Reverse-engineering the locomotion of a stem amniote.

Reconstructing the locomotion of extinct vertebrates offers insights into their palaeobiology and helps to conceptualize major transitions in vertebrate evolution1-4. However, estimating the locomotor behaviour of a fossil species remains a challenge because of the limited information preserved and the lack of a direct correspondence between form and function5,6. The evolution of advanced locomotion on land-that is, locomotion that is more erect, balanced and mechanically power-saving than is assumed of anamniote early tetrapods-has previously been linked to the terrestrialization and diversification of amniote lineages7. To our knowledge, no reconstructions of the locomotor characteristics of stem amniotes based on multiple quantitative methods have previously been attempted: previous methods have relied on anatomical features alone, ambiguous locomotor information preserved in ichnofossils or unspecific modelling of locomotor dynamics. Here we quantitatively examine plausible gaits of the stem amniote Orobates pabsti, a species that is known from a complete body fossil preserved in association with trackways8. We reconstruct likely gaits that match the footprints, and investigate whether Orobates exhibited locomotor characteristics that have previously been linked to the diversification of crown amniotes. Our integrative methodology uses constraints derived from biomechanically relevant metrics, which also apply to extant tetrapods. The framework uses in vivo assessment of locomotor mechanics in four extant species to guide an anatomically informed kinematic simulation of Orobates, as well as dynamic simulations and robotics to filter the parameter space for plausible gaits. The approach was validated using two extant species that have different morphologies, gaits and footprints. Our metrics indicate that Orobates exhibited more advanced locomotion than has previously been assumed for earlier tetrapods7,9, which suggests that advanced terrestrial locomotion preceded the diversification of crown amniotes. We provide an accompanying website for the exploration of the filters that constrain our simulations, which will allow revision of our approach using new data, assumptions or methods.

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.

Horse-like walking, trotting, and galloping derived from kinematic Motion Primitives (kMPs) and their application to walk/trot transitions in a compliant quadruped robot.

This manuscript proposes a method to directly transfer the features of horse walking, trotting, and galloping to a quadruped robot, with the aim of creating a much more natural (horse-like) locomotion profile. A principal component analysis on horse joint trajectories shows that walk, trot, and gallop can be described by a set of four kinematic Motion Primitives (kMPs). These kMPs are used to generate valid, stable gaits that are tested on a compliant quadruped robot. Tests on the effects of gait frequency scaling as follows: results indicate a speed optimal walking frequency around 3.4 Hz, and an optimal trotting frequency around 4 Hz. Following, a criterion to synthesize gait transitions is proposed, and the walk/trot transitions are successfully tested on the robot. The performance of the robot when the transitions are scaled in frequency is evaluated by means of roll and pitch angle phase plots.

Animal robots in the African wilderness: Lessons learned and outlook for field robotics.

In early 2016, we had the opportunity to test a pair of sprawling posture robots, one designed to mimic a crocodile and another designed to mimic a monitor lizard, along the banks of the Nile River in Uganda, Africa. These robots were developed uniquely for a documentary by the BBC called Spy in the Wild and fell at the intersection of our interests in developing robots to study animals and robots for disaster response and other missions in challenging environments. The documentary required that these robots not only walk and swim in the same harsh, natural environments as the animals that they were modeled on and film up close but also move and even look exactly like the real animals from an aesthetic perspective. This pushed us to take a fundamentally different approach to the design and building of biorobots compared with our typical laboratory-residing robots, in addition to collaborating with sculpting artists to enhance our robots' aesthetics. The robots needed to be designed on the basis of a systematic study of data on the model specimens, be fabricated rapidly, and be reliable and robust enough to handle what the wild would throw at them. Here, we share the research efforts of this collaboration, the design specifications of the robots' hardware and software, the lessons learned from testing these robots in the field first hand, and how the eye-opening experience shaped our subsequent work on disaster response robotics and biorobotics for challenging amphibious scenarios.

Identification of the trade-off between speed and efficiency in undulatory swimming using a bio-inspired robot.

Anguilliform swimmers, like eels or lampreys, are highly efficient swimmers. Key to understanding their performances is the relationship between the body's kinematics and resulting swimming speed and efficiency. But, we cannot prescribe kinematics to living fish, and it is challenging to measure their power consumption. Here, we characterise the swimming speed and cost of transport of a free-swimming undulatory bio-inspired robot as we vary its kinematic parameters, including joint amplitude, body wavelength, and frequency. We identify a trade-off between speed and efficiency. Speed, in terms of stride length, increases for increasing maximum tail angle, described by the newly proposed specific tail amplitude and reaches a maximum value around the specific tail amplitude of unity. Efficiency, in terms of the cost of transport, is affected by the whole-body motion. Cost of transport decreases for increasing travelling wave-like kinematics, and lower specific tail amplitudes. Our results suggest that live eels tend to choose efficiency over speed and provide insights into the key characteristics affecting undulatory swimming performance.

The role of feedback in morphological computation with compliant bodies.

The generation of robust periodic movements of complex nonlinear robotic systems is inherently difficult, especially, if parts of the robots are compliant. It has previously been proposed that complex nonlinear features of a robot, similarly as in biological organisms, might possibly facilitate its control. This bold hypothesis, commonly referred to as morphological computation, has recently received some theoretical support by Hauser et al. (Biol Cybern 105:355-370, doi: 10.1007/s00422-012-0471-0 , 2012). We show in this article that this theoretical support can be extended to cover not only the case of fading memory responses to external signals, but also the essential case of autonomous generation of adaptive periodic patterns, as, e.g., needed for locomotion. The theory predicts that feedback into the morphological computing system is necessary and sufficient for such tasks, for which a fading memory is insufficient. We demonstrate the viability of this theoretical analysis through computer simulations of complex nonlinear mass-spring systems that are trained to generate a large diversity of periodic movements by adapting the weights of a simple linear feedback device. Hence, the results of this article substantially enlarge the theoretically tractable application domain of morphological computation in robotics, and also provide new paradigms for understanding control principles of biological organisms.

Biologically inspired kinematic synergies enable linear balance control of a humanoid robot.

Despite many efforts, balance control of humanoid robots in the presence of unforeseen external or internal forces has remained an unsolved problem. The difficulty of this problem is a consequence of the high dimensionality of the action space of a humanoid robot, due to its large number of degrees of freedom (joints), and of non-linearities in its kinematic chains. Biped biological organisms face similar difficulties, but have nevertheless solved this problem. Experimental data reveal that many biological organisms reduce the high dimensionality of their action space by generating movements through linear superposition of a rather small number of stereotypical combinations of simultaneous movements of many joints, to which we refer as kinematic synergies in this paper. We show that by constructing two suitable non-linear kinematic synergies for the lower part of the body of a humanoid robot, balance control can in fact be reduced to a linear control problem, at least in the case of relatively slow movements. We demonstrate for a variety of tasks that the humanoid robot HOAP-2 acquires through this approach the capability to balance dynamically against unforeseen disturbances that may arise from external forces or from manipulating unknown loads.

Towards a theoretical foundation for morphological computation with compliant bodies.

The control of compliant robots is, due to their often nonlinear and complex dynamics, inherently difficult.The vision of morphological computation proposes to view these aspects not only as problems, but rather also as parts of the solution. Non-rigid body parts are not seen anymore as imperfect realizations of rigid body parts, but rather as potential computational resources. The applicability of this vision has already been demonstrated for a variety of complex robot control problems. Nevertheless, a theoretical basis for understanding the capabilities and limitations of morphological computation has been missing so far. We present a model for morphological computation with compliant bodies, where a precise mathematical characterization oft he potential computational contribution of a complex physical body is feasible. The theory suggests that complexity and nonlinearity, typically unwanted properties of robots, are desired features in order to provide computational power. We demonstrate that simple generic models of physical bodies,based on mass-spring systems, can be used to implement complex nonlinear operators. By adding a simple readout(which is static and linear) to the morphology, such devices are able to emulate complex mappings of input to output streams in continuous time. Hence, by outsourcing parts of the computation to the physical body, the difficult problem of learning to control a complex body, could be reduced to a simple and perspicuous learning task, which can not get stuck in local minima of an error 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.

Emergence of robust self-organized undulatory swimming based on local hydrodynamic force sensing.

Undulatory swimming represents an ideal behavior to investigate locomotion control and the role of the underlying central and peripheral components in the spinal cord. Many vertebrate swimmers have central pattern generators and local pressure-sensitive receptors that provide information about the surrounding fluid. However, it remains difficult to study experimentally how these sensors influence motor commands in these animals. Here, using a specifically designed robot that captures the essential components of the animal neuromechanical system and using simulations, we tested the hypothesis that sensed hydrodynamic pressure forces can entrain body actuation through local feedback loops. We found evidence that this peripheral mechanism leads to self-organized undulatory swimming by providing intersegmental coordination and body oscillations. Swimming can be redundantly induced by central mechanisms, and we show that, therefore, a combination of both central and peripheral mechanisms offers a higher robustness against neural disruptions than any of them alone, which potentially explains how some vertebrates retain locomotor capabilities after spinal cord lesions. These results broaden our understanding of animal locomotion and expand our knowledge for the design of robust and modular robots that physically interact with the environment.

Exploring the Contribution of Proprioceptive Reflexes to Balance Control in Perturbed Standing.

Humans control balance using different feedback loops involving the vestibular system, the visual system, and proprioception. In this article, we focus on proprioception and explore the contribution of reflexes based on force and length feedback to standing balance. In particular, we address the questions of how much proprioception alone could explain balance control, and whether one modality, force or length feedback, is more important than the other. A sagittal plane neuro-musculoskeletal model was developed with six degrees of freedom and nine muscles in each leg. A controller was designed using proprioceptive reflexes and a dead zone. No feedback control was applied inside the dead zone. Reflexes were active once the center of mass moved outside the dead zone. Controller parameters were found by solving an optimization problem, where effort was minimized while the neuro-musculoskeletal model should remain standing upright on a perturbed platform. The ground was perturbed with random square pulses in the sagittal plane with different amplitudes and durations. The optimization was solved for three controllers: using force and length feedback (base model), using only force feedback, and using only length feedback. Simulations were compared to human data from previous work, where an experiment with the same perturbation signal was performed. The optimized controller yielded a similar posture, since average joint angles were within 5 degrees of the experimental average joint angles. The joint angles of the base model, the length only model, and the force only model correlated weakly (ankle) to moderately with the experimental joint angles. The ankle moment correlated weakly to moderately with the experimental ankle moment, while the hip and knee moment were only weakly correlated, or not at all. The time series of the joint angles showed that the length feedback model was better able to explain the experimental joint angles than the force feedback model. Changes in time delay affected the correlation of the joint angles and joint moments. The objective of effort minimization yielded lower joint moments than in the experiment, suggesting that other objectives are also important in balance control, which cause an increase in effort and thus larger joint moments.

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.

Reproducing Five Motor Behaviors in a Salamander Robot With Virtual Muscles and a Distributed CPG Controller Regulated by Drive Signals and Proprioceptive Feedback.

Diverse locomotor behaviors emerge from the interactions between the spinal central pattern generator (CPG), descending brain signals and sensory feedback. Salamander motor behaviors include swimming, struggling, forward underwater stepping, and forward and backward terrestrial stepping. Electromyographic and kinematic recordings of the trunk show that each of these five behaviors is characterized by specific patterns of muscle activation and body curvature. Electrophysiological recordings in isolated spinal cords show even more diverse patterns of activity. Using numerical modeling and robotics, we explored the mechanisms through which descending brain signals and proprioceptive feedback could take advantage of the flexibility of the spinal CPG to generate different motor patterns. Adapting a previous CPG model based on abstract oscillators, we propose a model that reproduces the features of spinal cord recordings: the diversity of motor patterns, the correlation between phase lags and cycle frequencies, and the spontaneous switches between slow and fast rhythms. The five salamander behaviors were reproduced by connecting the CPG model to a mechanical simulation of the salamander with virtual muscles and local proprioceptive feedback. The main results were validated on a robot. A distributed controller was used to obtain the fast control loops necessary for implementing the virtual muscles. The distributed control is demonstrated in an experiment where the robot splits into multiple functional parts. The five salamander behaviors were emulated by regulating the CPG with two descending drives. Reproducing the kinematics of backward stepping and struggling however required stronger muscle contractions. The passive oscillations observed in the salamander's tail during forward underwater stepping could be reproduced using a third descending drive of zero to the tail oscillators. This reduced the drag on the body in our hydrodynamic simulation. We explored the effect of local proprioceptive feedback during swimming and forward terrestrial stepping. We found that feedback could replace or reduce the need for different drives in both cases. It also reduced the variability of intersegmental phase lags toward values appropriate for locomotion. Our work suggests that different motor behaviors do not require different CPG circuits: a single circuit can produce various behaviors when modulated by descending drive and sensory feedback.

Design and development of the efficient anguilliform swimming robot- MAR.

Propulsion of swimming robots at the surface and underwater is largely dominated by rotary propellers due to high thrust, but at the cost of low efficiency. Due to their inherently high speed turning motion, sharp propeller blades and generated noise, they also present a disturbance to maritime ecosystems. Our work presents a bio-inspired approach to efficient and eco-friendly swimming with moderate to high thrust. This paper describes the concept, development and experimental validation of the novel anguilliform robot MAR. With 15 elements making up the 0.5 m long propulsive section and driven by a single, speed-controlled brushless DC motor (BLDC), the robot creates a smooth continuous traveling wave for propulsion. Steering and autonomy are realized by an actuated head with integrated batteries that serves as a front-rudder. Almost neutral buoyancy paired with individually actuated pectoral fins furthermore enable submerged swimming and diving maneuvers. MAR accomplished high thrusts at a moderate power consumption in first performance tests. The achieved maximum velocity and the speed related efficiency (defined as the achieved speed over the power consumption m Ws-1) did not fulfill the expectations in the first tests (in comparison to commercial rotary thrusters), which can be largely attributed to the spatial limitations and an imperfect test setup. Nevertheless, the potential towards highly efficient and high thrust propulsion is visible and will be further investigated in future efforts.

Decentralized control with cross-coupled sensory feedback between body and limbs in sprawling locomotion.

Quadrupeds achieve rapid and highly adaptive locomotion owing to the coordination between their legs and other body parts such as their trunk, head, and tail, i.e. body-limb coordination. Therefore, a better understanding of the mechanism underlying body-limb coordination could provide informative insights into the improvement of legged robot mobility. Sprawling locomotion is a walking gait with lateral bending exhibited in primitive legged vertebrates such as salamanders and newts. Because primitive animals are anticipated to possess the essence of quadruped motor control, their locomotion helps better understand body-limb coordination mechanisms. Previous studies modeled neural networks in salamanders and employed it to control robots and investigate and emulate sprawling locomotion. However, these models predefined the relationship between the legs and the trunk, such that how body-limb coordination is attained is largely unknown. In this article, we demonstrate that sensory feedback facilitates body-limb coordination in sprawling locomotion and improves mobility through mathematical modeling and robot simulations. Our proposed model has cross-coupled sensory feedback, that is, bidirectional feedback from body to limb and limb to body, which leads to an appropriate relationship between the legs and the trunk without any predefined relationship. Resulting gaits are similar to the sprawling locomotion of salamanders and achieve high speed and energy efficiency that are at the same level as those of a neural network model, such as conventional models, optimizing the relationship between the legs and the trunk. Furthermore, sensory feedback contributes to the adaptability toward leg failure, and the bidirectionality of feedback facilitates parameter tuning for stable locomotion. These results suggest that cross-coupled sensory feedback facilitates sprawling locomotion and potentially plays an important role in the body-limb coordination mechanism.

Decoding the essential interplay between central and peripheral control in adaptive locomotion of amphibious centipedes.

Amphibious animals adapt their body coordination to compensate for changing substrate properties as they transition between terrestrial and aquatic environments. Using behavioural experiments and mathematical modelling of the amphibious centipede Scolopendra subspinipes mutilans, we reveal an interplay between descending command (brain), local pattern generation, and sensory feedback that controls the leg and body motion during swimming and walking. The elongated and segmented centipede body exhibits a gradual transition in the locomotor patterns as the animal crosses between land and water. Changing environmental conditions elicit a mechano-sensory feedback mechanism, inducing a gait change at the local segment level. The body segments operating downstream of a severed nerve cord (no descending control) can generate walking with mechano-sensory inputs alone while swimming behaviour is not recovered. Integrating the descending control for swimming initiation with the sensory feedback control for walking in a mathematical model successfully generates the adaptive behaviour of centipede locomotion, capturing the possible mechanism for flexible motor control in animals.

Haptic Feedback Perception and Learning With Cable-Driven Guidance in Exosuit Teleoperation of a Simulated Drone.

Robotics teleoperation enables human operators to control the movements of distally located robots. The development of new wearable interfaces as alternatives to hand-held controllers has created new modalities of control, which are more intuitive to use. Nevertheless, such interfaces also require a period of adjustment before operators can carry out their tasks proficiently. In several fields of human-machine interaction, haptic guidance has proven to be an effective training tool for enhancing user performance. This paper presents the results of psychophysical and motor learning studies that were carried out with human participant to assess the effect of cable-driven haptic guidance for a task involving aerial robotic teleoperation. The guidance system was integrated into an exosuit, called the Flyjacket, that was developed to control drones with torso movements. Results for the just noticeable difference and from the Stevens Power Law suggest that the perception of force on the users' torso scales linearly with the amplitude of the force exerted through the cables and the perceived force is close to the magnitude of the stimulus. Motor learning studies reveal that this form of haptic guidance improves user performance in training, but this improvement is not retained when participants are evaluated without guidance.

Mechanics of very slow human walking.

Human walking speeds can be influenced by multiple factors, from energetic considerations to the time to reach a destination. Neurological deficits or lower-limb injuries can lead to slower walking speeds, and the recovery of able-bodied gait speed and behavior from impaired gait is considered an important rehabilitation goal. Because gait studies are typically performed at faster speeds, little normative data exists for very slow speeds (less than 0.6 ms[Formula: see text]). The purpose of our study was to investigate healthy gait mechanics at extremely slow walking speeds. We recorded kinematic and kinetic data from eight adult subjects walking at four slow speeds from 0.1 ms[Formula: see text]   to 0.6 ms[Formula: see text]   and at their self-selected speed. We found that known relations for spatiotemporal and work measures are still valid at very slow speeds. Trends derived from slow speeds largely provided reasonable estimates of gait measures at self-selected speeds. Our study helps enable valuable comparisons between able-bodied and impaired gait, including which pathological behaviors can be attributed to slow speeds and which to gait deficits. We also provide a slow walking dataset, which may serve as normative data for clinical evaluations and gait rehabilitative devices.

A simple model of mechanical effects to estimate metabolic cost of human walking.

Since the advent of energy measurement devices, gait experiments have shown that energetic economy has a large influence on human walking behavior. However, few cost models have attempted to capture the major energy components under comprehensive walking conditions. Here we present a simple but unified model that uses walking mechanics to estimate metabolic cost at different speeds and step lengths and for six other biomechanically-relevant gait experiments in literature. This includes at various gait postures (e.g. extra foot lift), anthropometric dimensions (e.g. added mass), and reduced gravity conditions, without the need for parameter tuning to design new gait trajectories. Our results suggest that the metabolic cost of walking can largely be explained by the linear combination of four costs-swing and torso dynamics, center of mass velocity redirection, ground clearance, and body weight support. The overall energetic cost is a tradeoff among these separable components, shaped by how they manifest under different walking conditions.