System design of a quadrupedal galloping machine

In this paper we present the system design of a machine that we have constructed to study a quadrupedal gallop gait. The gallop gait is the preferred high-speed gait of most cursorial quadrupeds. To gallop, an animal must generate ballistic trajectories with characteristic strong impacts, coordinate leg movements with asymmetric footfall phasing, and effectively use compliant members, all the while maintaining dynamic stability. In this paper we seek to further understand the primary biological features necessary for galloping by building and testing a robotic quadruped similar in size to a large goat or antelope. These features include high-speed actuation, energy storage, on-line learning control, and high-performance attitude sensing. Because body dynamics are primarily influenced by the impulses delivered by the legs, the successful design and control of single leg energetics is a major focus of this work. The leg stores energy during flight by adding tension to a spring acting across an articulated knee. During stance, the spring energy is quickly released using a novel capstan design. As a precursor to quadruped control, two intelligent strategies have been developed for verification on a one-legged system. The Levenberg-Marquardt on-line learning method is applied to a simple heuristic controller and provides good control over height and forward velocity. Direct adaptive fuzzy control, which requires no system modeling but is more computationally expensive, exhibits better response. Using these techniques we have been successful in operating one leg at speeds necessary for a dynamic gallop of a machine of this scale. Another necessary component of quadruped locomotion is high-resolution and high-bandwidth attitude sensing. The large ground impact accelerations, which cause problems for any single traditional sensor, are overcome through the use of an inertial sensing approach using updates from optical sensors and vehicle kinematics

Empirical validation of a spined sagittal-plane quadrupedal model

We document empirically stable bounding using an actively powered spine on the Inu quadrupedal robot, and propose a reduced-order model to capture the dynamics associated with this additional, actuated spine degree of freedom. This model is sufficiently accurate as to roughly describe the robots mass center trajectory during a bounding limit cycle, thus making it a potential option for low dimensional representations of spine actuation in steady-state legged locomotion

Energetics and Passive Dynamics of Quadruped Robot Planar Running Gaits

Quadruped robots find application in military for load carrying over uneven terrain, humanitarian de-mining, and search and rescue missions. The energy required for quadruped robot locomotion needs to be supplied from on-board energy source which can be either electrical batteries or fuels such as gasolene/diesel. The range and duration of missions very much depend on the amount of energy carried, which is highly limited. Hence, energy efficiency is of paramount importance in building quadruped robots. Study of energy efficiency in quadruped robots not only helps in efficient design of quadruped robots, but also helps understand the biomechanics of quadrupedal animals. This thesis focuses on the energy efficiency of planar running gaits and presents: (a) derivation of cost of transport expressions for trot and bounding gaits, (b) advantages of articulated torso over rigid torso for quadruped robot, (c) symmetry based control laws for passive dynamic bounding and design for inherent stability, and (d) effect of asymmetry in zero-energy bounding gaits

Thrust control, stabilization and energetics of a quadruped running robot

In order to achieve powered autonomous running robots it is essential to develop efficient actuator systems, especially for generating the radial thrust in the legs. In addition, the control of the radial thrust of the legs can be a simple, effective method for stabilizing the body pitch in a running gait. This paper presents the mechanical systems, models and control strategies employed to generate and control leg thrust in the KOLT quadruped running robot. An analytical model of the electro-pneumatic leg thrusting system is presented and analyzed to evaluate its performance and to facilitate the design of control strategies. Several experiments have been conducted to estimate the energy losses and determine their origins as well as to compute the energetic efficiency of the actuation system. Two thrust control methods are also proposed and tested experimentally. The closed loop method regulates thrust through the control of the hip liftoff speed, a conceptually simple control strategy that stabilizes the body pitch in pronk and trot gaits without the need for central feedback, even on irregular terrain. The open-loop control method regulates the energy added in each hop based on the model of the actuator system. The efficacy of these models and techniques is tested in several planar trot and pronk experiments, and the results are analyzed focusing on the body stabilization, the power consumption and the energetic efficiency. © SAGE Publications 2008 Los Angeles

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

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

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

LeggedWalking on Inclined Surfaces

The main contribution of this MS Thesis is centered around taking steps towards successful multi-modal demonstrations using Northeastern's legged-aerial robot, Husky Carbon. This work discusses the challenges involved in achieving multi-modal locomotion such as trotting-hovering and thruster-assisted incline walking and reports progress made towards overcoming these challenges. Animals like birds use a combination of legged and aerial mobility, as seen in Chukars' wing-assisted incline running (WAIR), to achieve multi-modal locomotion. Chukars use forces generated by their flapping wings to manipulate ground contact forces and traverse steep slopes and overhangs. Husky's design takes inspiration from birds such as Chukars. This MS thesis presentation outlines the mechanical and electrical details of Husky's legged and aerial units. The thesis presents simulated incline walking using a high-fidelity model of the Husky Carbon over steep slopes of up to 45 degrees.Comment: Masters thesi

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