Biomechanical evolution of solid bones in large animals: a microanatomical investigation

International audienc

BIOMECHANICS OF TERRESTRIAL LOCOMOTION: ASYMMETRIC OCTOPEDAL AND QUADRUPEDAL GAITS

The main goal of this dissertation is to investigate the biomechanics of octopedal and quadrupedal locomotion in terrestrial animals, common determinants, advantages and limits, in particular of the asymmetric gaits. Two different approach have been chosen: i) a kinematic study of a terrestrial spider, the Brazilian giant tawny-red tarantula, an octopods predator species that hide in burrows, ambush and rapidly bounce the prey with a sprint, and ii) a comparative study of the two types of gallop of the cursorial terrestrial mammals. Eight-legs locomotion has been one of the first travelling modes on land, and spiders display one of the most versatile locomotor repertoire: they move at slow and fast speed, forward-backward-sideways, they climb and even jump, both on firm terrain and from the water surface. Spiders can walk in the two senses at the same speed, just by reversing their diagonal footfall scheme. They turn on the spot like an armoured tank, with opposite direction of the two treads of limbs. Also, the high number of limbs ensures an increased locomotor versatility on uneven and rough terrains, particularly in the likely unawareness of each endpoint location on the ground. The aims of this first part were: i) identifying the principal octopod gaits, ii) calculating the mechanical external and internal work at the different speeds/gaits, iii) assessing any tendency to exchange potential and kinetic energy of the body centre of mass, as in pendulum-like gaits, and iv) evaluating how spiders\u2019 mechanical performance and variables allometrically compare to other species. Another question was: can the octopod gaits be considered as different combinations of two quadrupeds\u2019 locomotion? In this investigation we used inverse dynamics to study the locomotor performance of a terrestrial spider. 9 reflective markers have been placed on the tip of the 8 legs and on the cephalothorax, and their position recorded at a frequency of 50 Hz and digitized through a motion analysis system. Data have been processed using LabView (National Instruments, USA) specific development. The 3D trajectories of the body centre of mass in local coordinates, as during locomotion on a treadmill, have been calculated by applying a mathematical method based on the Fourier analysis of the three coordinates of the centre of mass (COM) over time. Two main gaits, a slow and a fast one characterised by distinctive 3D trajectories of COM, have been identified. The calculated total mechanical work (= external+internal) and metabolic data from the literature allowed estimating the locomotion efficiency of this species, which resulted less than 4%. Octopod gait pattern due to alternating limb support, which generates asymmetrical COM trajectories and a small but consistent energy transfer between potential and kinetic energies of COM, can be considered as formed by two subsequent quadrupeds, where the first two pairs of feet (1 and 2) are the fore and the hind feet of the first quadruped, and the third and fourth pairs are the fore and hind feet of the second quadruped. The two quadrupeds are almost in phase, being the first and third pairs synchronised in their movements as well as the second and fourth. Octopedal locomotion exhibits two main gaits, neither of which incorporating a flight phase, characterised by a consistent limb pattern and a small but remarkable energy recovery index. Gallop has been chosen as model of asymmetric cursorial locomotion in quadrupeds. In transverse gallop the placement of the second hind foot is followed by that of the contralateral forefoot, while in rotary gallop is followed by the ipsilateral forefoot, and the sequence of footfalls appears to rotate around the body. The question are: why two models of gallop? Are they specie-specific? Which are the biomechanical determinants of the choice between transverse and rotary gallop? Aims of this part of the research were: i) assess, when possible, the specie-specificity of the gallop type in different cursorial mammal species, ii) phylogenetically classify the investigated species, iii) Made a comparative analysis based on morphological, physiological and environmental differences. 351 filmed sequences have been analysed to assess the gallop type of 89 investigated mammal species belonging to Carnivora, Artiodactyla and Perissodactyla orders. 23 biometrical, ecological and physiological parameters have been collected for each species both from literature data and from experimental measures. Most of the species showed only one kind of gallop: transverse (42%) or rotary (39%), while some species performed rotary gallop only at high speed (19%). In a multivariate factorial analysis the first principal component (PC), which accounted for 40% of the total variance, was positively correlated to the relative speed and negatively correlated to size and body mass. The second PC was correlated to the ratio between autopodial and zygopodial limb segments. Large size and longer proximal limb segments resulted associated to transverse gallop, while rotary and speed dependent species showed higher metacarpus/humerus and metatarsus/femur length ratio and faster relative speeds. The maximum angular excursion resulted proportional to the maximum Froude number, and significantly higher in rotary galloper. The gait pattern analysis provided significant differences between transverse and rotary gallop in fore and hind duty factor, and in duration of the fore contact. Our results assessed that a typical gallop gait is adopted by a large number of mammal species, and indicated that the gallop pattern depends on diverse environmental, morphometrical and biomechanical characters. Even if mammals and spiders can be considered far and different worlds, we can recognize common pattern of locomotion. The quadruped gaits have been modelled as the combination of two biped gaits with some difference in the phase-cycle, in the same way, we described the octopods gaits as the combination of two quadruped gaits in series. In conclusion, this work shed light on some aspects of octopedal and quadrupedal asymmetric gaits, opening to the raising of new questions and new perspective of research

Master of Science

thesisThis research studies the passive dynamics of an under-actuated trotting quadruped. The goal of this project is to perform three-dimensional (3D) dynamic simulations of a trotting quadruped robot to find proper leg configurations and stiffness range, in order to achieve stable trotting gait. First, a 3D simulation framework that includes all the six degrees of freedom of the body is introduced. Directionally compliant legs together with different leg configurations are employed to achieve passive stability. Compliant legs passively support the body during stance phase and during flight phase a motor is used to retract the legs. Leg configurations in the robot's sagittal and frontal plane are introduced. Numerical experiments are conducted to search the design space of the leg, focusing on increasing the passive stability of the robot. Increased stability is defined as decreased pitching, rolling, and yawing motion of the robot. The results indicate that optimized leg parameters can guarantee passive stable trotting with reduced roll, pitch, and yaw. Studies suggest that a quadruped robot with compliant legs is dynamically stable while trotting. Results indicate that the robot based on a biological model (i.e., caudal inclination of humeri and cranial inclination of femora) has the best performance. Stiff springs at hips and shoulders, soft spring at knees and elbows, and stiff springs at ankles and wrists are recommended. The results of this project provide a conceptual framework for understanding the movements of a trotting quadruped

Minimalist analogue robot discovers animal-like walking gaits

Robots based on simplified or abstracted biomechanical concepts can be a useful tool for investigating how and why animals move the way they do. In this paper we present an extremely simple quadruped robot, which is able to walk with no form of software or controller. Instead, individual leg movements are triggered directly by switches on each leg which detect leg loading and unloading. As the robot progresses, pitching and rolling movements of its body result in a gait emerging with a consistent leg movement order, despite variations in stride and stance time. This gait has similarities to the gaits used by walking primates and grazing livestock, and is close to the gait which was recently theorised to derive from animal body geometry. As well as presenting the design and construction of the robot, we present experimental measurements of the robot's gait kinematics and ground reaction forces determined using high speed video and a pressure mat, and compare these to gait parameters of animals taken from literature. Our results support the theory that body geometry is a key determinant of animal gait at low speeds, and also demonstrate that steady state locomotion can be achieved with little to no active control

Estimating sauropod body mass and gait : by the analysis of recent and fossil tetrapod tracks with photogrammetry and soil mechanics

This dissertation presents an analysis of recent and fossil tracks with quantitative and in-terdisciplinary methods for estimating the body mass and locomotion of a sauropod trackmaker. By employing methods from natural and engineering sciences, this research demonstrates that interdisciplinary research on tetrapod tracks can provide insights beyond conventional paleontological research. The novelty in this dissertation is that it brings as-pects from traditional vertebrate ichnology together with modern methods and considera-tions from biomechanics and soil mechanics to gain additional information about sauropod paleobiology. Track and trackways are structures left behind by an animal. Their formation is dependent on the substrate (i.e., soil or sediment) that contains the tracks, as well as the anatomy and locomotion of the trackmaker. Fossil tracks can provide a great deal of information about the extinct trackmaker, such as type, size, speed, behavior, and even pathologies. Although, it would be intuitive to think that the body mass of the trackmaker can also be determined from tracks, this has not been done before. Particularly, since body mass, which, for example, can reach record-breaking values in the case of the sauropod dinosaurs, is one of the fundamental attributes of any animal. Common mass estimation methods require body fossils for reconstructing density/volume or to make scaling relationships from long bones. However, body fossils are usually not available in most tracksites due to preservation conditions. Thus, estimating the weight of the trackmaker from its tracks, both extant and extinct, is the object of research in this dissertation. For determining the exact geometry and dimensions of both recent and fossil tracks, pre-cise documentation is required. Photogrammetry is a method from geodesy that has proved to be very useful for vertebrate ichnology. It uses digital images to generate three-dimensional (3D) models. The interpretability of these 3D models is improved by the geo-logical method of vertical exaggeration, which stretches the vertical axis of a model to vis-ualize previously unseen structures in the tracks. Applying vertical exaggeration is novel to vertebrate ichnology and reveals important information of the trackmaker from its tracks, such as travel direction and anatomical details of the hands and feet. To test if estimating the weight from fossil tracks is feasible, studying recent trackmakers for calibration is necessary. Elephants are the largest living land animals and often used as living analogs to the extinct sauropod dinosaurs. Elephant footprints are digitized and used as the basis of a numerical simulation (finite element analysis), constrained by the substrate properties. The load required to generate these footprints was reconstructed and the ele-phant’s weight was back calculated. Although, weight estimation for a recent trackmaker is possible with an error of about 15%, careful assessment of the influence of the trackmak-er’s locomotion is also important. For fossil trackmakers, precise evaluation of the locomo-tion, let alone the gait, is difficult to ascertain from tracks. The main gaits, such as walk, trot, pace, and gallop, are determined by studying horses, which make them a prime exam-ple for understanding locomotion from tracks. Together with basic estimations of the trackmaker’s size, it is possible to estimate the gait from tracks. Different gaits also mean varying distribution of the mass among the limbs during locomotion, which is of particular interest for any mass estimation approach on tracks. For instance, the fraction of the weight distributed on the hindlimbs is high when the center of mass of the animal is positioned posteriorly and low when the position of the center of mass is positioned anteriorly. Considering all these influencing factors, mass estimation and reconstruction of movement are possible from recent, as well from fossil tracks. For example, in the case of a 150 million year old sauropod trackway, the mass of the trackmaker was estimated to be about 16 tonnes, which is in good agreement with other mass estimates from body fossils. With these results, this research intends to provide a foundation for future applications of the gait and mass estimation approaches based on tracks, and hopes to inspire others to employ interdisciplinary methods to tetrapod tracks to exploit their, often underestimated, high information content

ロボティクスのための深層強化学習による運動シナジー発現と冗長性定量化に関する研究

Tohoku University林部充宏課

Exploring Passive Dynamics in Legged Locomotion

A common observation among legged animals is that they move their limbs differently as they change their speed. The observed distinct patterns of limb movement are usually referred to as different gaits. Experiments with humans and mammals have shown that switching between different gaits as locomotion speed changes, enables energetically more economical locomotion. However, it still remains unclear why animals with very different morphologies use similar gaits, where these gaits come from, and how they are related. This dissertation approaches these questions by exploring the natural passive dynamic motions of a range of simplified mechanical models of legged locomotion. Recent research has shown that a simple bipedal model with compliant legs and a single set of parameters can match ground reaction forces of both human walking and running. As first contribution of this dissertation, this concept is extended to quadrupeds. A unified model is developed to reproduce many quadrupedal gaits by only varying the initial states of a motion. In addition, the model parameters are optimized to match the experimental data of real horses, as measured by an instrumented treadmill. It is shown that the proposed model is able to not only create similar kinematic motion trajectories, but can also explain the ground reaction forces of real horses moving with different gaits. In order to reveal the mechanical contribution to gaits, the simplistic bipedal and quadrupedal models are then augmented to have passive swing leg motions by including torsional springs at the hip joints. Through a numerical continuation of periodic motions, this work shows that a wide range of gaits emerges from a simple bouncing-in-place motion starting with different footfall patterns. For both, bipedal and quadrupedal models, these gaits arise along one-dimensional manifolds of solutions with varying total energy. Through breaking temporal and spatial symmetries of the periodic motions, these manifolds bifurcate into distinct branches with various footfall sequences. That is, passive gaits are obtained as different oscillatory motions of a single mechanical system with a single set of parameters. By reproducing a variety of gaits as a manifestation of the passive dynamics of unified models, this work provides insights into the underlying dynamics of legged locomotion and may help design of more economical controllers for legged machines.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147585/1/ganzheny_1.pd

Understanding and Improving Locomotion: The Simultaneous Optimization of Motion and Morphology in Legged Robots

There exist many open design questions in the field of legged robotics. Should leg extension and retraction occur with a knee or a prismatic joint? Will adding a compliant ankle lead to improved energetics compared to a point foot? Should quadrupeds have a flexible or a rigid spine? Should elastic elements in the actuation be placed in parallel or in series with the motors? Though these questions may seem basic, they are fundamentally difficult to approach. A robot with either discrete choice will likely need very different components and use very different motion to perform at its best. To make a fair comparison between two design variations, roboticists need to ask, is the best version of a robot with a discrete morphological variation better than the best version of a robot with the other variation? In this dissertation, I propose to answer these type of questions using an optimization based approach. Using numerical algorithms, I let a computer determine the best possible motion and best set of parameters for each design variation in order to be able to compare the best instance of each variation against each other. I developed and implemented that methodology to explore three primary robotic design questions. In the first, I asked if parallel or series elastic actuation is the more energetically economical choice for a legged robot. Looking at a variety of force and energy based cost functions, I mapped the optimal motion cost landscape as a function of configurable parameters in the hoppers. In the best case, the series configuration was more economical for an energy based cost function, and the parallel configuration was better for a force based cost function. I then took this work a step further and included the configurable parameters directly within the optimization on a model with gear friction. I found, for the most realistic cost function, the electrical work, that series was the better choice when the majority of the transmission was handled by a low-friction rotary-to-linear transmission. In the second design question, I extended this analysis to a two-dimensional monoped moving at a forward velocity with either parallel or series elastic actuation at the hip and leg. In general it was best to have a parallel elastic actuator at the hip, and a series elastic actuator at the leg. In the third design question, I asked if there is an energetic benefit to having an articulated spinal joint instead of a rigid spinal joint in a quadrupedal legged robot. I found that the answer was gait dependent. For symmetrical gaits, such as walking and trotting, the rigid and articulated spine models have similar energetic economy. For asymmetrical gaits, such as bounding and galloping, the articulated spine led to significant energy savings at high speeds. The combination of the above studies readily presents a methodology for simultaneously optimizing for motion and morphology in legged robots. Aside from giving insight into these specific design questions, the technique can also be extended to a variety of other design questions. The explorations in turn inform future hardware development by roboticists and help explain why animals in nature move in the ways that they do.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144074/1/yevyes_1.pd

Influence of Compliant Joints in Four-Legged Robots

Legged animals are capable of rapid movements, are efficient from the energy point of view, and are able to adapt their gaits to environmental conditions. Motions like walking, trotting, galloping, and jumping, are difficult to evaluate and replicate due to their being consequences of complex interactions of different systems (such as the musculoskeletal system and the central and peripheral nervous systems, including also the influence of the environment). In this paper, we analyzed the behavior of a four-legged robot constituted by one active DOF in each leg (using commercial servomotors) and one passive DOF in each knee and in the spine (using springs). Our objective was to increase the motion performances of the robot by varying the stiffness of the springs. The results obtained from the simulation underline how the stiffness of the spine influences the performance of the robot by increasing the speed and reducing the energy required by the servomotors

Control of Dynamic Gaits for a Quadrupedal Robot

Quadrupedal animals move through their environments with unmatched agility and grace. An important part of this is the ability to choose between different gaits in order to travel optimally at a certain speed or to robustly deal with unanticipated perturbations. In this paper, we present a control framework for a quadrupedal robot that is capable of locomoting using several gaits. We demonstrate the flexibility of the algorithm by performing experiments on StarlETH, a recently-developed quadrupedal robot. We implement controllers for a static walk, a walking trot, and a running trot, and show that smooth transitions between them can be performed. Using this control strategy, StarlETH is able to trot unassisted in 3D space with speeds of up to 0.7m/s, it can dynamically navigate over unperceived 5-cm high obstacles and it can recover from significant external pushes