Quadrupedal Locomotion Research Articles

Enhancing postural stability in musculoskeletal quadrupedal locomotion through tension feedback for CPG-based controller

A central pattern generator (CPG)-based controller enhances the adaptability of quadrupedal locomotion, for example, by controlling the trunk posture. The conventional CPG-based controllers with attitude control often utilized the posture angle as feedback information. However, if the robot's body is as soft as a musculoskeletal structure, it can detect the over-tilting of the trunk based on proprioceptive information of the muscles. In general, proprioceptive information such as muscle tension changes more rapidly than posture angle information. Therefore, a feedback loop based on proprioceptive information has great potential to respond to sudden disturbances that occur during locomotion over uneven terrain. In this research, we proposed a CPG-based controller utilizing the tension of soft pneumatic artificial muscles (PAMs). Musculoskeletal quadruped robots driven by PAMs are so soft, which prevents over-tilting of the trunk because the soft leg acts like a suspension. In addition, tension, one of the proprioceptive information of PAMs, exhibits high sensitivity to changes in trunk posture because the soft body's motion easily is affected by over-tilting of the trunk. To validate the efficacy of the proposed controller, we conducted numerical simulations with a simple quadruped model and experiments with a musculoskeletal quadruped robot. As a result, the tension feedback is not effective for posture stabilization on flat terrain whereas it is effective on uneven terrain. Moreover, the tension feedback improved the running velocity over uneven terrain. These results will enhance the locomotion capability of musculoskeletal quadruped robots, advancing their practical application.

Real-time robust nonlinear model predictive control with monotonically increasing weight for quadruped locomotion

Real-time robust nonlinear model predictive control with monotonically increasing weight for quadruped locomotion

Changes in intra- and interlimb reflexes from forelimb cutaneous afferents after staggered thoracic lateral hemisections during locomotion in cats.

In quadrupeds, such as cats, cutaneous afferents from the forepaw dorsum signal external perturbations and send inputs to spinal circuits to co-ordinate the activity in muscles of all four limbs. How these cutaneous reflex pathways from forelimb afferents are reorganized after an incomplete spinal cord injury is not clear. Using a staggered thoracic lateral hemisections paradigm, we investigated changes in intralimb and interlimb reflex pathways by electrically stimulating the left and right superficial radial nerves in seven adult cats and recording reflex responses in five forelimb and ten hindlimb muscles. After the first (right T5-T6) and second (left T10-T11) hemisections, forelimb-hindlimb co-ordination was altered and weakened. After the second hemisection, cats required balance assistance to perform quadrupedal locomotion. Short-, mid- and long-latency homonymous and crossed reflex responses in forelimb muscles and their phase modulation remained largely unaffected after staggered hemisections. The occurrence of homolateral and diagonal mid- and long-latency responses in hindlimb muscles evoked with left and right superficial radial nerve stimulation was significantly reduced at the first time point after the first hemisection, but partially recovered at the second time point with left superficial radial nerve stimulation. These responses were lost or reduced after the second hemisection. When present, all reflex responses, including homolateral and diagonal, maintained their phase-dependent modulation. Therefore, our results show a considerable loss in cutaneous reflex transmission from cervical to lumbar levels after incomplete spinal cord injury, albeit with preservation of phase modulation, probably affecting functional responses to external perturbations. KEY POINTS: Cutaneous afferent inputs co-ordinate muscle activity in the four limbs during locomotion when the forepaw dorsum contacts an obstacle. Thoracic spinal cord injury disrupts communication between spinal locomotor centres located at cervical and lumbar levels, impairing balance and limb co-ordination. We investigated cutaneous reflexes from forelimb afferents during quadrupedal locomotion by electrically stimulating the superficial radial nerve bilaterally, before and after staggered lateral thoracic hemisections in cats. We showed a loss/reduction of mid- and long-latency homolateral and diagonal reflex responses in hindlimb muscles early after the first hemisection that partially recovered with left superficial radial nerve stimulation, before being reduced after the second hemisection. Targeting cutaneous reflex pathways from forelimb afferents projecting to the four limbs could help develop therapeutic approaches aimed at restoring transmission in ascending and descending spinal pathways.

Learning quadrupedal locomotion on tough terrain using an asymmetric terrain feature mining network

Learning quadrupedal locomotion on tough terrain using an asymmetric terrain feature mining network

How bipedalism shapes humans' actions with hand tools.

The task for an embodied cognitive understanding of humans' actions with tools is to elucidate how the human body, as a whole, supports the perception of affordances and dexterous action with objects in relation to other objects. Here, we focus on the relationship between humans' actions with handheld tools and bipedal posture. Posture plays a pivotal role in shaping animals' perception and action dynamics. While humans stand and locomote bipedally, other primates predominantly employ quadrupedal postures and locomotion, relying on both hands and feet to support the body. Drawing upon evidence from evolutionary biology, developmental psychology and performance studies, we elucidate the influence of bipedalism on our actions with objects and on our proficiency in using tools. We use the metaphor of cascades to capture the dynamic, nonlinear transformations in morphology and behaviour associated with posture and the use of tools across evolutionary and developmental timescales. Recent work illustrates the promise of multifractal cascade analysis to reveal nonlinear, cross-scale interactions across the entire body in real-time, supporting the perception of affordances for actions with tools. Cascade analysis enriches our comprehension of real-time performance and facilitates exploration of the relationships among whole-body coordination, individual development, and evolutionary processes.This article is part of the theme issue 'Minds in movement: embodied cognition in the age of artificial intelligence'.

Quadrupedal Locomotion With Parallel Compliance: E-Go Design, Modeling, and Control

Quadrupedal Locomotion With Parallel Compliance: E-Go Design, Modeling, and Control

Sensory feedback and central neuronal interactions in mouse locomotion.

Locomotion is a complex process involving specific interactions between the central neural controller and the mechanical components of the system. The basic rhythmic activity generated by locomotor circuits in the spinal cord defines rhythmic limb movements and their central coordination. The operation of these circuits is modulated by sensory feedback from the limbs providing information about the state of the limbs and the body. However, the specific role and contribution of central interactions and sensory feedback in the control of locomotor gait and posture remain poorly understood. We use biomechanical data on quadrupedal locomotion in mice and recent findings on the organization of neural interactions within the spinal locomotor circuitry to create and analyse a tractable mathematical model of mouse locomotion. The model includes a simplified mechanical model of the mouse body with four limbs and a central controller composed of four rhythm generators, each operating as a state machine controlling the state of one limb. Feedback signals characterize the load and extension of each limb as well as postural stability (balance). We systematically investigate and compare several model versions and compare their behaviour to existing experimental data on mouse locomotion. Our results highlight the specific roles of sensory feedback and some central propriospinal interactions between circuits controlling fore and hind limbs for speed-dependent gait expression. Our models suggest that postural imbalance feedback may be critically involved in the control of swing-to-stance transitions in each limb and the stabilization of walking direction.

Learning to Walk with Adaptive Feet

In recent years, tasks regarding autonomous mobility favoredthe use of legged robots rather than wheeled ones thanks to their higher mobility on rough and uneven terrains. This comes at the cost of more complex motion planners and controllers to ensure robot stability and balance. However, in the case of quadrupedal robots, balancing is simpler than it is for bipeds thanks to their larger support polygons. Until a few years ago, most scientists and engineers addressed the quadrupedal locomotion problem with model-based approaches, which require a great deal of modeling expertise. A new trend is the use of data-driven methods, which seem to be quite promising and have shown great results. These methods do not require any modeling effort, but they suffer from computational limitations dictated by the hardware resources used. However, only the design phase of these algorithms requires large computing resources (controller training); their execution in the operational phase (deployment), takes place in real time on common processors. Moreover, adaptive feet capable of sensing terrain profile information have been designed and have shown great performance. Still, no dynamic locomotion control method has been specifically designed to leverage the advantages and supplementary information provided by this type of adaptive feet. In this work, we investigate the use and evaluate the performance of different end-to-end control policies trained via reinforcement learning algorithms specifically designed and trained to work on quadrupedal robots equipped with passive adaptive feet for their dynamic locomotion control over a diverse set of terrains. We examine how the addition of the haptic perception of the terrain affects the locomotion performance.

Muscle-Driven Predictive Physics Simulations of Quadrupedal Locomotion in the Horse.

Musculoskeletal simulations can provide insights into the underlying mechanisms that govern animal locomotion. In this study, we describe the development of a new musculoskeletal model of the horse, and to our knowledge present the first fully muscle-driven, predictive simulations of equine locomotion. Our goal was to simulate a model that captures only the gross musculoskeletal structure of a horse, without specialized morphological features. We mostly present simulations acquired using feedforward control, without state feedback ("top-down control"). Without using kinematics or motion capture data as an input, we have simulated a variety of gaits that are commonly used by horses (walk, pace, trot, tölt, and collected gallop). We also found a selection of gaits that are not normally seen in horses (half bound, extended gallop, ambling). Due to the clinical relevance of the trot, we performed a tracking simulation that included empirical joint angle deviations in the cost function. To further demonstrate the flexibility of our model, we also present a simulation acquired using spinal feedback control, where muscle control signals are wholly determined by gait kinematics. Despite simplifications to the musculature, simulated footfalls and ground reaction forces followed empirical patterns. In the tracking simulation, kinematics improved with respect to the fully predictive simulations, and muscle activations showed a reasonable correspondence to electromyographic signals, although we did not predict any anticipatory firing of muscles. When sequentially increasing the target speed, our simulations spontaneously predicted walk-to-run transitions at the empirically determined speed. However, predicted stride lengths were too short over nearly the entire speed range unless explicitly prescribed in the controller, and we also did not recover spontaneous transitions to asymmetric gaits such as galloping. Taken together, our model performed adequately when simulating individual gaits, but our simulation workflow was not able to capture all aspects of gait selection. We point out certain aspects of our workflow that may have caused this, including anatomical simplifications and the use of massless Hill-type actuators. Our model is an extensible, generalized horse model, with considerable scope for adding anatomical complexity. This project is intended as a starting point for continual development of the model and code that we make available in extensible open-source formats.

SYNLOCO‐VE: Synthesizing central pattern generator with reinforcement learning and velocity estimator for quadruped locomotion

AbstractIt is a challenging task to learn a robust and natural locomotion controller for quadruped robots at different terrains and velocities. In particular, the locomotion learning task will be even more difficult for the case with no exteroceptive sensors. In this article, the learning‐based locomotion control is, therefore, investigated for quadruped robots only using proprioceptive sensors. A new framework called SYNLOCO‐VE is proposed by synthesizing a feedforward gait planner, a trunk velocity estimator, and reinforcement learning (RL). The feedforward gait planner is developed based on the well‐known central pattern generator, but it can change the foot length for improved velocity tracking performance. The trunk velocity estimator is designed based on deep learning, which estimates the trunk velocity using historical data from proprioceptive sensors. The introduction of the trunk velocity estimator can mitigate the influence of the partial observation issue due to the lack of exteroceptive sensors. RL is employed to learn a feedback controller to regulate the robot gaits using feedback from proprioceptive sensors and the trunk velocity estimation. In the proposed framework, the feedforward gait planner can also guide the training process of RL, thus resulting in more stable and faster policy learning. Ablation studies are provided to demonstrate the efficiency of different modules in the proposed design. Extensive experiments are performed using a quadruped robot Go1, which only has proprioceptive sensors. The proposed framework is able to learn robust and stable locomotion at different terrains and tasks. Experimental comparisons are also conducted to illustrate the advantages of the proposed design over the state‐of‐the‐art methods.

Forelimb movements contribute to hindlimb cutaneous reflexes during locomotion in cats.

During quadrupedal locomotion, interactions between spinal and supraspinal circuits and somatosensory feedback coordinate forelimb and hindlimb movements. How this is achieved is not clear. To determine whether forelimb movements modulate hindlimb cutaneous reflexes involved in responding to an external perturbation, we stimulated the superficial peroneal nerve in six intact cats during quadrupedal locomotion and during hindlimb-only locomotion (with forelimbs standing on stationary platform) and in two cats with a low spinal transection (T12-T13) during hindlimb-only locomotion. We compared cutaneous reflexes evoked in six ipsilateral and four contralateral hindlimb muscles. Results showed similar occurrence and phase-dependent modulation of short-latency inhibitory and excitatory responses during quadrupedal and hindlimb-only locomotion in intact cats. However, the depth of modulation was reduced in the ipsilateral semitendinosus during hindlimb-only locomotion. Additionally, longer-latency responses occurred less frequently in extensor muscles bilaterally during hindlimb-only locomotion, whereas short-latency inhibitory and longer-latency excitatory responses occurred more frequently in the ipsilateral and contralateral sartorius anterior, respectively. After spinal transection, short-latency inhibitory and excitatory responses were similar to both intact conditions, whereas mid- or longer-latency excitatory responses were reduced or abolished. Our results in intact cats and the comparison with spinal-transected cats suggest that the absence of forelimb movements suppresses inputs from supraspinal structures and/or cervical cord that normally contribute to longer-latency reflex responses in hindlimb extensor muscles.NEW & NOTEWORTHY During quadrupedal locomotion, the coordination of forelimb and hindlimb movements involves central circuits and somatosensory feedback. To demonstrate how forelimb movement affects hindlimb cutaneous reflexes during locomotion, we stimulated the superficial peroneal nerve in intact cats during quadrupedal and hindlimb-only locomotion as well as in spinal-transected cats during hindlimb-only locomotion. We show that forelimb movement influences the modulation of hindlimb cutaneous reflexes, particularly the occurrence of long-latency reflex responses.

Changes in intra- and interlimb reflexes from hindlimb cutaneous afferents after staggered thoracic lateral hemisections during locomotion in cats.

When the foot dorsum contacts an obstacle during locomotion, cutaneous afferents signal central circuits to coordinate muscle activity in the four limbs. Spinal cord injury disrupts these interactions, impairing balance and interlimb coordination. We evoked cutaneous reflexes by electrically stimulating left and right superficial peroneal nerves before and after two thoracic lateral hemisections placed on opposite sides of the cord at 9- to 13-week interval in seven adult cats (4males and 3 females). We recorded reflex responses in ten hindlimb and five forelimb muscles bilaterally. After the first (right T5-T6) and second (left T10-T11) hemisections, coordination of the fore- and hindlimbs was altered and/or became less consistent. After the second hemisection, cats required balance assistance to perform quadrupedal locomotion. Short-latency reflex responses in homonymous and crossed hindlimb muscles largely remained unaffected after staggered hemisections. However, mid- and long-latency homonymous and crossed responses in both hindlimbs occurred less frequently after staggered hemisections. In forelimb muscles, homolateral and diagonal mid- and long-latency response occurrence significantly decreased after the first and second hemisections. In all four limbs, however, when present, short-, mid- and long-latency responses maintained their phase-dependent modulation. We also observed reduced durations of short-latency inhibitory homonymous responses in left hindlimb extensors early after the first hemisection and delayed short-latency responses in the right ipsilesional hindlimb after the first hemisection. Therefore, changes in cutaneous reflex responses correlated with impaired balance/stability and interlimb coordination during locomotion after spinal cord injury. Restoring reflex transmission could be used as a biomarker to facilitate locomotor recovery. KEY POINTS: Cutaneous afferent inputs coordinate muscle activity in the four limbs during locomotion when the foot dorsum contacts an obstacle. Thoracic spinal cord injury disrupts communication between spinal locomotor centres located at cervical and lumbar levels, impairing balance and limb coordination. We investigated cutaneous reflexes during quadrupedal locomotion by electrically stimulating the superficial peroneal nerve bilaterally, before and after staggered lateral thoracic hemisections of the spinal cord in cats. We showed a loss/reduction of mid- and long-latency responses in all four limbs after staggered hemisections, which correlated with altered coordination of the fore- and hindlimbs and impaired balance. Targeting cutaneous reflex pathways projecting to the four limbs could help develop therapeutic approaches aimed at restoring transmission in ascending and descending spinal pathways.

Viability leads to the emergence of gait transitions in learning agile quadrupedal locomotion on challenging terrains

Quadruped animals are capable of seamless transitions between different gaits. While energy efficiency appears to be one of the reasons for changing gaits, other determinant factors likely play a role too, including terrain properties. In this article, we propose that viability, i.e., the avoidance of falls, represents an important criterion for gait transitions. We investigate the emergence of gait transitions through the interaction between supraspinal drive (brain), the central pattern generator in the spinal cord, the body, and exteroceptive sensing by leveraging deep reinforcement learning and robotics tools. Consistent with quadruped animal data, we show that the walk-trot gait transition for quadruped robots on flat terrain improves both viability and energy efficiency. Furthermore, we investigate the effects of discrete terrain (i.e., crossing successive gaps) on imposing gait transitions, and find the emergence of trot-pronk transitions to avoid non-viable states. Viability is the only improved factor after gait transitions on both flat and discrete gap terrains, suggesting that viability could be a primary and universal objective of gait transitions, while other criteria are secondary objectives and/or a consequence of viability. Moreover, our experiments demonstrate state-of-the-art quadruped robot agility in challenging scenarios.

Quadrupedal Locomotion in an Energy-efficient Way Based on Reinforcement Learning

Quadrupedal Locomotion in an Energy-efficient Way Based on Reinforcement Learning

From such great heights: The effects of substrate height and the perception of risk on lemur locomotor mechanics.

An accident during arboreal locomotion can lead to risky falls, but it remains unclear that the extent to which primates, as adept arborealists, change their locomotion in response to the perceived risk of moving on high supports in the tree canopy. By using more stable forms of locomotion on higher substrates, primates might avoid potentially fatal consequences. Using high-speed cameras, we recorded the quadrupedal locomotion of four wild lemur species-Eulemur rubriventer, Eulemur rufifrons, Hapalemur aureus, and Lemur catta (N = 113 total strides). We quantified the height, diameter, and angular orientation of locomotor supports using remote sensors and tested the influence of support parameters on gait kinematics, specifically predicting that in response to increasing substrate height, lemurs would decrease speed and stride frequency, but increase stride length and the mean number of supporting limbs. Lemurs did not adjust stride frequency on substrates of varying height. Adjustments to speed, stride length, and the mean number of supporting limbs in response to varying height often ran counter to predictions. Only E. rubriventer decreased speed and increased the mean number of supporting limbs on higher substrates. Results suggest that quadrupedal walking is a relatively safe form of locomotion for lemurs, requiring subtle changes in gait to increase stability on higher-that is, potentially riskier-substrates. Continued investigation of the impact of height on locomotion will be important to determine how animals assess risk in their environment and how they choose to use this information to move more safely.

Ecological and phylogenetic influences on limb joint kinematics in wild primates

Abstract Arboreal locomotion is precarious and places multiple challenges upon stability. Studies have shown that captive primates respond to narrower and steeper supports by flexing limb joints and adopting a compliant gait. We tested whether these same kinematic responses are adopted by wild primates freely ranging over a variety of supports in their natural habitats. We recorded five species of platyrrhines, five species of catarrhines, and four species of strepsirrhines with modified GoPro cameras and used remote measurement to quantify substrate characteristics. Video images were imported into ImageJ to measure the angular kinematics of limb joints during quadrupedal locomotion on a variety of arboreal supports. We statistically tested for associations between joint posture and substrate characteristics, and then disentangled the influence of phylogeny and substrate on limb joint kinematics using variation partitioning and redundancy analysis. Our results partially confirm previous kinematic studies and suggest variation in support orientation, more than diameter or compliance, influences quadrupedal gait kinematics. Phylogenetic relatedness explained more variation in the data than substrate properties. This suggests primates either prospectively choose relatively ‘safe’ substrates for locomotion, or that they possess locomotor adaptations independent of limb joint kinematics per se to overcome the challenges of the precarious arboreal environment.

Variation of thoracolumbar vertebral morphology in anthropoid primates.

Morphological variation among extant primates in the lumbar vertebral column is well studied. However, knowledge concerning the thoracic spine, an important region responsible for supporting and facilitating movement in the upper trunk, remains relatively scarce. Consequently, our comprehension of the functional differentiation exhibited throughout the thoracolumbar vertebral column among various primate species remains constrained. In this study, we examined patterns of morphological variation in the thoracolumbar vertebral column of extant hominoids, cercopithecoids, and Ateles. We collected external shape data on 606 thoracic and lumbar vertebrae from Homo sapiens, Pan troglodytes, Hylobates lar, Macaca fuscata, Chlorocebus aethiops, Colobus guereza, Ateles geoffroyi, and A. belzebuth. Forty-four landmarks were obtained on the three-dimensional surface. Geometric morphometrics was used to quantify the centroid size and variation of the shapes of thoracic and lumbar vertebrae. Cercopithecoids exhibited greater variation in the size and shape of their thoracic and lumbar vertebrae compared to hominoids and Ateles. Although many vertebral features contributed to the observed variation throughout the thoracolumbar vertebral column within the taxon, the transverse and spinous processes exhibited relatively major contributions. Our results suggest that quadrupedal locomotion requires the functional differentiation between thoracic and lumbar vertebrae, and for hominoids, functional adaptation to orthograde posture necessitates a relatively more uniform shape of thoracic and lumbar vertebrae.

Free Gait Generation of Quadruped Robots via Impulse-Based Feasibility Analysis

Online gait adaptation is crucial for improving the dynamic performance of quadruped locomotion systems, while current approaches often adopt the predefined periodic gait pattern. This article proposes a free gait generation algorithm that only takes the robot state as input. Specifically, we introduce the feasible impulse polytope, which takes into account both linear and angular momentum impulses acting on the body in a prediction horizon. This naturally leads us to formulate a leg capability metric related to the effect of take-off and touch-down on the body motion. Then, gait sequence, take-off timing, and touch-down location can be automatically adjusted online as long as a metric threshold is given. To cope with rough terrain, a series of quadratic programming problems are established for online pose optimization under mild assumptions. Furthermore, we fully integrate the proposed algorithms with the robot control and estimation framework for real-time implementation. We first validate our approach with the quadruped robot SCIT-Dog through locomotion with speed changes, on stairs and slopes, and under lateral disturbances. Besides, a push-recovery experiment is established to show the superiority of the proposed approach over the baseline method with prespecified gait patterns. Experiment results verify the ability of the proposed algorithms to achieve autonomous gait transitions in response to various emergencies.

Energy Consumption Minimization of Quadruped Robot Based on Reinforcement Learning of DDPG Algorithm

Energy consumption is one of the most critical factors in determining the kinematic performance of quadruped robots. However, existing research methods often encounter challenges in quickly and efficiently reducing the energy consumption associated with quadrupedal robotic locomotion. In this paper, the deep deterministic policy gradient (DDPG) algorithm was used to optimize the energy consumption of the Cyber Dog quadruped robot. Firstly, the kinematic and energy consumption models of the robot were established. Secondly, energy consumption was optimized by reinforcement learning using the DDPG algorithm. The optimized plantar trajectory was then compared with two common plantar trajectories in simulation experiments, with the same period and the number of synchronizations but varying velocities. Lastly, real experiments were conducted using a prototype machine to validate the simulation data. The analysis results show that, under the same conditions, the proposed method can reduce energy consumption by 7~9% compared with the existing optimal trajectory methods.

Quadrupedal locomotion in Uner Tan syndrome: A neurological viewpoint

Quadrupedal locomotion in Uner Tan syndrome: A neurological viewpoint