Trot Gait Design and CPG Method for a Quadruped Robot

Developing efficient walking gaits for quadruped robots has intrigued investigators for years. Trot gait, as a fast locomotion gait, has been widely used in robot control. This paper follows the idea of the six determinants of gait and designs a trot gait for a parallel-leg quadruped robot, Baby Elephant. The walking period and step length are set as constants to maintain a relatively fast speed while changing different foot trajectories to test walking quality. Experiments show that kicking leg back improves body stability. Then, a steady and smooth trot gait is designed. Furthermore, inspired by Central Pattern Generators （CPG）, a series CPG model is proposed to achieve robust and dynamic trot gait. It is generally believed that CPG is capable of producing rhythmic movements, such as swimming, walking, and flying, even when isolated from brain and sensory inputs. The proposed CPG model, inspired by the series concept, can automatically learn the previous well-designed trot gait and reproduce it, and has the ability to change its walking frequency online as well. Experiments are done in real world to verify this method.     

Analysis of the gait generation principle by a simulated quadruped model with a CPG incorporating vestibular modulation

This study aims to understand the principles of gait generation in a quadrupedal model. It is difficult to determine the essence of gait generation simply by observation of the movement of complicated animals composed of brains, nerves, muscles, etc. Therefore, we build a planar quadruped model with simplified nervous system and mechanisms, in order to observe its gaits under simulation. The model is equipped with a mathematical central pattern generator (CPG), consisting of four coupled neural oscillators, basically producing a trot pattern. The model also contains sensory feedback to the CPG, measuring the body tilt (vestibular modulation). This spontaneously gives rise to an unprogrammed lateral walk at low speeds, a transverse gallop while running, in addition to trotting at a medium speed. This is because the body oscillation exhibits a double peak per leg frequency at low speeds, no peak (little oscillation) at medium speeds, and a single peak while running. The body oscillation autonomously adjusts the phase differences between the neural oscillators via the feedback. We assume that the oscillations of the four legs produced by the CPG and the body oscillation varying according to the current speed are synchronized along with the varied phase differences to keep balance during locomotion through postural adaptation via the vestibular modulation, resulting in each gait. We succeeded in determining a single simple principle that accounts for gait transition from walking to trotting to galloping, even without brain control, complicated leg mechanisms, or a flexible trunk.     

Control of a Quadruped Robot with Bionic Springy Legs in Trotting Gait

Legged robots have better performance on discontinuous terrain than that of wheeled robots. However, the dynamic trotting and balance control of a quadruped robot is still a challenging problem, especially when the robot has multi-joint legs. This paper presents a three-dimensional model of a quadruped robot which has 6 Degrees of Freedom （DOF） on torso and 5 DOF on each leg. On the basis of the Spring-Loaded Inverted Pendulum （SLIP） model, body control algorithm is discussed in the first place to figure out how legs work in 3D trotting. Then, motivated by the principle of joint function separation and introducing certain biological characteristics, two joint coordination approaches are developed to produce the trot and provide balance. The robot reaches the highest speed of 2.0 m.s-1, and keeps balance under 250 Kg.m.s-1 lateral disturbance in the simulations. The effectiveness of these approaches is also verified on a prototype robot which runs to 0.83 m.s-1 on the treadmill, The simulations and experiments show that legged robots have good biological properties, such as the ground reaction force, and spring-like leg behavior.     

Virtual Constraint Based Control of Bounding Gait of Quadruped Robots

This paper presents a control approach for bounding gait of quadruped robots by applying the concept of Virtual Constraints (VCs).A VC is a relative motion relation between two related joints imposed to the robots in terms of a specified gait,which can drive the robot to run with desired gait.To determine VCs for highly dynamic bounding gait,the limit cycle motions of the passive dynamic model of bounding gait are analyzed.The leg length and hip/shoulder angle trajectories corresponding to the limit cycles are parameterized by leg angles using 4 th-order polynomials.In order to track the calculated periodic motions,the polynomials are imposed on the robot as virtual motion constraints by a high-level state machine controller.A bounding speed feedback strategy is introduced to stabilize the robot running speed and enhance the stability.The control approach was applied to a newly designed lightweight bioinspired quadruped robot,AgiDog.The experimental results demonstrate that the robot can bound at a frequency up to 5 Hz and bound at a maximum speed of 1.2 m·s-1 in sagittal plane with a Froude number approximating to 1.     

Design and demonstration of a dynamometric horseshoe for measuring ground reaction loads of horses during racing conditions

Because musculoskeletal injuries to racehorses are common, instrumentation for the study of factors (e.g. track surface), which affect the ground reaction loads in horses during racing conditions, would be useful. The objectives of the work reported by this paper were to (1) design and construct a novel dynamometric horseshoe that is capable of measuring the complete ground reaction loading during racing conditions, (2) characterize static and dynamic measurement errors, and (3) demonstrate the usefulness of the instrument by collecting example data during the walk, trot, canter, and gallop for a single subject. Using electrical resistance strain gages, a dynamometric horseshoe was designed and constructed to measure the complete ground reaction force and moment vectors and the center of pressure. To mimic the load transfer surface of the hoof, the shape of the surface contacting the ground was similar to that of the solar surface of the hoof. Following static calibration, the measurement accuracy was determined. The root mean squared errors (RMSE) were 3% of full scale for the force component normal to the hoof and 9% for force components in the plane of the hoof. The dynamic calibration determined that the natural frequency with the full weight of a typical horse was 1744 Hz. Example data were collected during walking on a ground surface and during trotting, cantering, and galloping on a treadmill. The instrument successfully measured the complete ground reaction load during all four gaits. Consequently the dynamometric horseshoe is useful for studying factors, which affect ground reaction loads during racing conditions.     

Extended Evolutionary Fast Learn-to-Walk Approach for Four-Legged Robots

Robot locomotion is an active research area. In this paper we focus on the locomotion of quadruped robots. An effective walking gait of quadruped robots is mainly concerned with two key aspects, namely speed and stability. The large search space of potential parameter settings for leg joints means that hand tuning is not feasible in general. As a result walking parameters are typically determined using machine learning techniques. A major shortcoming of using machine learning techniques is the significant wear and tear of robots since many parameter combinations need to be evaluated before an optimal solution is found.This paper proposes a direct walking gait learning approach, which is specifically designed to reduce wear and tear of robot motors, joints and other hardware. In essence we provide an effective learning mechanism that leads to a solution in a faster convergence time than previous algorithms. The results demonstrate that the new learning algorithm obtains a faster convergence to the best solutions in a short run. This approach is significant in obtaining faster walking gaits which will be useful for a wide range of applications where speed and stability are important. Future work will extend our methods so that the faster convergence algorithm can be applied to a two legged humanoid and lead to less wear and tear whilst still developing a fast and stable gait.     

Three-dimensional analysis of horse and human gaits in therapeutic riding

Therapeutic horse riding or hippotherapy is used as an intervention for treating individuals with mental and physical disabilities. Equine-assisted interventions are based on the hypothesis that the movement of the horse's pelvis during horseback riding resembles human ambulation, and thus provides motor and sensory inputs similar to those received during human walking. However, this hypothesis has not been investigated quantitatively and qualitatively. This study aimed to verify the hypothesis by conducting a three-dimensional analysis of the horse's movements while walking and human ambulation. Using four sets of equipments, we analysed the acceleration patterns of walking in 50 healthy humans and 11 horses. In addition, we analysed the exercise intensity by comparing the heart rate, breathing rate, and blood pressure of 127 healthy individuals before and after walking and horse riding. The acceleration data series of the stride phase of horse walking were compared with those of human walking, and the frequencies (in Hz) were analysed by Fast Fourier transform.The acceleration curves of human walking overlapped with those of horse walking, with the frequency band of human walking corresponding with that of horse walking. Exercise intensity, as measured by the heart rate and breathing rate, was not significantly different between horse riding and human walking. The levels of diastolic blood pressure were slightly higher during horse riding than during walking, but were lower during both conditions compared with those in normal conditions (P < 0.01). The present study shows that, although not completely matched, the accelerations of the horse and human walking are comparable quantitatively and qualitatively. Horse riding at a walking gait could generate motor and sensory inputs similar to those produced by human walking, and thus could provide optimum benefits to persons with ambulatory difficulties.     

An Efficient Gait-generating Method for Electrical Quadruped Robot Based on Humanoid Power Planning Approach

The research field of legged robots has always relied on the bionic robotic research,especially in locomotion regulating approaches,such as foot trajectory planning,body stability regulating and energy efficiency prompting.Minimizing energy consumption and keeping the stability of body are considered as two main characteristics of human walking.This work devotes to develop an energy-efficient gait control method for electrical quadruped robots with the inspiration of human walking pattern.Based on the mechanical power distribution trend,an efficient humanoid power redistribution approach is established for the electrical quadruped robot.Through studying the walking behavior acted by mankind,such as the foot trajectory and change of mechanical power,we believe that the proposed controller which includes the bionic foot movement trajectory and humanoid power redistribution method can be implemented on the electrical quadruped robot prototype.The stability and energy efficiency of the proposed controller are tested by the simulation and the single-leg prototype experi-ment.The results verify that the humanoid power planning approach can improve the energy efficiency of the electrical quadruped robots.     

Symmetrical gaits of dogs in relation to body build

Symmetrical gaits of 37 breeds of dogs were analyzed. Usual walking and trotting gaits resemble those of other carnivores of similar size and conformation. Only certain long-legged dogs pace – usually at the fast walk or slow run. At the moderate walk, long-legged dogs tend to use lateral-couplets gaits, whereas short-legged breeds tend to use single-foot gaits. Many dogs must turn the axis of the body slightly from the line of travel at the trot to prevent interference between fore and hind feet. The relative duration with the ground made by fore and hind feet is discussed, usual support-sequences of the varicus gaits are presented, and the amount of variation is shown.     

Muscle mechanical advantage of human walking and running: implications for energy cost.

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force (R) and therefore the effective mechanical advantage (EMA = r/R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154-176 degrees) during much of the support phase of walking, its flexed position (134-164 degrees) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% (P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.     

The metabolic and mechanical costs of step time asymmetry in walking

Animals use both pendular and elastic mechanisms to minimize energy expenditure during terrestrial locomotion. Elastic gaits can be either bilaterally symmetric (e.g. run and trot) or asymmetric (e.g. skip, canter and gallop), yet only symmetric pendular gaits (e.g. walk) are observed in nature. Does minimizing metabolic and mechanical power constrain pendular gaits to temporal symmetry? We measured rates of metabolic energy expenditure and calculated mechanical power production while healthy humans walked symmetrically and asymmetrically at a range of step and stride times. We found that walking with a 42 per cent step time asymmetry required 80 per cent (2.5 W kg⁻¹) more metabolic power than preferred symmetric gait. Positive mechanical power production increased by 64 per cent (approx. 0.24 W kg⁻¹), paralleling the increases we observed in metabolic power. We found that when walking asymmetrically, subjects absorbed more power during double support than during symmetric walking and compensated by increasing power production during single support. Overall, we identify inherent metabolic and mechanical costs to gait asymmetry and find that symmetry is optimal in healthy human walking.     

Design and validation of a dynamometric horseshoe for the measurement of three-dimensional ground reaction force on a moving horse

Properties of ground surfaces condition locomotion, and quality of track surfaces is believed to be involved in the pathogenesis of many musculoskeletal injuries in the horse. Measuring ground reaction forces (GRF) is an interesting approach to assess those interactions. Forceplates are the most commonly used but they are not well suited to compare different ground surfaces at fast gaits. Embarked equipment, fixed under the horse's hoof, would allow force measurement on any track. The objective of this work was (1) to design a device which enables the measurement of 3-D GRF on any ground, at any gait, for a given subject, (2) to determine its accuracy, and (3) to evaluate its performance and usefulness under physiological conditions. The resulting dynamometric horseshoe was composed of 4 piezoelectric sensors sandwiched between 2 aluminium plates designed at the shape of an equine shoe. The measurements, evaluated after a quasi-static calibration, revealed that the root mean square error was 1.3% in the normal direction, and 3.1% in the transversal direction. In vivo tests at the walk and trot in straight line and at the trot on circles, were conducted on 3 different ground surfaces. The results demonstrate that this dynamometric horseshoe is well suited to study the effects of different ground surfaces on GRF in the moving horse.     

Gait Transitions in Human Infants: Coping with Extremes of Treadmill Speed

Spinal pattern generators in quadrupedal animals can coordinate different forms of locomotion, like trotting or galloping, by altering coordination between the limbs (interlimb coordination). In the human system, infants have been used to study the subcortical control of gait, since the cerebral cortex and corticospinal tract are immature early in life. Like other animals, human infants can modify interlimb coordination to jump or step. Do human infants possess functional neuronal circuitry necessary to modify coordination within a limb (intralimb coordination) in order to generate distinct forms of alternating bipedal gait, such as walking and running? We monitored twenty-eight infants (7–12 months) stepping on a treadmill at speeds ranging between 0.06–2.36 m/s, and seventeen adults (22–47 years) walking or running at speeds spanning the walk-to-run transition. Six of the adults were tested with body weight support to mimic the conditions of infant stepping. We found that infants could accommodate a wide range of speeds by altering stride length and frequency, similar to adults. Moreover, as the treadmill speed increased, we observed periods of flight during which neither foot was in ground contact in infants and in adults. However, while adults modified other aspects of intralimb coordination and the mechanics of progression to transition to a running gait, infants did not make comparable changes. The lack of evidence for distinct walking and running patterns in infants suggests that the expression of different functional, alternating gait patterns in humans may require neuromuscular maturation and a period of learning post-independent walking.     

Cavemen Were Better at Depicting Quadruped Walking than Modern Artists: Erroneous Walking Illustrations in the Fine Arts from Prehistory to Today

The experts of animal locomotion well know the characteristics of quadruped walking since the pioneering work of Eadweard Muybridge in the 1880s. Most of the quadrupeds advance their legs in the same lateral sequence when walking, and only the timing of their supporting feet differ more or less. How did this scientific knowledge influence the correctness of quadruped walking depictions in the fine arts? Did the proportion of erroneous quadruped walking illustrations relative to their total number (i.e. error rate) decrease after Muybridge? How correctly have cavemen (upper palaeolithic Homo sapiens) illustrated the walking of their quadruped prey in prehistoric times? The aim of this work is to answer these questions. We have analyzed 1000 prehistoric and modern artistic quadruped walking depictions and determined whether they are correct or not in respect of the limb attitudes presented, assuming that the other aspects of depictions used to determine the animals gait are illustrated correctly. The error rate of modern pre-Muybridgean quadruped walking illustrations was 83.5%, much more than the error rate of 73.3% of mere chance. It decreased to 57.9% after 1887, that is in the post-Muybridgean period. Most surprisingly, the prehistoric quadruped walking depictions had the lowest error rate of 46.2%. All these differences were statistically significant. Thus, cavemen were more keenly aware of the slower motion of their prey animals and illustrated quadruped walking more precisely than later artists.     

Symmetrical gaits of primates

Walking and symmetrical running gaits of 26 genera of primates are analyzed using numerical and graphical methods described previously. The raw data are 1701 feet of 16 mm motion picture film mostly exposed at 64 frames per second. Adult monkeys and apes usually use the walking trot or diagonal-sequence walks. Individual monkeys occasionally use lateral-sequence walks resembling those that are usual for human infants. Human children moving on hands and feet use gaits ranging from the walking pace through the lateral-sequence walks to the walking trot. An infant macaque studied from age 17 hours to 96 days first walked with a lateral-sequence, diagonal-couplets gait and then gradually shifted to the diagonal-sequence, diagonal-couplets gait of the adult. Few non-primates use the diagonal-sequence walks which are typical of primates. Typical support sequences are figured. Relative placement of feet and consequent slight asymmetry are described.     

Quantitative Comparison of the Walk and Trot of Border Collies and Labrador Retrievers,Breeds with Different Performance Requirements

Introduction

We hypothesized that breed differences of Border Collies and Labrador Retrievers would be reflected in the temporospatial characteristics of the walk and trot.

Materials and Methods

Twenty healthy Border Collies and 20 healthy Labrador Retrievers made three passes across a pressure sensing walkway system that recorded quantitative temporospatial information at a walk and a trot. The following variables were measured for each dog: velocity, total pressure index percentage (TPI%), ratio of weight borne on the thoracic vs. pelvic limbs (T/P TPI%), stance time percentage (ST%), and thoracic limb stride length (TSrL).

Results

The mean T/P TPI% for Border Collies at a walk and at a trot were significantly lower than for Labrador Retrievers (p = 0.0007 and p = 0.0003). Border Collies had a significantly lower ST% than Labrador Retrievers for the thoracic limbs and pelvic limbs at a walk (p = 0.0058 and 0.0003) and the trot (p = 0.0280 and 0.0448). There was no relationship between ST% and TSrL in Border Collies and an inverse correlation between ST% and TSrL in Labrador Retrievers (p = 0.0002).

Discussion

Key quantitative gait differences were identified in Border Collies and Labrador Retrievers, which could potentially provide each breed with an advantage for their working function.     

Worldwide frequency distribution of the ‘Gait keeper’ mutation in the DMRT3 gene

For centuries, domestic horses have represented an important means of transport and served as working and companion animals. Although their role in transportation is less important today, many horse breeds are still subject to intense selection based on their pattern of locomotion. A striking example of such a selected trait is the ability of a horse to perform additional gaits other than the common walk, trot and gallop. Those could be four‐beat ambling gaits, which are particularly smooth and comfortable for the rider, or pace, used mainly in racing. Gaited horse breeds occur around the globe, suggesting that gaitedness is an old trait, selected for in many breeds. A recent study discovered that a nonsense mutation in DMRT3 has a major impact on gaitedness in horses and is present at a high frequency in gaited breeds and in horses bred for harness racing. Here, we report a study of the worldwide distribution of this mutation. We genotyped 4396 horses representing 141 horse breeds for the DMRT3 stop mutation. More than half (2749) of these horses also were genotyped for a SNP situated 32 kb upstream of the DMRT3 nonsense mutation because these two SNPs are in very strong linkage disequilibrium. We show that the DMRT3 mutation is present in 68 of the 141 genotyped horse breeds at a frequency ranging from 1% to 100%. We also show that the mutation is not limited to a geographical area, but is found worldwide. The breeds with a high frequency of the stop mutation (>50%) are either classified as gaited or bred for harness racing.     

A comparative collision-based analysis of human gait

This study compares human walking and running, and places them within the context of other mammalian gaits. We use a collision-based approach to analyse the fundamental dynamics of the centre of mass (CoM) according to three angles derived from the instantaneous force and velocity vectors. These dimensionless angles permit comparisons across gait, species and size. The collision angle Φ, which is equivalent to the dimensionless mechanical cost of transport CoT_mech, is found to be three times greater during running than walking of humans. This threefold difference is consistent with previous studies of walking versus trotting of quadrupeds, albeit tends to be greater in the gaits of humans and hopping bipeds than in quadrupeds. Plotting the collision angle Φ together with the angles of the CoM force vector Θ and velocity vector Λ results in the functional grouping of bipedal and quadrupedal gaits according to their CoM dynamics—walking, galloping and ambling are distinguished as separate gaits that employ collision reduction, whereas trotting, running and hopping employ little collision reduction and represent more of a continuum that is influenced by dimensionless speed. Comparable with quadrupedal mammals, collision fraction (the ratio of actual to potential collision) is 0.51 during walking and 0.89 during running, indicating substantial collision reduction during walking, but not running, of humans.     

BigDog-inspired studies in the locomotion of goats and dogs

Collision-based expenditure of mechanical energy and the compliance and geometry of the leg are fundamental, interrelated considerations in the mechanical design of legged runners. This article provides a basic context and rationale for experiments designed to inform each of these key areas in Boston Dynamic's BigDog robot. Although these principles have been investigated throughout the past few decades within different academic disciplines, BigDog required that they be considered together and in concert with an impressive set of control algorithms that are not discussed here. Although collision reduction is an important strategy for reducing mechanical cost of transport in the slowest and fastest quadrupedal gaits, walking and galloping, BigDog employed an intermediate-speed trotting gait without collision reduction. Trotting, instead, uses a spring-loaded inverted pendulum mechanism with potential for storage and return of elastic strain energy in appropriately compliant structures. Rather than tuning BigDog's built-in leg springs according to a spring-mass model-based virtual leg-spring constant , a much stiffer distal leg spring together with actuation of the adjacent joint provided good trotting dynamics and avoided functional limitations that might have been imposed by too much compliance in real-world terrain. Adjusting the directional compliance of the legs by adopting a knee-forward, elbow-back geometry led to more robust trotting dynamics by reducing perturbations about the pitch axis of the robot's center of mass (CoM). BigDog is the most successful large-scale, all-terrain trotting machine built to date and it continues to stimulate our understanding of legged locomotion in comparative biomechanics as well as in robotics.     

Development of a Biomimetic Quadruped Robot

This paper presents the design and prototype of a small quadruped robot whose walking motion is realized by two piezocomposite actuators. In the design, biomimetic ideas are employed to obtain the agility of motions and sustainability of a heavy load. The design of the robot legs is inspired by the leg configuration of insects, two joints （hip and knee） of the leg enable two basic motions, lifting and stepping. The robot frame is designed to have a slope relative to the horizontal plane, which makes the robot move forward. In addition, the bounding locomotion of quadruped animals is implemented in the robot. Experiments show that the robot can carry an additional load of about 100 g and run with a fairly high velocity. The quadruped prototype can be an important step towards the goal of building an autonomous mobile robot actuated by piezocomposite actuators.