Quadruped Walking Research Articles

Reevaluating the energy cost in locomotion: quadrupedal vs. bipedal walking in humans

This study examines the energy expenditure and physiological responses associated with short-term quadrupedal locomotion compared to bipedal walking in humans. It aims to support evolutionary theory and explore quadrupedal locomotion's potential for enhancing fitness and health. In a randomized crossover design, twelve participants performed quadrupedal and bipedal walking on a treadmill at identical speeds. Physiological responses, including energy expenditure, carbohydrate oxidation rates, respiratory rate, and heart rate, were measured during both forms. Quadrupedal walking significantly increased total energy expenditure by 4.15 Kcal/min [95% CI, 3.11 - 5.19 Kcal/min], due to a rise in carbohydrate oxidation of 1.70 g/min [95% CI, 1.02 - 2.24 g/min]. It also increased respiratory and heart rates, indicating higher metabolic demands. The exercise mainly activated upper limb muscles and the gluteus maximus in the lower limbs. Ten minutes of quadrupedal walking at the same speed as bipedal walking resulted in a 254.48% increase in energy consumption. This simple form of locomotion offers a strategy for enhancing physical activity and supports the idea that energy optimization influenced the evolution of efficient bipedal locomotion.

Night life: Positional behaviors and activity patterns of the Neotropical kinkajou, Potos flavus (Carnivora, Procyonidae)

AbstractStudying positional behaviors is important for understanding how animals interact with their immediate environment. This is particularly important in arboreal species since arboreal milieus are primarily characterized by three‐dimensional problems that arboreal species must overcome to efficiently access resources. Similarly, a fundamental aspect of an animal's ecology is its daily activity pattern. This information is important for understanding the basic ecology of animal species and their eco‐evolutionary dynamics. This study sought to understand the habitat use and nocturnal lifestyle of the highly arboreal kinkajou (Potos flavus) by documenting variation in positional behaviors and activity patterns using 2223 photographs obtained from 27 camera traps in French Guiana. Data were analyzed using descriptive statistics, Kernel density estimation (KDE), and Gantt charts. Our results indicate that kinkajous show a strictly nocturnal activity pattern beginning from 19:00 h to 05:57 h, with peak active periods between 01:00 h and 02:00 h. The most frequent activities were scanning (48.33%) and traveling (47.13%). Quadrupedal walking (95.43%) was the main locomotor behavior during traveling. However, when crossing gaps between two substrates, kinkajous would either bridge (42.22%), leap (33.33%), or drop (26.67%) across gaps. Inactive periods were characterized by grooming (77.32%) and resting (27.84%) while mostly assuming a sitting (90.67%) or a catlike body curl posture (92.59%), interchangeably. This study highlights the broad array of positional behaviors displayed by kinkajous, further providing information to understand its basic ecology and eco‐evolutionary dynamics.

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.

Position Tracking Control of 4-DOF Underwater Robot Leg Using Deep Learning

This paper presents a novel hybrid control method for position tracking of an underwater quadruped walking robot. The proposed approach combines an existing position-tracking control method with a deep-learning neural network. The neural network compensates for non-linear dynamic characteristics, such as the effect of fluid, without relying on mathematical modeling. To achieve this, a Multi-Layer Perceptron neural network is designed to analyze joint torque in relation to the joint angle and angular velocity of the robot, as well as the position and orientation of the foot tip and environmental data. The improvement in tracking control performance is evaluated using a 4-DOF underwater robot leg. For the neural network design, position tracking control data, including dynamic characteristics, were collected through position command-based position tracking control. Afterward, a learning model was constructed and trained to predict joint torque related to the robot’s motion and posture. This learning process incorporates non-linear dynamic characteristics, such as joint friction and the influence of fluid, in the joint torque prediction. The proposed method is then combined with conventional task-space PD control to perform position-tracking control with enhanced performance. Finally, the proposed method is evaluated using the underwater robot leg and compared to a single task-space PD controller. The proposed method demonstrates higher position accuracy with similar joint torque output, thereby increasing compliance and tracking performance simultaneously.

Beakiation: how a novel parrot gait expands the locomotor repertoire of living birds.

Occupation of arboreal habitats poses myriad locomotor challenges, driving both anatomical and behavioural innovations across various tetrapod lineages. Here, we report and biomechanically assess a novel, beak-driven locomotor mode-'beakiation'-by which parrots advance along the underside of narrow arboreal substrates. Using high-speed videography and kinetic analyses, we describe the limb loading patterns and pendular mechanics of beakiation, and compare the biomechanical characteristics of this gait with other suspensory behaviours (namely, forelimb-driven brachiation and inverted quadrupedal walking). We report that the parrot beak experiences comparable force magnitudes (approx. 150% body weight in the normal plane; approx. 50% body weight in the fore-aft plane) to the forelimbs of brachiating primates. Parrot beakiation is also characterized by longer-than-expected pendular periods, similar to observations of gibbon brachiation. However, in terms of mechanical energy recovery, beakiation is typified by lower levels of energetic recovery than brachiating specialists: a product of its slower, more careful nature. The observation of this novel behaviour-which adds to a growing base of literature regarding beak-assisted locomotor strategies in birds-highlights the extraordinary behavioural plasticity of birds, the functional versatility of the avian beak, and the difficulties in reconstructing an animal's locomotor repertoire from morphological characteristics alone.

Sim-to-Real: A Performance Comparison of PPO, TD3, and SAC Reinforcement Learning Algorithms for Quadruped Walking Gait Generation

Sim-to-Real: A Performance Comparison of PPO, TD3, and SAC Reinforcement Learning Algorithms for Quadruped Walking Gait Generation

Automated Point Cloud Registration Approach Optimized for a Stop-and-Go Scanning System.

The latest advances in mobile platforms, such as robots, have enabled the automatic acquisition of full coverage point cloud data from large areas with terrestrial laser scanning. Despite this progress, the crucial post-processing step of registration, which aligns raw point cloud data from separate local coordinate systems into a unified coordinate system, still relies on manual intervention. To address this practical issue, this study presents an automated point cloud registration approach optimized for a stop-and-go scanning system based on a quadruped walking robot. The proposed approach comprises three main phases: perpendicular constrained wall-plane extraction; coarse registration with plane matching using point-to-point displacement calculation; and fine registration with horizontality constrained iterative closest point (ICP). Experimental results indicate that the proposed method successfully achieved automated registration with an accuracy of 0.044 m and a successful scan rate (SSR) of 100% within a time frame of 424.2 s with 18 sets of scan data acquired from the stop-and-go scanning system in a real-world indoor environment. Furthermore, it surpasses conventional approaches, ensuring reliable registration for point cloud pairs with low overlap in specific indoor environmental conditions.

Analytical solution to a time-varying LIP model for quadrupedal walking on a vertically oscillating surface

This paper introduces an analytically tractable and computationally efficient model for legged robot dynamics during locomotion on a dynamic rigid surface (DRS), along with an approximate analytical solution and a real-time walking pattern generator synthesized based on the model and solution. By relaxing the static-surface assumption, we extend the classical, time-invariant linear inverted pendulum (LIP) model for legged locomotion on a static surface to dynamic-surface locomotion, resulting in a time-varying LIP model termed as “DRS-LIP”. Sufficient and necessary stability conditions of the time-varying DRS-LIP model are obtained based on the Floquet theory. This model is also transformed into Mathieu’s equation to derive an approximate analytical solution that provides reasonable accuracy with a relatively low computational cost. Using the extended model and its solution, a walking pattern generator is developed to efficiently plan physically feasible trajectories for quadrupedal walking on a vertically oscillating surface. Finally, simulations and hardware experiments from a Laikago quadrupedal robot walking on a pitching treadmill (with a maximum vertical acceleration of 1 m/s2) confirm the accuracy and efficiency of the proposed analytical solution, as well as the efficiency, feasibility, and robustness of the pattern generator, under various surface motions and gait parameters.

Multi-Modal Mobility Morphobot (M4) with appendage repurposing for locomotion plasticity enhancement

Robot designs can take many inspirations from nature, where there are many examples of highly resilient and fault-tolerant locomotion strategies to navigate complex terrains by recruiting multi-functional appendages. For example, birds such as Chukars and Hoatzins can repurpose wings for quadrupedal walking and wing-assisted incline running. These animals showcase impressive dexterity in employing the same appendages in different ways and generating multiple modes of locomotion, resulting in highly plastic locomotion traits which enable them to interact and navigate various environments and expand their habitat range. The robotic biomimicry of animals’ appendage repurposing can yield mobile robots with unparalleled capabilities. Taking inspiration from animals, we have designed a robot capable of negotiating unstructured, multi-substrate environments, including land and air, by employing its components in different ways as wheels, thrusters, and legs. This robot is called the Multi-Modal Mobility Morphobot, or M4 in short. M4 can employ its multi-functional components composed of several actuator types to (1) fly, (2) roll, (3) crawl, (4) crouch, (5) balance, (6) tumble, (7) scout, and (8) loco-manipulate. M4 can traverse steep slopes of up to 45 deg. and rough terrains with large obstacles when in balancing mode. M4 possesses onboard computers and sensors and can autonomously employ its modes to negotiate an unstructured environment. We present the design of M4 and several experiments showcasing its multi-modal capabilities.

Electric Epidural Stimulation of the Spinal Cord of the Decerebrated Rat

Decerebrated animals are often used in experimental neurophysiology to study multilevel physiological processes. The model of a decerebrated cat is traditionally used to study locomotion in acute experiments. We wondered if it would be possible to replace it with electrical epidural stimulation of the spinal cord with a decerebrated rat model. On an acute preparation of 16 Wistar rats decerebrated at the precollicular level, the tonic muscles activity, muscles evoked potentials and the possibility of inducing locomotion during electrical epidural stimulation of the spinal cord, were studied. Histological control of the level of decerebration was performed in 10 rats. Quadrupedal walking was induced in five animals, bipedal hindlimb walking – in one animal; the parameters of the evoked locomotion do not depend on the substantia nigra degree of damage. The tonic activity and the amplitude of the sensory component of the evoked potential of the hindlimb muscles (mm. tibialis anterior and gastrocnemius medialis) depend on the rostrocaudal level of decerebration – they are higher when the substantia nigra is damaged. Thus, the model under consideration makes it possible to successfully study muscle tonic activity and evoked muscle potentials; however, the use of this model in the study of controlled locomotion requires additional research.

BIM-based scan planning for scanning with a quadruped walking robot

Scan positioning for documenting the geometry of an existing building still relies on the experience of an expert surveyor. Therefore, it is important to utilize optimal scan positioning for an automated scanning process with an autonomous robot platform. This study presents an automated framework to determine the optimal scan planning for a stop-and-go mapping procedure with a quadruped walking robot based on BIM. The proposed framework comprises four main phases: Generation of scan-position candidates; optimal scan positioning; ordering of the optimal scan positions; data collection with an autonomous scanning system. The experimental results showed that the proposed framework presented better performance than those of the conventional approaches. Furthermore, the number of scan positions and the scan operation time were significantly reduced compared with manual scanning by skilled surveyors in real-world indoor environments. A future work will focus on an automated registration process and enhancement of computational performance.

Description of the Pliocene marsupial Ambulator keanei gen. nov. (Marsupialia: Diprotodontidae) from inland Australia and its locomotory adaptations.

Diprotodontids were the largest marsupials to exist and an integral part of Australian terrestrial ecosystems until the last members of the group became extinct approximately 40 000 years ago. Despite the frequency with which diprotodontid remains are encountered, key aspects of their morphology, systematics, ecology and evolutionary history remain poorly understood. Here we describe new skeletal remains of the Pliocene taxon Zygomaturus keanei from northern South Australia. This is only the third partial skeleton of a late Cenozoic diprotodontid described in the last century, and the first displaying soft tissue structures associated with footpad impressions. Whereas it is difficult to distinguish Z. keanei and the type species of the genus, Z. trilobus, on dental grounds, the marked cranial and postcranial differences suggest that Z. keanei warrants genus-level distinction. Accordingly, we place it in the monotypic Ambulator gen. nov. We, also recognize the late Miocene Z. gilli as a nomen dubium. Features of the forelimb, manus and pes reveal that Ambulator keanei was more graviportal with greater adaptation to quadrupedal walking than earlier diprotodontids. These adaptations may have been driven by a need to travel longer distances to obtain resources as open habitats expanded in the late Pliocene of inland Australia.

Personality expression in cartoon animal characters using Sasang typology

AbstractThe movement style is an adequate descriptor of different personalities. While many studies investigate the relationship between apparent personality and high‐level motion qualities in humans, similar research for animal characters still needs to be done. The variety in animals' skeletal configurations and texture complicates their pose estimation process. Our affect analysis framework includes a workflow for pose extraction in animal characters and a parameterization of the high‐level animal motion descriptors inspired by Laban movement analysis. Using a data set of quadruped walk cycles, we prove the display of typologies in cartoon animal characters, reporting the point‐biserial correlation between our motion parameters and the Sasang categories that reflect different personalities.

Time Efficiency Improvement in Quadruped Walking with Supervised Training Joint Model

To generate stable walking of a quadruped, the complexity of the configuration of the robot involves a significant amount of optimization that decreases to its time efficiency. To address this issue, a machine learning method was used to build a simplified control policy using joint models for the supervised training of quadruped robots. This study considered 12 joints for a four-legged robot, and each joint value was determined based on the conventional method of walking simulation and prepossessed, equaling 2508 sets of data. For data training, the multilayer perceptron model was used, and the optimized number of epochs used to train the model was 5000. The trained models were implemented in robot walking simulations, and they improved performance with an average distance error of 0.0719 m and a computational time as low as 91.98 s.

Trunk viscoelasticity and gait stability in quadruped walking

Trunk viscoelasticity and gait stability in quadruped walking

A Comparison of PPO, TD3 and SAC Reinforcement Algorithms for Quadruped Walking Gait Generation

A Comparison of PPO, TD3 and SAC Reinforcement Algorithms for Quadruped Walking Gait Generation

Design of a Flexure-Jointed Linkage in a Quadruped Walking Robot

Flexure-jointed linkages (FJLs) have distinct advantages, such as ease of manufacturing and assembly, no backlash, and light weight designs, over their rigid counterparts. However, the synthesis and analysis of FJLs are more complicated, especially when the compliant flexures have large deflections. This article addresses the optimal design of a large-deflection FJL, which is used as the leg of a compliant quadruped robot. The proposed FJL originates from a rigid six-bar linkage to mimic the foot path of walking mammals by replacing the passive revolute joints with two-segment combined flexible beams. Its kinematic and strain energy models are derived and verified by numerical simulations. Subjecting to material failures and geometrical constraints, the optimization of the FJL is carried out by minimizing the path deviation and strain energy to reduce needed input power, leading to the development of a quadruped walking robot. Experimental tests on the output path of the FJL and the motion capability of the robot are implemented. The results demonstrate the effectiveness of the derived models in predicting the deflections of the FJL and the feasibility of applying compliant linkages for legged robots.

Competing Models of Work in Quadrupedal Walking: Center of Mass Work is Insufficient to Explain Stereotypical Gait.

The walking gaits of cursorial quadrupedal mammals tend to be highly stereotyped as a four-beat pattern with interspersed periods of double and triple stance, often with double-hump ground reaction force profiles. This pattern has long been associated with high energetic economy, due to low apparent work. However, there are differing ways of approximating the work performed during walking and, consequently, different interpretations of the primary mechanism leading to high economy. A focus on Net Center of Mass (COM) Work led to the claim that quadrupedal walking is efficient because it effectively trades potential and kinetic energy of the COM. Individual Limbs COM Work instead focuses on the ability of the limbs to manage the trajectory of the COM to limit energetic losses to the ground (“collisions”). By focusing on the COM, both these metrics effectively dismiss the importance of rotation of the elongate quadrupedal body. Limb Extension Work considers work required to extend and contract each limb like a strut, and accounts for the work of body pitching. We tested the prescriptive ability of these approximations of work by optimizing them within a quadrupedal model with two approximations of the body as a point-mass or a rigid distributed mass. Perfect potential-kinetic energy exchange of the COM was possible when optimizing Net COM Work, resulting in highly compliant gaits with duty factors close to one, far different than observed mammalian gaits. Optimizing Individual Limbs COM Work resulted in alternating periods of single limb stance. Only the distributed mass model, with Limb Extension Work as the cost, resulted in a solution similar to the stereotypical mammalian gait. These results suggest that maintaining a near-constant limb length, with distributed contacts, are more important mechanisms of economy than either transduction of potential-kinetic energy or COM collision mitigation for quadrupedal walking.

Testing mechanisms for weight support distribution during inverted quadrupedalism in primates.

A key characteristic of primate above-branch arboreal locomotion is hindlimb-biased weight support, subverting the typical mammalian condition in which the majority of the body weight is supported by the forelimb. This shift is thought to reflect an adaptation toward the arboreal niches exploited by early primates. However, above-branch quadrupedalism represents only one locomotor mode employed by primates in arboreal contexts. Inverted quadrupedal gaits, in which primates are suspended beneath branches by their hands and feet, have been documented in more than 50primate taxa. This gait is characterized by a return to forelimb-biased weight distributions and a transition from peak vertical forces being greatest in the hindlimb to being greatest in the forelimb, which may occur to protect the hindlimb from high magnitudes of tensile loading when inverted. In this study, we compare kinetic and kinematic data during upright and inverted quadrupedalism in Lemur catta, Varecia variegata, Cebus capucinus, and Saimiri sciureus. These data are referenced against a classical inverted quadrupedal model: the two-toed sloth (Choloepus didactylus). Our findings show that inverted quadrupedalism in primates is differentiated from above-branch quadrupedalism by increases in forelimb weight support, forelimb contact times, and both forelimb and hindlimb joint excursions. Previously postulated biomechanical models outlining mechanisms relating to the control of weight support during upright walking do not translate well to inverted quadrupedal walking. We suggest that inverted primates may simply be adopting basal neuromuscular gait characteristics and applying them facultatively to this infrequent locomotor behavior.

The impact of walking posture on trabecular structure in the femur of Rattus norvegicus

Bone responds to mechanical loads through growth. This response to external loading has been important for understanding skeletal form and function relationships. However, uncertainty still exists regarding how different locomotor behaviors, (e.g., bipedalism, quadrupedalism) are reflected in bone morphology. This study assesses the effects of locomotor posture on femoral bone structure in a rodent model (Rattus norvegicus). The study individuals come from a previously‐executed experiment (Foster, 2019) that utilized a treadmill‐mounted harness to induce bipedal walking postures in rats over 12‐weeks. The sample includes individuals from two experimental groups plus a control: bipedal walking, quadrupedal walking, and no exercise controls. Proximal and distal femora were microCT scanned at 20µm and trabecular bone volume fraction (BV/TV) and degree of anisotropy (DA) were analyzed and compared among groups to assess the impacts of differences in hip loading. In the proximal femur, the bipedal group had higher DA inferior to the neck and greater trochanter than the quadrupedal group, suggesting more unidirectional loading in bipeds. However, the quadrupedal group had greater BV/TV throughout the proximal metaphysis; particularly at the greater trochanter, which may be due to a higher demand for hip extension. In the distal femur, the bipedal group had higher mean BV/TV (0.39) when compared to the quadrupedal group (0.36), with a larger concentration of BV/TV in the medial condyle. These results suggest that the femoral epiphyses are responsive to changes in hip postural angle due to locomotion, however cortical bone structure and a larger sample size may be more informative.