Bipedal Walking Model Research Articles

An Improved ZMP-Based CPG Model of Bipedal Robot Walking Searched by SaDE

This paper proposed a method to improve the walking behavior of bipedal robot with adjustable step length. Objectives of this paper are threefold. (1) Genetic Algorithm Optimized Fourier Series Formulation (GAOFSF) is modified to improve its performance. (2) Self-adaptive Differential Evolutionary Algorithm (SaDE) is applied to search feasible walking gait. (3) An efficient method is proposed for adjusting step length based on the modified central pattern generator (CPG) model. The GAOFSF is modified to ensure that trajectories generated are continuous in angular position, velocity, and acceleration. After formulation of the modified CPG model, SaDE is chosen to optimize walking gait (CPG model) due to its superior performance. Through simulation results, dynamic balance of the robot with modified CPG model is better than the original one. In this paper, four adjustable factors (Rhs,support, Rhs,swing, Rks,support, and Rks,swing) are added to the joint trajectories. Through adjusting these four factors, joint trajectories are changed and hence the step length achieved by the robot. Finally, the relationship between (1) the desired step length and (2) an appropriate set of Rhs,support, Rhs,swing, Rks,support, and Rks,swing searched by SaDE is learnt by Fuzzy Inference System (FIS). Desired joint angles can be found without the aid of inverse kinematic model.

The role of series ankle elasticity in bipedal walking

The elastic stretch-shortening cycle of the Achilles tendon during walking can reduce the active work demands on the plantarflexor muscles in series. However, this does not explain why or when this ankle work, whether by muscle or tendon, needs to be performed during gait. We therefore employ a simple bipedal walking model to investigate how ankle work and series elasticity impact economical locomotion. Our model shows that ankle elasticity can use passive dynamics to aid push-off late in single support, redirecting the body's center-of-mass (COM) motion upward. An appropriately timed, elastic push-off helps to reduce dissipative collision losses at contralateral heelstrike, and therefore the positive work needed to offset those losses and power steady walking. Thus, the model demonstrates how elastic ankle work can reduce the total energetic demands of walking, including work required from more proximal knee and hip muscles. We found that the key requirement for using ankle elasticity to achieve economical gait is the proper ratio of ankle stiffness to foot length. Optimal combination of these parameters ensures proper timing of elastic energy release prior to contralateral heelstrike, and sufficient energy storage to redirect the COM velocity. In fact, there exist parameter combinations that theoretically yield collision-free walking, thus requiring zero active work, albeit with relatively high ankle torques. Ankle elasticity also allows the hip to power economical walking by contributing indirectly to push-off. Whether walking is powered by the ankle or hip, ankle elasticity may aid walking economy by reducing collision losses.

Finite Element Analysis of Pedestrian-Bridge Dynamic Interaction

The pedestrian-bridge dynamic interaction problem in the vertical direction based on a bipedal walking model and damped compliant legs is presented in this work. The classical finite element method, combined with a moving finite element, represents the motion of the pedestrian in the dynamic analysis of a footbridge. A control force is provided by the pedestrian to compensate for the energy loss due to the system damping in walking and to regulate the walking performance of the pedestrian. The effects of leg stiffness, the landing angle of attack, the damping ratio of the leg and the mass ratio of the human and structure are investigated in the numerical studies. Simulation results show that the dynamic interaction will increase with a larger vibration level of the structure. More external energy must be input to maintain steady walking and uniform dynamic behavior of the pedestrian in the process. The simple bipedal walking model could well describe the human-structure dynamic interaction.

Pedestrian–bridge dynamic interaction, including human participation

The pedestrian–bridge dynamic interaction problem based on bipedal walking model and damped compliant legs is presented in this work. A time-variant damper is modeled at a given walking speed. A control force is applied by the pedestrian to compensate for energy dissipated with the system damping in walking and to regulate the walking performance of the pedestrian. The effects of stiffness, damping of the leg and the landing angle of attack are investigated in the numerical studies. Simulation results show that the dynamic interaction will increase with a larger vibration level of structure. More external energy must be input to maintain steady walking and uniform dynamic behavior of the pedestrian in the process. The simple bipedal walking model could well describe the human–structure dynamic interaction.

Gait Selection and Transition of Passivity-Based Bipeds with Adaptable Ankle Stiffness

Stable bipedal walking is one of the most important components of humanoid robot design, which can help us better understand natural human walking. In this paper, to study gait selection and gait transition of efficient bipedal walking, we proposed a dynamic bipedal walking model with an upper body, flat feet and compliant joints. The model can achieve stable cyclic motion with different walking gaits. The hip actuation and ankle stiffness behavior of the model are quite similar to those of human normal walking. In simulation, we studied the influence of hip actuation and ankle stiffness on walking performance of each gait. The effects of ankle stiffness on gait selection are also analyzed. Gait transition is realized by adjusting ankle stiffness during walking.

Gait strategy changes with acceleration to accommodate the biomechanical constraint on push-off propulsion

To maintain steady and level walking, push-off propulsion during the double support phase compensates for the energy loss through heel strike collisions in an energetically optimal manner. However, a large portion of daily gait activities also contains transient gait responses, such as acceleration or deceleration, during which the observed dominance of the push-off work or the energy optimality may not hold. In this study, we examined whether the push-off propulsion during the double support phase served as a major energy source for gait acceleration, and we also studied the energetic optimality of accelerated gait using a simple bipedal walking model. Seven healthy young subjects participated in the over-ground walking experiments. The subjects walked at four different constant gait speeds ranging from a self-selected speed to a maximum gait speed, and then they accelerated their gait from zero to the maximum gait speed using a self-selected acceleration ratio. We measured the ground reaction force (GRF) of three consecutive steps and the corresponding leg configuration using force platforms and an optical marker system, respectively, and we compared the mechanical work performed by the GRF during each single and double support phase. In contrast to the model prediction of an increase in the push-off propulsion that is proportional to the acceleration and minimizes the mechanical energy cost, the push-off propulsion was slightly increased, and a significant increase in the mechanical work during the single support phase was observed. The results suggest that gait acceleration occurs while accommodating a feasible push-off propulsion constraint.

Persistent homology for automatic determination of human-data based cost of bipedal walking

Robotic walking research, since its inception, has attempted to generate anthropomorphic gait, but the community as a whole has struggled to agree even upon the correct ordering of discrete events during walking. In this paper, we propose a universal temporal ordering of discrete events for bipedal walking based on motion capture data collected from a nine subject straight line walking experiment. To construct this ordering, we develop a technique based on persistent homology to process the motion capture data to determine when the number of contact points changes during the course of a step which automatically dictates the ordering of discrete events. Surprisingly the findings of this work are that every subject regardless of age, sex, weight or height in the experiment had an identical temporal ordering of such events. This result allows for the development of a universal anthropomorphic bipedal robotic walking model because the temporal ordering of events together with the Lagrangian modeling of the robot completely determines the mathematical model of the system. Importantly, this universal ordering allows us to propose a cost function based on human data: the human-based cost, which we use to gauge the “human-like” quality of robotic walking.

ファジィルールを用いたヒト歩行のモデル化及び２脚モデルによるシミュレーション

ファジィルールを用いたヒト歩行のモデル化及び２脚モデルによるシミュレーション

Stabilization of the Capture Point Dynamics for Bipedal Walking based on Model Predictive Control

Considering a reduced center-of-mass model for bipedal walking, by utilizing the Capture Point as a system coordinate one can separate the stable and unstable components of the dynamics. In this paper, previous works on the stabilization of the Capture Point dynamics are extended by employing model predictive control (MPC). This allows to explicitly incorporate constraints on the zero-moment-point (ZMP) in the controller design. The proposed Capture-Point-MPC is evaluated in simulation and experiments with the DLR-Biped.

J163012 一定リズムを刻む胴を伴う一次元受動歩行波動アルゴリズム : 尻尾への加振を用いた3体結合衝突振動子モデル

We formulate one dimensional biped passive walking model with periodic rhythmic movement of a tail and a torso. The legs and the torso were modeled by globally coupled vibro-impact oscillators. The Grover like wave algorithm realizes indirect movement of a swing leg by transporting energy from the driven tail. Periodic leg exchange attains stable passive walking like movement. By using the designed mechanism, one central pattern generator can control multiple limbs movement.

New walking dynamics in the simplest passive bipedal walking model

This paper revisits the simplest passive walking model by Garcia et al. which displays chaos through period doubling from a stable period-1 gait. By carefully numerical studies, two new gaits with period-3 and -4 are found, whose stability is verified by estimates of eigenvalues of the corresponding Jacobian matrices. A surprising phenomenon uncovered here is that they both lead to higher periodic cycles and chaos via period doubling. To study the three different types of chaotic gaits rigorously, the existence of horseshoes is verified and estimates of the topological entropies are made by computer-assisted proofs in terms of topological horseshoe theory.

Hoffmann reflex in a rat bipedal walking model

The rat bipedal walking model (RBWM) refers to rats that acquired anatomical and functional characteristics for bipedal walking after the completion of a long-term motor training program. We recorded the Hoffmann reflex (H-reflex) of the forelimb and hindlimb in RBWM and control (not trained, normal) rats to evaluate the effects of bipedal walking on central nervous system (CNS) activity. The H-reflex recorded from the hindlimbs of the RBWM was significantly inhibited compared with that in the control. Furthermore, the inhibition of the H-reflex recorded from both forelimbs and hindlimbs by paired pulse stimulation tended to be enhanced in RBWM. These results indicate that bipedal walking or bipedal walking training cause functional changes in spinal reflex pathways in the CNS.

Modelling of an lower-extremity prostheses and its ankle trajectory control

In this survey, solid work model and strength analysis of lower-extremity prostheses with ankle trajectory control depending on hip angle measurement as reference motion, is introduced. After modelling and designing of certain prosthesis and its parts, strength analysis under various pedestal loads are given, to ensure optimal and convenient prostheses. A mathematical model for bipedal walking is then executed as a combination of two serial manipulators, each having two revolute joints, in other words, having two degrees of freedom. Inverse kinematics analysis and recursive Newton–Euler computation methods are given to obtain the dynamic equations, which describe the motion of the walking system. For desired walking characteristics, hip and ankle trajectories are derived. As ankle joint actuator in the system a permanent magnet direct current (DC) servo-motor with position feedback and its state space representation is given. By using the hip trajectory as reference the relevant angular position of ankle joint is calculated and is realised via DC motor. With this novel method besides ankle joint even the knee joint positions in the case of upper knee amputees can be determined for various gait instants. With these calculated values optimal ankle and knee trajectories can be realised via DC Servo motors. Thus best gait conditions for relevant prostheses and patients can be determined and evaluated. For future works this kind of a method may be very efficient solution in tracking problem of bipedal walking with under knee prostheses to obtain a quasi-natural walking.

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.

Modelling of an Under-Hip Prosthesis with Ankle and Knee Trajectory Control by Using Human Gait Analysis

AbstractIn this paper, depending on bipedal human walking analysis, knee and ankle joint control of special under-hip prosthesis is investigated. After the designing of the prosthesis and its parts by using SolidWorks, strength analyses under various pedestal loads are given, to ensure an optimal and convenient model.Depending on measurements of hip, knee and ankle motions by using vision techniques, bipedal human gait analysis is investigated. After these measurements using the hip motion as reference, knee and ankle joint angles are derived and calculated.The calculated values are then used to control the motions of knee and ankle joints via DC-motors so that the investigated trajectories for optimal bipedal walking could be realized.A mathematical model for bipedal walking is then executed as a combination of two serial manipulators, each having two revolute joints, in other words, having two degrees of freedom. Inverse kinematics analysis and recursive Newton-Euler computation methods are given to obtain the dynamic equations, which describe the motion of the walking system. For desired walking characteristics, knee and ankle trajectories are derived.With this novel method both ankle and knee joint positions in case of upper knee amputees can be determined and controlled for various gait instants.

Walking Pattern Generation for a Biped Walking Robot Using Convolution Sum

This paper describes a novel walking pattern generation method for a biped humanoid robot using a convolution sum. For a biped walking model, a single mass inverted pendulum model is generally used and the zero moment point (ZMP) equation is described by a decoupled linear differential equation. As a walking pattern generation method for the robot model, a novel method using a convolution sum is proposed in this paper. From the viewpoint of the linear system response, walking pattern generation can be regarded as a convolution of an arbitrary reference ZMP and the walking pattern for an impulse reference ZMP. For the calculation of convolution, the walking pattern for an impulse reference ZMP is first derived from the analytic walking pattern for a step reference ZMP. The convolution sum is then derived in two recursive forms, which can be applied online and offline, respectively. The proposed algorithm requires low computation power, since the walking pattern equation is composed of a recursive form. As the algorithm is expressed in analytic form, it is not necessary to solve optimization problems or calculate the fast Fourier transform, contrary to previous approaches. A computer simulation of walking demonstrates that the proposed algorithm yields excellent accuracy compared to the preview control method — one of the most highly regarded walking pattern generation methods. In addition, the application on the multi-point mass model is shown with the computer simulation.

Humanoid Walking Robot: Modeling, Inverse Dynamics, and Gain Scheduling Control

This article presents reference-model-based control design for a 10 degree-of-freedom bipedal walking robot, using nonlinear gain scheduling. The main goal is to show concentrated mass models can be used for prediction of the required joint torques for a bipedal walking robot. Relatively complicated architecture, high DOF, and balancing requirements make the control task of these robots difficult. Although linear control techniques can be used to control bipedal robots, nonlinear control is necessary for better performance. The emphasis of this work is to show that the reference model can be a bipedal walking model with concentrated mass at the center of gravity, which removes the problems related to design of a pseudo-inverse system. Another significance of this approach is the reduced calculation requirements due to the simplified procedure of nominal joint torques calculation. Kinematic and dynamic analysis is discussed including results for joint torques and ground force necessary to implement a prescribed walking motion. This analysis is accompanied by a comparison with experimental data. An inverse plant and a tracking error linearization-based controller design approach is described. We propose a novel combination of a nonlinear gain scheduling with a concentrated mass model for the MIMO bipedal robot system.

Influences of bipedal walking on the central nervous system —H-Reflex in the rat bipedal walking model

Influences of bipedal walking on the central nervous system —H-Reflex in the rat bipedal walking model

EMG burst pattern in quadrupedal and bipedal walking in man and the rat bipedal walking model (RBWM) on the treadmill

EMG burst pattern in quadrupedal and bipedal walking in man and the rat bipedal walking model (RBWM) on the treadmill

Design and Stability Analysis of a 3D Rimless Wheel with Flat Feet and Ankle Springs

A two-dimensional rimless wheel provides a simple model of bipedal walking. The motion of the rimless wheel is stable, and this particular property has clarified the fundamental role of a swing leg in planar bipedal walking that addresses the problem of falling forward. In this paper, a three-dimensional rimless wheel is investigated as a simple model of three-dimensional bipedal walking. The 3D rimless wheel model is useful in understanding the essential dynamics of 3D bipedal locomotion. The model consists of two rimless wheels connected by a link at the center of the wheels, and flat feet connected to the spokes with springs. The first numerical stability studies indicated that the motion of the 3D rimless wheel could be unstable; however, numerical simulations and experimental results showed that for a given slope and physical parameters, including the spring constant at the ankles, a stable motion is obtained. This indicates the usefulness of ankle springs in providing stable bipedal locomotion in three-dimensions.