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.     

Dynamic simulation and Doppler Ultrasonography validation of blood flow behavior in Abdominal Aortic Aneurysm

Criteria for rupture prediction of Abdominal Aortic Aneurysm (AAA) are based only on the diameter of AAA. This method does not consider complex hemodynamic forces exerted on AAA wall. The methodology used in our study combines Computer-Aided Design (CAD) with Computational Fluid Dynamics (CFD). Three-dimensional vascular structures reconstructions were based on Computed Tomography (CT) images and CAD. CFD theory was used for mathematical modeling and simulations. In this way, dynamic behavior of blood flow in bounded three-dimensional space was described. Doppler Ultrasonography (US) was used for model results validation. All simulations were based on medical investigation of 4 patients (male older than 65 years) with diagnosed AAA. Good correspondence between computed velocities in AAA and measured values with Doppler US (Patient 1 0.60 m·s⁻¹ versus 0.61 m·s⁻¹, Patient 2 0.80 m·s⁻¹ versus 0.80 m·s⁻¹, Patient 3 0.75 m·s⁻¹ versus 0.78 m·s⁻¹, Patient 4 0.50 m·s⁻¹ versus 0.49 m·s⁻¹) was noticed. The good agreement between measured and simulated velocities validates our methodology and the other data available from simulations (eg. von Misses stress) could be used to provide useful information about the possibility of AAA rupture.     

Bio-Inspired Controller for a Robot Cheetah with a Neural Mechanism Controlling Leg Muscles

The realization of a high-speed running robot is one of the most challenging problems in developing legged robots.The excellent performance of cheetahs provides inspiration for the control and mechanical design of such robots.This paper presents a three-dimensional model of a cheetah that predicts the locomotory behaviors of a running cheetah.Applying biological knowledge of the neural mechanism,we control the muscle flexion and extension during the stance phase,and control the positions of the joints in the flight phase via a PD controller to minimize complexity.The proposed control strategy is shown to achieve similar locomotion of a real cheetah.The simulation realizes good biological properties,such as the leg retraction,ground reaction force,and spring-like leg behavior.The stable bounding results show the promise of the controller in high-speed locomotion.The model can reach 2.7 m·s- 1 as the highest speed,and can accelerate from 0 to 1.5 m·s -1 in one stride cycle.A mechanical structure based on this simulation is designed to demonstrate the control approach,and the most recently developed hindlimb controlled by the proposed controller is presented in swinging-leg experiments and jump-force experiments.     

Directionally compliant legs influence the intrinsic pitch behaviour of a trotting quadruped

Limb design is well conserved among quadrupeds, notably, the knees point forward (i.e. cranial inclination of femora) and the elbows point back (i.e. caudal inclination of humeri). This study was undertaken to examine the effects of joint orientation on individual leg forces and centre of mass dynamics. Steady-speed trotting was simulated in two quadrupedal models. Model I had the knee and elbow orientation of a quadruped and model II had a reversed leg configuration in which knees point back and elbows point forward. The model's legs showed directional compliance determined by the orientation of the knee/elbow. In both models, forward pointing knees/elbows produced a propulsive force bias, while rearward pointing knees/elbows produced a braking force bias. Hence, model I showed the same pattern of hind-leg propulsion and fore-leg braking observed in trotting animals. Simulations revealed minimal pitch oscillations during steady-speed trotting of model I, but substantially greater and more irregular pitch oscillations of model II. The reduced pitch oscillation of model I was a result of fore-leg and hind-leg forces that reduced pitching moments during early and late stance, respectively. This passive mechanism for reducing pitch oscillations was an emergent property of directionally compliant legs with the fore-hind configuration of model I. Such intrinsic stability resulting from mechanical design can simplify control tasks and lead to more robust running machines.     

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.     

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.     

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.     

Unholey shoes: Experimental considerations when estimating ankle joint complex power during walking and running

For studies that aim to assess biological ankle function, calculating ankle joint complex (AJC) power between the calcaneus and shank is recommended over conventional inverse dynamics estimates between a rigid-body foot and shank. However, when designing a new experiment, it remains unclear whether holes should be cut in footwear to permit motion tracking via skin-mounted markers, or whether marker placement locations should be tightly controlled across conditions. Here we provide data to assist researchers in answering these questions. We performed a gait analysis study of walking (0.8, 1.2, 1.6 m·s⁻¹) and running (2.6, 2.8, 3.0 m·s⁻¹) while subjects (N = 10) wore custom-modified footwear, which allowed markers to be placed either on the shoe, or on the skin via cut-out windows in the shoes. First, we compared foot markers affixed to the skin vs. on the same locations on the shoe. Using statistical non-parametric mapping techniques, we discovered that skin vs. shoe markers had no statistically significant effect on net AJC power estimates throughout stance phase, for all walking and running speeds. Second, we compared calcaneal markers in the nominal shoe configuration vs. markers in a nearby location (∼27 mm below) on the shoe. We observed significant differences when marker placement on the shoe was varied, which may be relevant to repeated-measures study designs. The results suggest that when computing AJC power for walking and running, you may want to put down the scissors (i.e., forego cutting holes in your footwear), and instead pick up a Sharpie® (pen) or use a template, to maintain consistent marker placement across trials and conditions.     

Biological Jumping Mechanism Analysis and Modeling for Frog Robot

This paper presents a mechanical model of jumping robot based on the biological mechanism analysis of frog. By biological observation and kinematic analysis the frog jump is divided into take-offphase, aerial phase and landing phase. We find the similar trajectories of hindlimb joints during jump, the important effect of foot during take-off and the role of forelimb in supporting the body. Based on the observation, the frog jump is simplified and a mechanical model is put forward. The robot leg is represented by a 4-bar spring/linkage mechanism model, which has three Degrees of Freedom （DOF） at hip joint and one DOF （passive） at tarsometatarsal joint on the foot. The shoulder and elbow joints each has one DOF for the balancing function of arm. The ground reaction force of the model is analyzed and compared with that of frog during take-off. The results show that the model has the same advantages of low likelihood of premature lift-off and high efficiency as the frog. Analysis results and the model can be employed to develop and control a robot capable of mimicking the jumping behavior of frog.     

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.     

Biomimetic Quadruped Robot with a Spinal Joint and Optimal Spinal Motion via Reinforcement Learning

Feline animals can run quickly using spinal joints as well as the joints that make up their four legs.This paper describes the development of a quadruped robot including a spinal joint that biomimics feline animals.The developed robot platform consists of four legs with a double 4-bar linkage type and one simplified rotary joint.In addition,Q-learning,a type of machine learning,was used to find the optimal motion profile of the spinal joint.The bounding gait was implemented on the robot system using the motion profile of the spinal joint,and it was confirmed that using the spinal joint can achieve a faster Center of Mass(CoM)forward speed than not using the spinal joint.Although the motion profile obtained through Q-learning did not exactly match the spinal angle of a feline animal,which is more multiarticular than that of the developed robot,the tendency of the actual feline animal spinal motion profile,which is sinusoidal,was similar.     

The Role of Relative Spinal Motion during Feline Galloping for Speed Performance

Felines use their spinal column to increase their running speed at rapid locomotion performance. However, its motion profile behavior during fast gait locomotion has little attention. The goal of this study is to examine the relative spinal motion profile during two different galloping gait speeds. To understand this dynamic behavior trend, a dynamic motion of the feline animal （Felis catus domestica） was measured and analyzed by motion capture devices. Based on the experiments at two different galloping gaits, we observed a significant increase in speed （from 3.2 m.s-1 to 4.33 m.s-1） during the relative motion profile synchronization between the spinal （range： 118.86~ to 168.00~） and pelvic segments （range： 46.35~ to 91.13~） during the hindlimb stance phase （time interval： 0.495 s to 0.600 s）. Based on this discovery, the relative angular speed profile was applied to understand the possibility that the role of the relative motion match during high speed locomotion generates bigger ground reaction force.     

Velocity Control of a Bounding Quadruped via Energy Control and Vestibular Reflexes

In this paper a bio-inspired approach of velocity control for a quadruped robot running with a bounding gait on compliant legs is set up. The dynamic properties ofa sagittal plane model of the robot are investigated. By analyzing the stable fixed points based on Poincare map, we find that the energy change of the system is the main source for forward velocity adjustment. Based on the analysis of the dynamics model of the robot, a new simple linear running controller is proposed using the energy control idea, which requires minimal task level feedback and only controls both the leg torque and ending impact angle. On the other hand, the functions of mammalian vestibular reflexes are discussed, and a reflex map between forward velocity and the pitch movement is built through statistical regression analysis. Finally, a velocity controller based on energy control and vestibular reflexes is built, which has the same structure as the mammalian nervous mechanism for body posture control. The new con- troller allows the robot to run autonomously without any other auxiliary equipment and exhibits good speed adjustment capa- bility. A series simulations and experiments were set to show the good movement agility, and the feasibility and validity of the robot system.     

Effect of Flexible Spine Motion on Energy Efficiency in Quadruped Running

Energy efficiency is important in the performance of quadruped robots and mammals.Flexible spine motion generally exists in quadruped mammals.This paper mainly explores the effect of flexible spinal motion on energy efficiency.Firstly,a planar simplified model of the quadruped robot with flexible spine motion is introduced and two simulation experiments are carried out.The results of simulation experiments demonstrate that both spine motion and spinal flexibility can indeed increase energy efficiency,and the curve of energy efficiency change along with spinal stiffness is acquired.So,in order to obtain higher energy efficiency,quadruped robots should have flexible spine motion.In a certain speed,there is an optimal spinal stiffness which can make energy efficiency to be the best.Secondly,a planar quadruped robot with flexible spine motion is designed and the conclusions drawn in the two simulation experiments are verified.Lastly,the third simulation experiment is carried out to explore the relationship between the optimal spinal stiffness,speed and total mass.The optimal spinal stiffness increases with both speed and total mass,which has important guiding significance for adjusting the spinal stiffness of quadruped robots to make them reach the best energy efficiency.     

Effect of leg kick on active drag in front-crawl swimming: Comparison of whole stroke and arms-only stroke during front-crawl and the streamlined position

The purpose of this study was to examine the effect of leg kick on the resistance force in front-crawl swimming. The active drag in front-crawl swimming with and without leg motion was evaluated using measured values of residual thrust (MRT method) and compared with the passive drag of the streamlined position (SP) for the same swimmers. Seven male competitive swimmers participated in this study, and the testing was conducted in a swimming flume. Each swimmer performed front-crawl under two conditions: using arms and legs (whole stroke: WS) and using arms only (arms-only stroke: AS). Active drag and passive drag were measured at swimming velocities of 1.1 and 1.3 m s⁻¹ using load cells connected to the swimmer via wires. We calculated a drag coefficient to compare the resistances of the WS, AS and SP at each velocity. For both the WS and AS at both swimming velocities, active drag coefficient was found to be about 1.6–1.9 times larger than that in passive conditions. In contrast, although leg movement did not cause a difference in drag coefficient for front-crawl swimming, there was a large effect size (d = 1.43) at 1.3 m s⁻¹. Therefore, although upper and lower limb movements increase resistance compared to the passive condition, the effect of leg kick on drag may depend on swimming velocity.     

THE MECHANISM OF DAYLENGTH PERCEPTION IN THE RED ALGA ACROSYMPHYTON PURPURIFERUM1

The red alga Acrosymphyton purpuriferum (J. Ag.) Sjöst. (Dumontiaceae) is a short day plant in the formation of its tetrasporangia. Tetrasporogenesis was not inhibited by 1 h night-breaks when given at any time during the long (16 h) dark period (tested at 2 h intervals). However, tetrasporogenesis was inhibited when short (8 h) main photoperiods were extended beyond the critical daylength with supplementary light periods (8 h) at an irradiance below photosynthetic compensation. The threshold irradiance for inhibition of tetrasporogenesis was far lower when supplementary light periods preceded the main photoperiod than when they followed it (<0.05 μmol·m⁻²·s⁻¹ vs. 3 μmol·m⁻²·s⁻¹). The threshold level also depended on the irradiance given during the main photoperiod and was higher after a main photoperiod in bright light than after one in dim light (threshold at 3 μmol·m⁻²·s⁻¹ after a main photoperiod at ca. 65 μmol·m⁻²·s⁻¹ vs. threshold at <0.5 μmol·m⁻²·s⁻¹ after a main photoperiod at ca. 35 μmol·m⁻²·s⁻¹). The spectral dependence of the response was investigated in day-extensions (supplementary light period (8 h) after main photoperiod (8 h) at 48 μmol·m⁻²·s⁻¹) with narrow band coloured light. Blue light (λ= 420 nm) was most effective, with 50% inhibition at a quantum-dose of 2.3 mmol·m⁻². However, yellow (λ= 563 nm) and red light (λ= 600 nm; λ= 670 nm) also caused some inhibition, with ca. 30% of the effectiveness of blue light. Only far-red light (λ= 710 nm; λ= 730 nm) was relatively ineffective with no significant inhibition of tetrasporogenesis at quantum-doses of up to 20 mmol·m⁻².     

Electrokinetic properties of asparaginase sensitive or resistant mouse leukemic cells treated with L-asparaginase

The electrophoretic mobility of L5178Y cells in 0.0145 M NaCl, 4.5% sorbitol, 0.6 mM NaHCO₃, pH 7.2, at 25°C was — 1.78 μ·s^?1·V^?1·cm^?1 while that of an L-asparaginase resistant subline, L5178Y/ASN, was — 1.11 μm·s^?1·V^?1·cm^?1. Both cell lines were characterized by terminal sialic acid residues on their surfaces. Treatment of L5178Y cells for 90 min with 10 units of L-asparaginase per ml in saline decreased the electrophoretic mobility of the cells to — 1.65 μm·s^?1·V^?1·cm^?1 while treatment in Fischer's medium decreased the mobility to — 1.25 μm·s^?1·V^?1·cm^?1; neither treatment had a significant effect on the L5178Y/ASN electrophoretic mobility. The results suggest that L-asparaginase has an immediate and specific effect on synthesis of cell surface asparaginyl glycoproteins.     

Morphology,cell growth,and polysaccharide production of <Emphasis Type="Italic">Nostoc flagelliforme</Emphasis> in liquid suspension culture at different agitation rates

Noscoc flagelliforme is a terrestrial macroscopic cyanobacterium with high economic value. Free-living cells that were separated from a natural colony of N. flagelliforme were cultivated in a 20-L photobioreactor for 16 days at five agitation rates with impeller tip speeds at 0.3, 0., 0.8, 1.0, and 1.5 m·s⁻¹. With different impeller tip speeds there were significant differences in the cell growth and polysaccharide production, and different types of cell colonies appeared because of different shear forces caused by agitation. At harvest time, cell concentrations with tip speeds of 0.8 and 1.0 m·s⁻¹ were clearly higher than those with the other three tip speeds, but dry cell weights with the tip speeds of 0.3, 0.5, 0.8, and 1.0 m·s⁻¹ were almost the same. The highest RPS (polysaccharide that released into liquid medium) production was obtained with the tip speeds of 0.8 and 1.0 m·s⁻¹, while the highest EPS (polysaccharide that formed capsule or slime layer) production was obtained with the tip speed of 0.5 m·s⁻¹. The tip speed of 1.5 m·s⁻¹ was harmful for both cell growth and polysaccharide production, indicating that an appropriate shear force was needed in the liquid suspension culture of N. flagelliforme.     

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.