawal reflex model in equine studies.

Abstract

The nociceptive withdrawal reflex (NWR) is used to investigate nociception in horses. The NWR threshold is a classical model endpoint. The aims of this study were to determine NWR tolerance and to compare threshold and tolerance reflexes in horses. In 12 horses, the NWR was evoked through electrical stimulation of the digital nerve and recorded via electromyography from the deltoid. Behavioral reactions were scored from 0 to 5 (tolerance). First, the individual NWR threshold was defined, then stimulation intensity was increased to tolerance. The median NWR threshold was 7.0 mA, whereas NWR tolerance was 10.7 mA. Upon visual inspection of the records, two main reflex components R1 (median latency 44 ms) and R2 (median latency 81 ms) were identified at threshold. Increasing stimulation intensity to tolerance led to a significant increase in the amplitude and duration of R1 and R2, whereas their latency decreased. At tolerance, a single burst of early, high-amplitude reflex activity, with a median latency of 39 ms, was detected in 15 out of 23 stimulations (65%). The results of this study suggest that (1) it is feasible to determine NWR tolerance in horses and (2) high-intensity stimuli initiate ultrafast bursts of reflex activity, which is well known in practice and has now been quantified using the NWR model.

Postural control in the elephant

As the largest extant legged animals, elephants arguably face the most extreme challenge for stable standing. In this study, we investigated the displacement of the centre of pressure of 12 elephants during quiet standing. We found that the average amplitude of the oscillations in the lateral and fore-aft directions was less than 1.5 cm. Such amplitudes for postural oscillation are comparable with those of dogs and other species, suggesting that some aspects of sensorimotor postural control do not scale with size.

Stretch reflexes

Many of us know about stretch reflexes from the doctor's office, when a physician taps the tendon near our kneecap to elicit a quick knee extension. This procedure is used as a diagnostic tool to determine the integrity of the spinal cord and the extension response it elicits may seem otherwise useless. In fact, the tendon tap taps into one aspect of a critical building block of mammalian motor control, the stretch reflexes. Stretch reflexes are often thought to quickly resist unexpected changes in muscle length via a very simple circuit in the spinal cord, and this is one circuit that the tendon tap engages. It turns out, however, that stretch reflexes support a myriad of functions and are highly flexible. Under naturalistic conditions, stretch reflexes are shaped by peripheral physiology and engage neural circuits spanning the spinal cord, brainstem and cerebral cortex. In this Primer, we outline what is currently known about stretch reflex function and its underlying mechanisms, with a specific focus on how the cascade of nested responses collectively known as stretch reflexes interact with and build off of one another to support real-world motor behavior.

Hybrid Parallel Compliance Allows Robots to Operate With Sensorimotor Delays and Low Control Frequencies

Animals locomote robustly and agile, albeit significant sensorimotor delays of their nervous system and the harsh loading conditions resulting from repeated, high-frequent impacts. The engineered sensorimotor control in legged robots is implemented with high control frequencies, often in the kilohertz range. Consequently, robot sensors and actuators can be polled within a few milliseconds. However, especially at harsh impacts with unknown touch-down timing, controllers of legged robots can become unstable, while animals are seemingly not affected. We examine this discrepancy and suggest and implement a hybrid system consisting of a parallel compliant leg joint with varying amounts of passive stiffness and a virtual leg length controller. We present systematic experiments both in computer simulation and robot hardware. Our system shows previously unseen robustness, in the presence of sensorimotor delays up to 60 ms, or control frequencies as low as 20 Hz, for a drop landing task from 1.3 leg lengths high and with a compliance ratio (fraction of physical stiffness of the sum of virtual and physical stiffness) of 0.7. In computer simulations, we report successful drop-landings from 3.8 leg lengths (1.2 m) for a 2 kg quadruped robot with 100 Hz control frequency and a sensorimotor delay of 35 ms.

The evolutionary biomechanics of locomotor function in giant land animals

Giant land vertebrates have evolved more than 30 times, notably in dinosaurs and mammals. The evolutionary and biomechanical perspectives considered here unify data from extant and extinct species, assessing current theory regarding how the locomotor biomechanics of giants has evolved. In terrestrial tetrapods, isometric and allometric scaling patterns of bones are evident throughout evolutionary history, reflecting general trends and lineage-specific divergences as animals evolve giant size. Added to data on the scaling of other supportive tissues and neuromuscular control, these patterns illuminate how lineages of giant tetrapods each evolved into robust forms adapted to the constraints of gigantism, but with some morphological variation. Insights from scaling of the leverage of limbs and trends in maximal speed reinforce the idea that, beyond 100-300 kg of body mass, tetrapods reduce their locomotor abilities, and eventually may lose entire behaviours such as galloping or even running. Compared with prehistory, extant megafaunas are depauperate in diversity and morphological disparity; therefore, turning to the fossil record can tell us more about the evolutionary biomechanics of giant tetrapods. Interspecific variation and uncertainty about unknown aspects of form and function in living and extinct taxa still render it impossible to use first principles of theoretical biomechanics to tightly bound the limits of gigantism. Yet sauropod dinosaurs demonstrate that >50 tonne masses repeatedly evolved, with body plans quite different from those of mammalian giants. Considering the largest bipedal dinosaurs, and the disparity in locomotor function of modern megafauna, this shows that even in terrestrial giants there is flexibility allowing divergent locomotor specialisations.

Multimodal integration across spatiotemporal scales to guide invertebrate locomotion

Locomotion is a hallmark of organisms that has enabled adaptive radiation to an extraordinarily diverse class of ecological niches, and allows animals to move across vast distances. Sampling from multiple sensory modalities enables animals to acquire rich information to guide locomotion. Locomotion without sensory feedback is haphazard, therefore sensory and motor systems have evolved complex interactions to generate adaptive behavior. Notably, sensory-guided locomotion acts over broad spatial and temporal scales to permit goal-seeking behavior, whether to localize food by tracking an attractive odor plume or to search for a potential mate. How does the brain integrate multimodal stimuli over different temporal and spatial scales to effectively control behavior? In this review, we classify locomotion into three ordinally ranked hierarchical layers that act over distinct spatiotemporal scales: stabilization, motor primitives, and higher-order tasks, respectively. We discuss how these layers present unique challenges and opportunities for sensorimotor integration. We focus on recent advances in invertebrate locomotion due to their accessible neural and mechanical signals from the whole brain, limbs and sensors. Throughout, we emphasize neural-level description of computations for multimodal integration in genetic model systems, including the fruit fly, Drosophila melanogaster, and the yellow fever mosquito, Aedes aegypti. We identify that summation (e.g. gating) and weighting-which are inherent computations of spiking neurons-underlie multimodal integration across spatial and temporal scales, therefore suggesting collective strategies to guide locomotion.

Computational modelling of muscle fibre operating ranges in the hindlimb of a small ground bird (Eudromia elegans), with implications for modelling locomotion in extinct species

The arrangement and physiology of muscle fibres can strongly influence musculoskeletal function and whole-organismal performance. However, experimental investigation of muscle function during in vivo activity is typically limited to relatively few muscles in a given system. Computational models and simulations of the musculoskeletal system can partly overcome these limitations, by exploring the dynamics of muscles, tendons and other tissues in a robust and quantitative fashion. Here, a high-fidelity, 26-degree-of-freedom musculoskeletal model was developed of the hindlimb of a small ground bird, the elegant-crested tinamou (Eudromia elegans, ~550 g), including all the major muscles of the limb (36 actuators per leg). The model was integrated with biplanar fluoroscopy (XROMM) and forceplate data for walking and running, where dynamic optimization was used to estimate muscle excitations and fibre length changes throughout both gaits. Following this, a series of static simulations over the total range of physiological limb postures were performed, to circumscribe the bounds of possible variation in fibre length. During gait, fibre lengths for all muscles remained between 0.5 to 1.21 times optimal fibre length, but operated mostly on the ascending limb and plateau of the active force-length curve, a result that parallels previous experimental findings for birds, humans and other species. However, the ranges of fibre length varied considerably among individual muscles, especially when considered across the total possible range of joint excursion. Net length change of muscle-tendon units was mostly less than optimal fibre length, sometimes markedly so, suggesting that approaches that use muscle-tendon length change to estimate optimal fibre length in extinct species are likely underestimating this important parameter for many muscles. The results of this study clarify and broaden understanding of muscle function in extant animals, and can help refine approaches used to study extinct species.

Rhythmic auditory stimuli modulate movement recovery in response to perturbation during locomotion

The capacity to recover after a perturbation is a well-known intrinsic property of physiological systems, including the locomotor system, and can be termed ‘resilience’. Despite an abundance of metrics proposed to measure the complex dynamics of bipedal locomotion, analytical tools for quantifying resilience are lacking. Here, we introduce a novel method to directly quantify resilience to perturbations during locomotion. We examined the extent to which synchronizing stepping with two different temporal structured auditory stimuli (periodic and 1/f structure) during walking modulates resilience to a large unexpected perturbation. Recovery time after perturbation was calculated from the horizontal velocity of the body's center of mass. Our results indicate that synchronizing stepping with a 1/f stimulus elicited greater resilience to mechanical perturbations during walking compared with the periodic stimulus (3.3 s faster). Our proposed method may help to gain a comprehensive understanding of movement recovery behavior of humans and other animals in their ecological contexts.

Summary: A new method for the evaluation of intrinsic resilience during unsteady locomotion in humans and animals, analysing the relationship between the structure of movement variability and resilience.

How fast do mobile organisms respond to stimuli? Response times from bacteria to elephants and whales

Quick responses to fast changes in the environment are crucial in animal behaviour and survival, for example to seize prey, escape predators, or negotiate obstacles. Here, we study the 'simple response time' that is the time elapsed between receptor stimulation and motor activation as typically shown in escape responses, for mobile organisms of various taxa ranging from bacteria to large vertebrates. We show that 95% of these simple response times lie within one order of magnitude of the overall geometric mean of about 25 ms, which is similar to that of a well-studied sensory time scale, the inverse of the critical flicker fusion frequency in vision, also lying within close bounds for all the organisms studied. We find that this time scale is a few times smaller than the minimum time to move by one body length, which is known to lie also within a relatively narrow range for all moving organisms. The remarkably small 10²-fold range of the simple response time among so disparate life forms varying over 10²⁰-fold in body mass suggests that it is determined by basic physicochemical constraints, independently on the structure and scale of the organism. We thus propose first-principle estimates of the simple response and sensory time scales in terms of physical constants and a few basic biological properties common to mobile organisms and constraining their responses.

Dysmetria and Errors in Predictions: The Role of Internal Forward Model

The terminology of cerebellar dysmetria embraces a ubiquitous symptom in motor deficits, oculomotor symptoms, and cognitive/emotional symptoms occurring in cerebellar ataxias. Patients with episodic ataxia exhibit recurrent episodes of ataxia, including motor dysmetria. Despite the consensus that cerebellar dysmetria is a cardinal symptom, there is still no agreement on its pathophysiological mechanisms to date since its first clinical description by Babinski. We argue that impairment in the predictive computation for voluntary movements explains a range of characteristics accompanied by dysmetria. Within this framework, the cerebellum acquires and maintains an internal forward model, which predicts current and future states of the body by integrating an estimate of the previous state and a given efference copy of motor commands. Two of our recent studies experimentally support the internal-forward-model hypothesis of the cerebellar circuitry. First, the cerebellar outputs (firing rates of dentate nucleus cells) contain predictive information for the future cerebellar inputs (firing rates of mossy fibers). Second, a component of movement kinematics is predictive for target motions in control subjects. In cerebellar patients, the predictive component lags behind a target motion and is compensated with a feedback component. Furthermore, a clinical analysis has examined kinematic and electromyography (EMG) features using a task of elbow flexion goal-directed movements, which mimics the finger-to-nose test. Consistent with the hypothesis of the internal forward model, the predictive activations in the triceps muscles are impaired, and the impaired predictive activations result in hypermetria (overshoot). Dysmetria stems from deficits in the predictive computation of the internal forward model in the cerebellum. Errors in this fundamental mechanism result in undershoot (hypometria) and overshoot during voluntary motor actions. The predictive computation of the forward model affords error-based motor learning, coordination of multiple degrees of freedom, and adequate timing of muscle activities. Both the timing and synergy theory fit with the internal forward model, microzones being the elemental computational unit, and the anatomical organization of converging inputs to the Purkinje neurons providing them the unique property of a perceptron in the brain. We propose that motor dysmetria observed in attacks of ataxia occurs as a result of impaired predictive computation of the internal forward model in the cerebellum.

Effective Viscous Damping Enables Morphological Computation in Legged Locomotion

Muscle models and animal observations suggest that physical damping is beneficial for stabilization. Still, only a few implementations of physical damping exist in compliant robotic legged locomotion. It remains unclear how physical damping can be exploited for locomotion tasks, while its advantages as sensor-free, adaptive force- and negative work-producing actuators are promising. In a simplified numerical leg model, we studied the energy dissipation from viscous and Coulomb damping during vertical drops with ground-level perturbations. A parallel spring- damper is engaged between touch-down and mid-stance, and its damper auto-decouples from mid-stance to takeoff. Our simulations indicate that an adjustable and viscous damper is desired. In hardware we explored effective viscous damping and adjustability, and quantified the dissipated energy. We tested two mechanical, leg-mounted damping mechanisms: a commercial hydraulic damper, and a custom-made pneumatic damper. The pneumatic damper exploits a rolling diaphragm with an adjustable orifice, minimizing Coulomb damping effects while permitting adjustable resistance. Experimental results show that the leg-mounted, hydraulic damper exhibits the most effective viscous damping. Adjusting the orifice setting did not result in substantial changes of dissipated energy per drop, unlike adjusting the damping parameters in the numerical model. Consequently, we also emphasize the importance of characterizing physical dampers during real legged impacts to evaluate their effectiveness for compliant legged locomotion.

Tuning of feedforward control enables stable muscle force-length dynamics after loss of autogenic proprioceptive feedback

Animals must integrate feedforward, feedback and intrinsic mechanical control mechanisms to maintain stable locomotion. Recent studies of guinea fowl (Numida meleagris) revealed that the distal leg muscles rapidly modulate force and work output to minimize perturbations in uneven terrain. Here we probe the role of reflexes in the rapid perturbation responses of muscle by studying the effects of proprioceptive loss. We induced bilateral loss of autogenic proprioception in the lateral gastrocnemius muscle (LG) using self-reinnervation. We compared in vivo muscle dynamics and ankle kinematics in birds with reinnervated and intact LG. Reinnervated and intact LG exhibit similar steady state mechanical function and similar work modulation in response to obstacle encounters. Reinnervated LG exhibits 23ms earlier steady-state activation, consistent with feedforward tuning of activation phase to compensate for lost proprioception. Modulation of activity duration is impaired in rLG, confirming the role of reflex feedback in regulating force duration in intact muscle.

The Cerebro-Cerebellum as a Locus of Forward Model: A Review

This review surveys physiological, behavioral, and morphological evidence converging to the view of the cerebro-cerebellum as loci of internal forward models. The cerebro-cerebellum, the phylogenetically newest expansion in the cerebellum, receives convergent inputs from cortical, subcortical, and spinal sources, and is thought to perform the predictive computation for both motor control, motor learning, and cognitive functions. This predictive computation is known as an internal forward model. First, we elucidate the theoretical foundations of an internal forward model and its role in motor control and motor learning within the framework of the optimal feedback control model. Then, we discuss a neural mechanism that generates various patterns of outputs from the cerebro-cerebellum. Three lines of supporting evidence for the internal-forward-model hypothesis are presented in detail. First, we provide physiological evidence that the cerebellar outputs (activities of dentate nucleus cells) are predictive for the cerebellar inputs [activities of mossy fibers (MFs)]. Second, we provide behavioral evidence that a component of movement kinematics is predictive for target motion in control subjects but lags behind a target motion in patients with cerebellar ataxia. Third, we provide morphological evidence that the cerebellar cortex and the dentate nucleus receive separate MF projections, a prerequisite for optimal estimation. Finally, we speculate that the predictive computation in the cerebro-cerebellum could be deployed to not only motor control but also to non-motor, cognitive functions. This review concludes that the predictive computation of the internal forward model is the unifying algorithmic principle for understanding diverse functions played by the cerebro-cerebellum.

Head stabilization in small vertebrates that run at high frequencies with a sprawled posture

Small animals face a large challenge when running. A stable head is key to maintenance of a stable gaze and a good sense of self-motion and spatial awareness. However, trunk undulations caused by the cyclic limb movements result in involuntary head movements. Hence, the head needs to be stabilized. Humans are capable of stabilizing their head up to 2–3 Hz, but small animals run at cycle frequencies that are up to six times higher. We wondered how natural selection has adapted their head stabilization control. We observed that the relative contributions of vision, on the one hand, and vestibular perception and proprioception, on the other hand, remain the same when lizards undergo fast or slow body undulations in an experimental set-up. Lizards also maintain a short phase lag at both low and high undulation frequencies. Hence, we found no indication that they use a different control mechanism at high frequencies. Instead, head stabilization probably remains possible owing to faster reflex pathways and a lower head inertia. Hence, the intrinsic physical and neurological characteristics of lizards seem to be sufficient to enable head stabilization at high frequencies, obviating the need for evolutionary adaptation of the control pathways. These properties are not unique to lizards and might, therefore, also facilitate head stabilization at high frequencies in other small, fast animals.

Scaling of inertial delays in terrestrial mammals

As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose the corrective motion, delaying the completion of the movement-we refer to this elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker, and limb inertia is proportionally larger. Consequently, the scaling of inertial delays is complex. Our intent is to determine how quickly different sized animals can produce corrective movements when their muscles act at their force capacity, relative to the time within which those movements need to be performed. Here, we quantify inertial delay using two biomechanical models representing common scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). We parameterized the anatomical, muscular, and inertial properties of these models using literature scaling relationships, then determined inertial delay for each task across a large range of movement magnitudes and the full range of terrestrial mammal sizes. We found that inertial delays scaled with an average of M0.28 in the swing task and M0.35 in the posture task across movement magnitudes-larger animals require more absolute time to perform the same movement as small animals. The time available to complete a movement also increases with animal size, but less steeply. Consequently, inertial delays comprise a greater fraction of swing duration and other characteristic movement times in larger animals. We also compared inertial delays to the other component delays within the stimulus-response pathway. As movement magnitude increased, inertial delays exceeded these sensorimotor delays, and this occurred for smaller movements in larger animals. Inertial delays appear to be a challenge for motor control, particularly for bigger movements in larger animals.

History-dependent perturbation response in limb muscle

Muscle mediates movement but movement is typically unsteady and perturbed. Muscle is known to behave non-linearly and with history-dependent properties during steady locomotion, but the importance of history dependence in mediating muscle function during perturbations remains less clear. To explore the capacity of muscles to mitigate perturbations during locomotion, we constructed a series of perturbations that varied only in kinematic history, keeping instantaneous position, velocity and time from stimulation constant. We found that the response of muscle to a perturbation is profoundly history dependent, varying 4-fold as baseline frequency changes, and dissipating energy equivalent to ∼6 times the kinetic energy of all the limbs in 5 ms (nearly 2400 W kg^-1). Muscle energy dissipation during a perturbation is predicted primarily by the force at the onset of the perturbation. This relationship holds across different frequencies and timings of stimulation. This history dependence behaves like a viscoelastic memory producing perturbation responses that vary with the frequency of the underlying movement.

Cortical pattern generation during dexterous movement is input-driven

Motor cortex controls skilled arm movement by sending temporal patterns of activity to lower motor centers¹. Local cortical dynamics are thought to shape these patterns throughout movement execution^2–4. External inputs have been implicated in setting the initial state of motor cortex^5,6, but they may also have a pattern-generating role. Here, we dissect the contribution of local dynamics and inputs to cortical pattern generation during a prehension task in mice. Perturbing cortex to an aberrant state prevented movement initiation, but after the perturbation was released, cortex either bypassed the normal initial state and immediately generated the pattern that controls reaching, or it failed to generate this pattern. The difference in these two outcomes was likely due to external inputs. We directly investigated the role of inputs by inactivating thalamus; this perturbed cortical activity and disrupted limb kinematics at any stage of the movement. Activation of thalamocortical axon terminals at different frequencies disrupted cortical activity and arm movement in a graded manner. Simultaneous recordings revealed that both thalamic activity and the current state of cortex predicted changes in cortical activity. Thus, the pattern generator for dexterous arm movement is distributed across multiple, strongly-interacting brain regions.

Some Challenges of Playing with Power: Does Complex Energy Flow Constrain Neuromuscular Performance?

Many studies of the flow of energy between the body, muscles, and elastic elements highlight advantages of the storage and recovery of elastic energy. The spring-like action of structures associated with muscles allows for movements that are less costly, more powerful and safer than would be possible with contractile elements alone. But these actions also present challenges that might not be present if the pattern of energy flow were simpler, for example, if power were always applied directly from muscle to motions of the body. Muscle is under the direct control of the nervous system, and precise modulation of activity can allow for finely controlled displacement and force. Elastic structures deform under load in a predictable way, but are not under direct control, thus both displacement and the flow of energy act at the mercy of the mechanical interaction of muscle and forces associated with movement. Studies on isolated muscle-tendon units highlight the challenges of controlling such systems. A carefully tuned activation pattern is necessary for effective cycling of energy between tendon and the environment; most activation patterns lead to futile cycling of energy between tendon and muscle. In power-amplified systems, "elastic backfire" sometimes occurs, where energy loaded into tendon acts to lengthen active muscles, rather than accelerate the body. Classic models of proprioception that rely on muscle spindle organs for sensing muscle and joint displacement illustrate how elastic structures might influence sensory feedback by decoupling joint movement from muscle fiber displacements. The significance of the complex flow of energy between muscles, elastic elements and the body for neuromotor control is worth exploring.

Translational methods to detect asymmetries in temporal and spatial walking metrics in parkinsonian mouse models and human subjects with Parkinson's disease

Clinical signs in Parkinson's disease (PD), including parkinsonian gait, are often asymmetric, but mechanisms underlying gait asymmetries in PD remain poorly understood. A translational toolkit, a set of standardized measures to capture gait asymmetries in relevant mouse models and patients, would greatly facilitate research efforts. We validated approaches to quantify asymmetries in placement and timing of limbs in mouse models of parkinsonism and human PD subjects at speeds that are relevant for human walking. In mice, we applied regression analysis to compare left and right gait metrics within a condition. To compare alternation ratios of left and right limbs before and after induction of parkinsonism, we used circular statistics. Both approaches revealed asymmetries in hind- and forelimb step length in a unilateral PD model, but not in bilateral or control models. In human subjects, a similar regression approach showed a step length asymmetry in the PD but not control group. Sub-analysis of cohorts with predominant postural instability-gait impairment and with predominant tremor revealed asymmetries for step length in both cohorts and for swing time only in the former cohort. This translational approach captures asymmetries of gait in mice and patients. Application revealed striking differences between models, and that spatial and temporal asymmetries may occur independently. This approach will be useful to investigate circuit mechanisms underlying the heterogeneity between models.