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Robots have to adjust their motor behavior to changing environments and variable task requirements to successfully operate in the real world and physically interact with humans. Thus, robotics strives to enable a broad spectrum of adjustable motor behavior, aiming to mimic the human ability to function in unstructured scenarios. In humans, motor behavior arises from the integrative action of the central nervous system and body biomechanics; motion must be understood from a neuromechanics perspective. Nervous regions such as the cerebellum facilitate learning, adaptation, and coordination of our motor responses, ultimately driven by muscle activation. Muscles, in turn, self-stabilize motion through mechanical viscoelasticity. In addition, the agonist-antagonist arrangement of muscles surrounding joints enables cocontraction, which can be regulated to enhance motion accuracy and adapt joint stiffness, thereby providing impedance modulation and broadening the motor repertoire. Here, we propose a control solution that harnesses neuromechanics to enable adjustable robot motor behavior. Our solution integrates a muscle model that replicates mechanical viscoelasticity and cocontraction together with a cerebellar network providing motor adaptation. The resulting cerebello-muscular controller drives the robot through torque commands in a feedback control loop. Changes in cocontraction modify the muscle dynamics, and the cerebellum provides motor adaptation without relying on prior analytical solutions, driving the robot in different motor tasks, including payload perturbations and operation across unknown terrains. Experimental results show that cocontraction modulates robot stiffness, performance accuracy, and robustness against external perturbations. Through cocontraction modulation, our cerebello-muscular torque controller enables a broad spectrum of robot motor behavior.

Most birds can navigate seamlessly between aerial and terrestrial environments. Whereas the forelimbs evolved into wings primarily for flight, the hindlimbs serve diverse functions such as walking, hopping and leaping, and jumping take-off for transitions into flight 1 . These capabilities have inspired engineers to aim for similar multimodality in aerial robots, expanding their range of applications across diverse environments. However, challenges remain in reproducing multimodal locomotion, across gaits with distinct kinematics and propulsive characteristics, such as walking and jumping, while preserving lightweight mass for flight. This trade-off between mechanical complexity and versatility 2 limits most existing aerial robots to only one additional locomotor mode 3-5 . Here we overcome the complexity-versatility trade-off with RAVEN (Robotic Avian-inspired Vehicle for multiple ENvironments), which uses its bird-inspired multifunctional legs to jump rapidly into flight, walk on the ground, and hop over obstacles and gaps similar to the multimodal locomotion of birds. We show that jumping for take-off contributes substantially to the initial flight take-off speed 6-9 and, remarkably, that it is more energy efficient than taking off without the jump. Our analysis suggests an important trade-off in mass distribution between legs and body among birds adapted for different locomotor strategies, with greater investment in leg mass among terrestrial birds with multimodal gait demands. Multifunctional robot legs expand the opportunities to deploy traditional fixed-wing aircraft in complex terrains through autonomous take-offs and multimodal gaits., Competing Interests: Competing interests: The authors declare no competing interests., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)

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.

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., (© 2023. Springer Nature Limited.)

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., Competing Interests: Competing interests The authors declare no competing or financial interests., (© 2023. Published by The Company of Biologists Ltd.)

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

This article examines the importance of integrating locomotion and cognitive information for achieving dynamic locomotion from a viewpoint combining biology and ecological psychology. We present a mammalian neuromusculoskeletal model from external sensory information processing to muscle activation, which includes: 1) a visual-attention control mechanism for controlling attention to external inputs; 2) object recognition representing the primary motor cortex; 3) a motor control model that determines motor commands traveling down the corticospinal and reticulospinal tracts; 4) a central pattern generation model representing pattern generation in the spinal cord; and 5) a muscle reflex model representing the muscle model and its reflex mechanism. The proposed model is able to generate the locomotion of a quadruped robot in flat and natural terrain. The experiment also shows the importance of a postural reflex mechanism when experiencing a sudden obstacle. We show the reflex mechanism when a sudden obstacle is separately detected from both external (retina) and internal (touching afferent) sensory information. We present the biological rationale for supporting the proposed model. Finally, we discuss future contributions, trends, and the importance of the proposed research.

Animal behavior emerges from an interaction between neural network dynamics, musculoskeletal properties and the physical environment. Accessing and understanding the interplay between these elements requires the development of integrative and morphologically realistic neuromechanical simulations. Here we present NeuroMechFly, a data-driven model of the widely studied organism, Drosophila melanogaster. NeuroMechFly combines four independent computational modules: a physics-based simulation environment, a biomechanical exoskeleton, muscle models and neural network controllers. To enable use cases, we first define the minimum degrees of freedom of the leg from real three-dimensional kinematic measurements during walking and grooming. Then, we show how, by replaying these behaviors in the simulator, one can predict otherwise unmeasured torques and contact forces. Finally, we leverage NeuroMechFly's full neuromechanical capacity to discover neural networks and muscle parameters that drive locomotor gaits optimized for speed and stability. Thus, NeuroMechFly can increase our understanding of how behaviors emerge from interactions between complex neuromechanical systems and their physical surroundings., (© 2022. The Author(s), under exclusive licence to Springer Nature America, Inc.)

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., (Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Suzuki, Kano, Ijspeert and Ishiguro.)

There are currently many quadruped robots suited to a wide range of applications, but traversing some terrains, such as vertical ladders, remains an open challenge. There is still a need to develop adaptive robots that can walk and climb efficiently. This paper presents an adaptive quadruped robot that, by mimicking feline structure, supports several novel capabilities. We design a novel paw structure and several point-cloud-based sensory structures incorporating a quad-composite time-of-flight sensor and a dual-laser range finder. The proposed robot is equipped with physical and cognitive capabilities which include: 1) a dynamic-density topological map building with attention model, 2) affordance perception using the topological map, and 3) a neural-based locomotion model. The novel capabilities show strong integration between locomotion and internal-external sensory information, enabling short-term adaptations in response to environmental changes. The robot performed well in several situations: walking on natural terrain, walking with a leg malfunction, avoiding a sudden obstacle, climbing a vertical ladder. Further, we consider current problems and future development., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Saputra, Takesue, Wada, Ijspeert and Kubota.)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Suzuki, Kano, Ijspeert and Ishiguro.)

In this paper, we present the design, control, and preliminary evaluation of the Symbitron exoskeleton, a lower limb modular exoskeleton developed for people with a spinal cord injury. The mechanical and electrical configuration and the controller can be personalized to accommodate differences in impairments among individuals with spinal cord injuries (SCI). In hardware, this personalization is accomplished by a modular approach that allows the reconfiguration of a lower-limb exoskeleton with ultimately eight powered series actuated (SEA) joints and high fidelity torque control. For SCI individuals with an incomplete lesion and sufficient hip control, we applied a trajectory-free neuromuscular control (NMC) strategy and used the exoskeleton in the ankle-knee configuration. For complete SCI individuals, we used a combination of a NMC and an impedance based trajectory tracking strategy with the exoskeleton in the ankle-knee-hip configuration. Results of a preliminary evaluation of the developed hardware and software showed that SCI individuals with an incomplete lesion could naturally vary their walking speed and step length and walked faster compared to walking without the device. SCI individuals with a complete lesion, who could not walk without support, were able to walk with the device and with the support of crutches that included a push-button for step initiation Our results demonstrate that an exoskeleton with modular hardware and control allows SCI individuals with limited or no lower limb function to receive tailored support and regain mobility.

Neural control of movement cannot be fully understood without careful consideration of interactions between the neural and biomechanical components. Recent advancements in mouse molecular genetics allow for the identification and manipulation of constituent elements underlying the neural control of movement. To complement experimental studies and investigate the mechanisms by which the neural circuitry interacts with the body and the environment, computational studies modeling motor behaviors in mice need to incorporate a model of the mouse musculoskeletal system. Here, we present the first fully articulated musculoskeletal model of the mouse. The mouse skeletal system has been developed from anatomical references and includes the sets of bones in all body compartments, including four limbs, spine, head and tail. Joints between all bones allow for simulation of full 3D mouse kinematics and kinetics. Hindlimb and forelimb musculature has been implemented using Hill-type muscle models. We analyzed the mouse whole-body model and described the moment-arms for different hindlimb and forelimb muscles, the moments applied by these muscles on the joints, and their involvement in limb movements at different limb/body configurations. The model represents a necessary step for the subsequent development of a comprehensive neuro-biomechanical model of freely behaving mice; this will close the loop between the neural control and the physical interactions between the body and the environment.

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer CL declared a past co-authorship with one of the authors AI to the handling editor., (Copyright © 2020 Knüsel, Crespi, Cabelguen, Ijspeert and Ryczko.)

How do four-legged animals adapt their locomotion to the environment? How do central and peripheral mechanisms interact within the spinal cord to produce adaptive locomotion and how is locomotion recovered when spinal circuits are perturbed? Salamanders are the only tetrapods that regenerate voluntary locomotion after full spinal transection. Given their evolutionary position, they provide a unique opportunity to bridge discoveries made in fish and mammalian models. Genetic dissection of salamander neural circuits is becoming feasible with new methods for precise manipulation, elimination, and visualisation of cells. These approaches can be combined with classical tools in neuroscience and with modelling and a robotic environment. We propose that salamanders provide a blueprint of the function, evolution, and regeneration of tetrapod locomotor circuits., (Copyright © 2020 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Powered exoskeletons (EXOs) have emerged as potential devices for Spinal Cord Injury (SCI) to support the intervention of physical therapists during therapy (rehabilitation EXOs) as well as to assist lower limb motion during the daily life (assistive EXOs). Although the ankle is considered a key joint for gait restoration after SCI, very few ankle exoskeletons were developed and tested in incomplete SCI (iSCI) population. Among those, the Achilles ankle exoskeleton is the only one embedding a Controller inspired by the neuromuscular system (NeuroMuscular Controller, NMC). In a previous study we demonstrated that a period dedicated to train iSCI subjects in using the Achilles EXO as an assistive aid, improved robot-aided walking speed and surprisingly also generated a positive trend in free walking speed on long and short distances thus suggesting a possible unexpected rehabilitation effect. To further investigate this result, a case-control longitudinal study was conducted in the present work. The aim of this study was to test the hypothesis that Achilles-aided training could improve performance of free walking of chronic iSCI people more than conventional intensity-matched gait rehabilitation. Before and after conventional and robot-aided rehabilitation a number of variables were analyzed, including spatiotemporal parameters, joint kinematics, ground reaction forces, muscle force, spasticity and its related symptoms, balance and personal experience about the training. Results showed that only the NMC-controlled Achilles training allowed participants to significantly walk faster, with a longer step length and a reduced gait cycle time. A slight force and spasticity improvements were also experienced. In terms of subjects' personal experience, Achilles training was perceived more interesting and less physically demanding than conventional rehabilitation., (Copyright 2020 Biolife Sas. www.biolifesas.org.)

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., (Copyright © 2020 Koelewijn and Ijspeert.)

Powered exoskeletons are among the emerging technologies claiming to assist functional ambulation. The potential to adapt robotic assistance based on specific motor abilities of incomplete spinal cord injury (iSCI) subjects, is crucial to optimize Human-Robot Interaction (HRI). Achilles, an autonomous wearable robot able to assist ankle during walking, was developed for iSCI subjects and utilizes a NeuroMuscular Controller (NMC). NMC can be used to adapt robotic assistance based on specific residual functional abilities of subjects. The main aim of this pilot study was to analyze the effects of the NMC-controlled Achilles, used as an assistive device, on chronic iSCI participants' performance, by assessing gait speed during 10-session training of robot-aided walking. Secondary aims were to assess training impact on participants' motion, clinical and functional features and to evaluate subjective perspective in terms of attitude towards technology, workload, usability and satisfaction. Results showed that 5 training sessions were necessary to significantly improve robot-aided gait speed on short paths and consequently to optimize HRI. Moreover, the training allowed participants who initially were not able to walk for 6 minutes, to improve gait endurance during Achilles-aided walking and to reduce perceived fatigue. Improvements were obtained also in gait speed during free walking, thus suggesting a potential rehabilitative impact, even if Achilles-aided walking was not faster than free walking. Participants' subjective evaluations indicated a positive experience.

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.

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.

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.

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.

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.

Reconstructing the locomotion of extinct vertebrates offers insights into their palaeobiology and helps to conceptualize major transitions in vertebrate evolution 1-4 . 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 function 5,6 . 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 lineages 7 . 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 trackways 8 . 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 tetrapods 7,9 , 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.

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.

We present Oncilla robot, a novel mobile, quadruped legged locomotion machine. This large-cat sized, 5.1 kg robot is one of a kind of a recent, bioinspired legged robot class designed with the capability of model-free locomotion control. Animal legged locomotion in rough terrain is clearly shaped by sensor feedback systems. Results with Oncilla robot show that agile and versatile locomotion is possible without sensory signals to some extend, and tracking becomes robust when feedback control is added (Ajallooeian, 2015). By incorporating mechanical and control blueprints inspired from animals, and by observing the resulting robot locomotion characteristics, we aim to understand the contribution of individual components. Legged robots have a wide mechanical and control design parameter space, and a unique potential as research tools to investigate principles of biomechanics and legged locomotion control. But the hardware and controller design can be a steep initial hurdle for academic research. To facilitate the easy start and development of legged robots, Oncilla-robot's blueprints are available through open-source. The robot's locomotion capabilities are shown in several scenarios. Specifically, its spring-loaded pantographic leg design compensates for overdetermined body and leg postures, i.e., during turning maneuvers, locomotion outdoors, or while going up and down slopes. The robot's active degree of freedom allow tight and swift direction changes, and turns on the spot. Presented hardware experiments are conducted in an open-loop manner, with little control and computational effort. For more versatile locomotion control, Oncilla-robot can sense leg joint rotations, and leg-trunk forces. Additional sensors can be included for feedback control with an open communication protocol interface. The robot's customized actuators are designed for robust actuation, and efficient locomotion. It trots with a cost of transport of 3.2 J/(Nm), at a speed of 0.63 m s-1 (Froude number 0.25). The robot trots inclined slopes up to 10°, at 0.25 m s-1. The multi-body Webots model of Oncilla robot, and Oncilla robot's extensive software architecture enables users to design and test scenarios in simulation. Controllers can directly be transferred to the real robot. Oncilla robot's blueprints are open-source published (hardware GLP v3, software LGPL v3)., (Copyright © 2018 Spröwitz, Tuleu, Ajallooeian, Vespignani, Möckel, Eckert, D'Haene, Degrave, Nordmann, Schrauwen, Steil and Ijspeert.)

In spite of extensive studies on human walking, less research has been conducted on human walking gait adaptation during interaction with another human. In this paper, we study a particular case of interactive locomotion where two humans carry a rigid object together. Experimental data from two persons walking together, one in front of the other, while carrying a stretcher-like object is presented, and the adaptation of their walking gaits and coordination of the foot-fall patterns are analyzed. It is observed that in more than 70% of the experiments the subjects synchronize their walking gaits; it is shown that these walking gaits can be associated to quadrupedal gaits. Moreover, in order to understand the extent by which the passive dynamics can explain this synchronization behaviour, a simple 2D model, made of two-coupled spring-loaded inverted pendulums, is developed, and a comparison between the experiments and simulations with this model is presented, showing that with this simple model we are able to reproduce some aspects of human walking behaviour when paired with another human.

Versatility is important for a wearable exoskeleton controller to be responsive to both the user and the environment. These characteristics are especially important for subjects with spinal cord injury (SCI), where active recruitment of their own neuromuscular system could promote motor recovery. Here we demonstrate the capability of a novel, biologically-inspired neuromuscular controller (NMC) which uses dynamical models of lower limb muscles to assist the gait of SCI subjects. Advantages of this controller include robustness, modularity, and adaptability. The controller requires very few inputs (i.e., joint angles, stance, and swing detection), can be decomposed into relevant control modules (e.g., only knee or hip control), and can generate walking at different speeds and terrains in simulation. We performed a preliminary evaluation of this controller on a lower-limb knee and hip robotic gait trainer with seven subjects ( N = 7, four with complete paraplegia, two incomplete, one healthy) to determine if the NMC could enable normal-like walking. During the experiment, SCI subjects walked with body weight support on a treadmill and could use the handrails. With controller assistance, subjects were able to walk at fast walking speeds for ambulatory SCI subjects-from 0.6 to 1.4 m/s. Measured joint angles and NMC-provided joint torques agreed reasonably well with kinematics and biological joint torques of a healthy subject in shod walking. Some differences were found between the torques, such as the lack of knee flexion near mid-stance, but joint angle trajectories did not seem greatly affected. The NMC also adjusted its torque output to provide more joint work at faster speeds and thus greater joint angles and step length. We also found that the optimal speed-step length curve observed in healthy humans emerged for most of the subjects, albeit with relatively longer step length at faster speeds. Therefore, with very few sensors and no predefined settings for multiple walking speeds or adjustments for subjects of differing anthropometry and walking ability, NMC enabled SCI subjects to walk at several speeds, including near healthy speeds, in a healthy-like manner. These preliminary results are promising for future implementation of neuromuscular controllers on wearable prototypes for real-world walking conditions.

While movement is essential to human wellbeing, we are still unable to reproduce the deftness and robustness of human movement in automatons or completely restore function to individuals with many types of motor impairment. To better understand how the human nervous system plans and controls movements, neuromechanists employ simple tasks such as upper extremity reaches and isometric force tasks. However, these simple tasks rarely consider impacts and may not capture aspects of motor control that arise from real-world complexity. Here we compared existing models of motor control with the results of a periodic targeted impact task extended from Bernstein's seminal work: hammering a nail into wood. We recorded impact forces and kinematics from 10 subjects hammering at different frequencies and with hammers with different physical properties (mass and face area). We found few statistical differences in most measures between different types of hammer, demonstrating human robustness to minor changes in dynamics. Because human motor control is thought to obey optimality principles, we also developed a feedforward optimal simulation with a neuromechanically inspired cost function that reproduces the experimental data. However, Fitts' Law, which relates movement time to distance traveled and target size, did not match our experimental data. We therefore propose a new model in which the distance moved is a logarithmic function of the time to move that yields better results ( R 2 ≥ 0.99 compared to R 2 ≥ 0.88). These results support the argument that humans control movement in an optimal way, but suggest that Fitts' Law may not generalize to periodic impact tasks.

To escape danger or catch prey, running vertebrates rely on dynamic gaits with minimal ground contact. By contrast, most insects use a tripod gait that maintains at least three legs on the ground at any given time. One prevailing hypothesis for this difference in fast locomotor strategies is that tripod locomotion allows insects to rapidly navigate three-dimensional terrain. To test this, we computationally discovered fast locomotor gaits for a model based on Drosophila melanogaster. Indeed, the tripod gait emerges to the exclusion of many other possible gaits when optimizing fast upward climbing with leg adhesion. By contrast, novel two-legged bipod gaits are fastest on flat terrain without adhesion in the model and in a hexapod robot. Intriguingly, when adhesive leg structures in real Drosophila are covered, animals exhibit atypical bipod-like leg coordination. We propose that the requirement to climb vertical terrain may drive the prevalence of the tripod gait over faster alternative gaits with minimal ground contact.

Robots are increasingly used as scientific tools to investigate animal locomotion. However, designing a robot that properly emulates the kinematic and dynamic properties of an animal is difficult because of the complexity of musculoskeletal systems and the limitations of current robotics technology. Here, we propose a design process that combines high-speed cineradiography, optimization, dynamic scaling, three-dimensional printing, high-end servomotors and a tailored dry-suit to construct Pleurobot: a salamander-like robot that closely mimics its biological counterpart, Pleurodeles waltl Our previous robots helped us test and confirm hypotheses on the interaction between the locomotor neuronal networks of the limbs and the spine to generate basic swimming and walking gaits. With Pleurobot, we demonstrate a design process that will enable studies of richer motor skills in salamanders. In particular, we are interested in how these richer motor skills can be obtained by extending our spinal cord models with the addition of more descending pathways and more detailed limb central pattern generator networks. Pleurobot is a dynamically scaled amphibious salamander robot with a large number of actuated degrees of freedom (DOFs: 27 in total). Because of our design process, the robot can capture most of the animal's DOFs and range of motion, especially at the limbs. We demonstrate the robot's abilities by imposing raw kinematic data, extracted from X-ray videos, to the robot's joints for basic locomotor behaviours in water and on land. The robot closely matches the behaviour of the animal in terms of relative forward speeds and lateral displacements. Ground reaction forces during walking also resemble those of the animal. Based on our results, we anticipate that future studies on richer motor skills in salamanders will highly benefit from Pleurobot's design., (© 2016 The Author(s).)

In tetrapods, limb and axial movements are coordinated during locomotion. It is well established that inter- and intralimb coordination show considerable variations during ongoing locomotion. Much less is known about the flexibility of the axial musculoskeletal system during locomotion and the neural mechanisms involved. Here we examined this issue in the salamander Pleurodeles waltlii, which is capable of locomotion in both aquatic and terrestrial environments. Kinematics of the trunk and electromyograms from the mid-trunk epaxial myotomes were recorded during four locomotor behaviors in freely moving animals. A similar approach was used during rhythmic struggling movements since this would give some insight into the flexibility of the axial motor system. Our results show that each of the forms of locomotion and the struggling behavior is characterized by a distinct combination of mid-trunk motor patterns and cycle durations. Using in vitro electrophysiological recordings in isolated spinal cords, we observed that the spinal networks activated with bath-applied N-methyl-d-aspartate could generate these axial motor patterns. In these isolated spinal cord preparations, the limb motor nerve activities were coordinated with each mid-trunk motor pattern. Furthermore, isolated mid-trunk spinal cords and hemicords could generate the mid-trunk motor patterns. This indicates that each side of the cord comprises a network able to generate coordinated axial motor activity. The roles of descending and sensory inputs in the behavior-related changes in axial motor coordination are discussed., (Copyright © 2015 the American Physiological Society.)

Crawling on hands and knees is an early pattern of human infant locomotion, which offers an interesting way of studying quadrupedalism in one of its simplest form. We investigate how crawling human infants compare to other quadruped mammals, especially primates. We present quantitative data on both the gait and kinematics of seven 10-month-old crawling infants. Body movements were measured with an optoelectronic system giving precise data on 3-dimensional limb movements. Crawling on hands and knees is very similar to the locomotion of non-human primates in terms of the quite protracted arm at touch-down, the coordination between the spine movements in the lateral plane and the limbs, the relatively extended limbs during locomotion and the strong correlation between stance duration and speed of locomotion. However, there are important differences compared to primates, such as the choice of a lateral-sequence walking gait, which is similar to most non-primate mammals and the relatively stiff elbows during stance as opposed to the quite compliant gaits of primates. These finding raise the question of the role of both the mechanical structure of the body and neural control on the determination of these characteristics.

The graceful and agile movements of animals are difficult to analyze and emulate because locomotion is the result of a complex interplay of many components: the central and peripheral nervous systems, the musculoskeletal system, and the environment. The goals of biorobotics are to take inspiration from biological principles to design robots that match the agility of animals, and to use robots as scientific tools to investigate animal adaptive behavior. Used as physical models, biorobots contribute to hypothesis testing in fields such as hydrodynamics, biomechanics, neuroscience, and prosthetics. Their use may contribute to the design of prosthetic devices that more closely take human locomotion principles into account., (Copyright © 2014, American Association for the Advancement of Science.)

In the attempt to build adaptive and intelligent machines, roboticists have looked at neuroscience for more than half a century as a source of inspiration for perception and control. More recently, neuroscientists have resorted to robots for testing hypotheses and validating models of biological nervous systems. Here, we give an overview of the work at the intersection of robotics and neuroscience and highlight the most promising approaches and areas where interactions between the two fields have generated significant new insights. We articulate the work in three sections, invertebrate, vertebrate and primate neuroscience. We argue that robots generate valuable insight into the function of nervous systems, which is intimately linked to behaviour and embodiment, and that brain-inspired algorithms and devices give robots life-like capabilities., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

In this work we research the role of body dynamics in the complexity of kinematic patterns in a quadruped robot with compliant legs. Two gait patterns, lateral sequence walk and trot, along with leg length control patterns of different complexity were implemented in a modular, feed-forward locomotion controller. The controller was tested on a small, quadruped robot with compliant, segmented leg design, and led to self-stable and self-stabilizing robot locomotion. In-air stepping and on-ground locomotion leg kinematics were recorded, and the number and shapes of motion primitives accounting for 95% of the variance of kinematic leg data were extracted. This revealed that kinematic patterns resulting from feed-forward control had a lower complexity (in-air stepping, 2-3 primitives) than kinematic patterns from on-ground locomotion (νm4 primitives), although both experiments applied identical motor patterns. The complexity of on-ground kinematic patterns had increased, through ground contact and mechanical entrainment. The complexity of observed kinematic on-ground data matches those reported from level-ground locomotion data of legged animals. Results indicate that a very low complexity of modular, rhythmic, feed-forward motor control is sufficient for level-ground locomotion in combination with passive compliant legged hardware.

Vertebrate animals exhibit impressive locomotor skills. These locomotor skills are due to the complex interactions between the environment, the musculo-skeletal system and the central nervous system, in particular the spinal locomotor circuits. We are interested in decoding these interactions in the salamander, a key animal from an evolutionary point of view. It exhibits both swimming and stepping gaits and is faced with the problem of producing efficient propulsive forces using the same musculo-skeletal system in two environments with significant physical differences in density, viscosity and gravitational load. Yet its nervous system remains comparatively simple. Our approach is based on a combination of neurophysiological experiments, numerical modeling at different levels of abstraction, and robotic validation using an amphibious salamander-like robot. This article reviews the current state of our knowledge on salamander locomotion control, and presents how our approach has allowed us to obtain a first conceptual model of the salamander spinal locomotor networks. The model suggests that the salamander locomotor circuit can be seen as a lamprey-like circuit controlling axial movements of the trunk and tail, extended by specialized oscillatory centers controlling limb movements. The interplay between the two types of circuits determines the mode of locomotion under the influence of sensory feedback and descending drive, with stepping gaits at low drive, and swimming at high drive.

The evolutionary transition from water to land required new locomotor modes and corresponding adjustments of the spinal "central pattern generators" for locomotion. Salamanders resemble the first terrestrial tetrapods and represent a key animal for the study of these changes. Based on recent physiological data from salamanders, and previous work on the swimming, limbless lamprey, we present a model of the basic oscillatory network in the salamander spinal cord, the spinal segment. Model neurons are of the Hodgkin-Huxley type. Spinal hemisegments contain sparsely connected excitatory and inhibitory neuron populations, and are coupled to a contralateral hemisegment. The model yields a large range of experimental findings, especially the NMDA-induced oscillations observed in isolated axial hemisegments and segments of the salamander Pleurodeles waltlii. The model reproduces most of the effects of the blockade of AMPA synapses, glycinergic synapses, calcium-activated potassium current, persistent sodium current, and [Formula: see text]-current. Driving segments with a population of brainstem neurons yields fast oscillations in the in vivo swimming frequency range. A minimal modification to the conductances involved in burst-termination yields the slower stepping frequency range. Slow oscillators can impose their frequency on fast oscillators, as is likely the case during gait transitions from swimming to stepping. Our study shows that a lamprey-like network can potentially serve as a building block of axial and limb oscillators for swimming and stepping in salamanders.

Salamanders have captured the interest of biologists and roboticists for decades because of their ability to locomote in different environments and their resemblance to early representatives of tetrapods. In this article, we review biological and robotic studies on the kinematics (i.e., angular profiles of joints) of salamander locomotion aiming at three main goals: (i) to give a clear view of the kinematics, currently available, for each body part of the salamander while moving in different environments (i.e., terrestrial stepping, aquatic stepping, and swimming), (ii) to examine what is the status of our current knowledge and what remains unclear, and (iii) to discuss how much robotics and modeling have already contributed and will potentially contribute in the future to such studies.

Animals have to coordinate a large number of muscles in different ways to efficiently move at various speeds and in different and complex environments. This coordination is in large part based on central pattern generators (CPGs). These neural networks are capable of producing complex rhythmic patterns when activated and modulated by relatively simple control signals. Although the generation of particular gaits by CPGs has been successfully modeled at many levels of abstraction, the principles underlying the generation and selection of a diversity of patterns of coordination in a single neural network are still not well understood. The present work specifically addresses the flexibility of the spinal locomotor networks in salamanders. We compare an abstract oscillator model and a CPG network composed of integrate-and-fire neurons, according to their ability to account for different axial patterns of coordination, and in particular the transition in gait between swimming and stepping modes. The topology of the network is inspired by models of the lamprey CPG, complemented by additions based on experimental data from isolated spinal cords of salamanders. Oscillatory centers of the limbs are included in a way that preserves the flexibility of the axial network. Similarly to the selection of forward and backward swimming in lamprey models via different excitation to the first axial segment, we can account for the modification of the axial coordination pattern between swimming and forward stepping on land in the salamander model, via different uncoupled frequencies in limb versus axial oscillators (for the same level of excitation). These results transfer partially to a more realistic model based on formal spiking neurons, and we discuss the difference between the abstract oscillator model and the model built with formal spiking neurons.

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.

Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.

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.

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.

In this article, we propose a new method for providing assistance during cyclical movements. This method is trajectory-free, in the sense that it provides user assistance irrespective of the performed movement, and requires no other sensing than the assisting robot's own encoders. The approach is based on adaptive oscillators, i.e., mathematical tools that are capable of learning the high level features (frequency, envelope, etc.) of a periodic input signal. Here we present two experiments that we recently conducted to validate our approach: a simple sinusoidal movement of the elbow, that we designed as a proof-of-concept, and a walking experiment. In both cases, we collected evidence illustrating that our approach indeed assisted healthy subjects during movement execution. Owing to the intrinsic periodicity of daily life movements involving the lower-limbs, we postulate that our approach holds promise for the design of innovative rehabilitation and assistance protocols for the lower-limb, requiring little to no user-specific calibration.

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.

We propose a novel method for movement assistance that is based on adaptive oscillators, i.e., mathematical tools that are capable of extracting the high-level features (amplitude, frequency, and offset) of a periodic signal. Such an oscillator acts like a filter on these features, but keeps its output in phase with respect to the input signal. Using a simple inverse model, we predicted the torque produced by human participants during rhythmic flexion-extension of the elbow. Feeding back a fraction of this estimated torque to the participant through an elbow exoskeleton, we were able to prove the assistance efficiency through a marked decrease of the biceps and triceps electromyography. Importantly, since the oscillator adapted to the movement imposed by the user, the method flexibly allowed us to change the movement pattern and was still efficient during the nonstationary epochs. This method holds promise for the development of new robot-assisted rehabilitation protocols because it does not require prespecifying a reference trajectory and does not require complex signal sensing or single-user calibration: the only signal that is measured is the position of the augmented joint. In this paper, we further demonstrate that this assistance was very intuitive for the participants who adapted almost instantaneously.