Passive Dynamic Walking Model Research Articles

Dynamic Stability of Passive Dynamic Walking Following Unexpected Perturbations.

Mitigating the risk of falling is an area of significant interest among clinicians due to the often profound health-related consequences of falls. Consequently, there is acute interest in characterizing the biomechanical conditions associated with increased fall risk, and in methods for quantifying gait stability under those conditions toward predicting and ultimately preventing falls. Considerable insights into the biomechanics of fall risk have been provided by examining the passive dynamic walking (PDW) model under nominal and perturbed conditions. This work aims to expand upon prior efforts and develop the PDW model as a model of tripping and slipping by simulating and analyzing the behavior of the model during transient perturbations. We show that fall risk increases with increasing perturbation magnitude, yet stable walking may be found even with fairly large perturbations. In cases where transient perturbations result in a fall, a nontrivial portion exhibit a substantial period of stumbling before the fall, indicating an opportunity for developing early fall-risk detection and intervention techniques. In such cases, we show that widely used kinematic metrics are able to predict whether or not a fall will occur with up to 82% balanced accuracy, even when a variety of gait kinematics are considered.

Single subject analysis of individual responses to prosthetic modifications based on passive dynamic walking model

BackgroundGroup statistical analysis may mask individual differences in response to interaction with rehabilitative devices such as prostheses. This study sets out to evaluate the effect of asymmetric prosthesis using a single subject methodology on individuals with unilateral transfemoral amputation. MethodsAcceleration data of 17 participants with unilateral transfemoral amputation were collected using a triaxial accelerometer attached at the L3 level of the spine during level ground walking under four prosthesis conditions: 1) no added mass; 2) the knee joint relocated downwards by 18% of the total shank length, shank mass decreased by 68%, thigh mass increased by 7%; 3) the knee joint relocated downwards by 37% of the total shank length, shank mass decreased by 68%, thigh mass increased by 7%, and 4) thigh mass increased 17%, shank mass decreased by 38%. Step length, step time, step length variability, step time variability and Floquet multiplier were statistically assessed. FindingsThe single subject analysis highlighted that under prosthetic modifications, intact limb step length was increased and prosthetic step length was deceased in most participants (n > 9). No significant changes were observed in Floquet multiplier (n > 14), step length (n > 6) and step time variability (n > 9) across all conditions. InterpretationSingle subject analysis showed that in response to the immediate effect of asymmetric prosthesis, increase in the intact limb step length and decrease in the prosthetic limb step length emerged as a dominant strategy for most participants. Regarding Floquet multiplier, step length, and step time variability, our prosthetic modifications did not produce the anticipated effects.

Experimental study of prosthesis modifications based on passive dynamic walking model: A limit cycle stability analysis

The aim of the current study was to examine the effect of asymmetric prosthesis derived from the passive dynamic walking (PDW) concept on dynamic stability and symmetry in unilateral transfemoral amputees. Seventeen transfemoral amputees were asked to walk on 77.8 m in preferred speed under four conditions: 1) no added mass, 2) the knee joint relocated downwards by 18% of the total shank length, shank mass decreased by 68%, thigh mass increased by 7%, 3) the knee joint relocated downwards by 37% of the total shank length, shank mass decreased by 68%, thigh mass increased by 7% and 4) thigh mass increased 17%, shank mass decreased by 38%. Trunk accelerations were recorded by a triaxle accelerometer, attached at the L3 level of spine. For each condition, stability (orbital and local), intra-limb step length and step time variability, step length and step time symmetry, were estimated from the vertical acceleration. Our findings showed no significant change in the orbital stability (P = 0.627) and the local stability (P = 0.748). In addition, no significant difference was found in the step length symmetry (P = 0.891), intra-limb step length variability (P > 0.234), the step time symmetry (P = 0.960) and intra-limb step time variability (P > 0.847) with the new prosthetic configurations. Our empirical findings indicate that contrary to the modeling predictions, manipulating physical parameters does not improve gait pattern in terms of stability, variability and symmetry in transfemoral amputees. It suggests that proposed modifications based on PDW cannot be directly applied to real human conditions without further elaborations.

Design of active biped walker based on passive dynamic walking model with torso

Design of active biped walker based on passive dynamic walking model with torso

On the stability of passive dynamic walker with flat foot and series ankle spring

In this study, the effects of a flat foot and series ankle spring on walking stability and efficiency are investigated with three passive dynamic walking models. These models are tuned on the same ...

Stability and control of planar compass gait walking with series-elastic ankle actuation

Passive dynamic walking models are capable of capturing basic properties of walking behaviours and can generate stable human-like walking without any actuation on inclined surfaces. The passive compass gait model is among the simplest of such models, consisting of a planar point mass and two stick legs. A number of different actuation methods have been proposed both for this model and its more complex extensions to eliminate the need for a sloped ground, balancing collision losses using gravitational potential energy. In this study, we introduce and investigate an extended model with series-elastic actuation at the ankle towards a similar goal, realizing stable walking on level ground. Our model seeks to capture the basic structure of how humans utilize toe push-off prior to leg liftoff, and is intended to eventually be used for controlling the ankle joint in a lower-body robotic orthosis. We derive hybrid equations of motion for this model, and show numerically through Poincaré analysis that it can achieve asymptotically stable walking on level ground for certain choices of system parameters. We then study the bifurcation regimes of period doubling with this model, leading up to chaotic walking patterns. Finally, we show that feedback control on the initial extension of the series ankle spring can be used to improve and extend system stability.

Study of human walking patterns based on the parameter optimization of a passive dynamic walking robot.

The study of human walking patterns mainly focuses on how control affects walking because control schemes are considered to be dominant in human walking. This study proposes that not only fine control schemes but also optimized body segment parameters are responsible for humans' low-energy walking. A passive dynamic walker provides the possibility of analyzing the effect of parameters on walking efficiency because of its ability to walk without any control. Thus, a passive dynamic walking model with a relatively human-like structure was built, and a parameter optimization process based on the gait sensitivity norm was implemented to determine the optimal mechanical parameters by numerical simulation. The results were close to human body parameters, thus indicating that humans can walk under a passive pattern based on their body segment parameters. A quasi-passive walking prototype was built on the basis of the optimization results. Experiments showed that a passive robot with optimized parameters could walk on level ground with only a simple hip actuation. This result implies that humans can walk under a passive pattern based on their body segment parameters with only simple control strategy implying that humans can opt to walk instinctively under a passive pattern.

System overview and walking dynamics of a passive dynamic walking robot with flat feet

The concept of “passive dynamic walking robot” refers to the robot that can walk down a shallow slope stably without any actuation and control which shows a limit cycle during walking. By adding actuation at some joints, the passive dynamic walking robot can walk stably on level ground and exhibit more versatile gaits than fully passive robot, namely, the “limit cycle walker.” In this article, we present the mechanical structures and control system design for a passive dynamic walking robot with series elastic actuators at hip joint and ankle joints. We built a walking model that consisted of an upper body, knee joints, and flat feet and derived its walking dynamics that involve double stance phases in a walking cycle based on virtual power principle. The instant just before impact was chosen as the start of one step to reduce the number of independent state variables. A numerical simulation was implemented by using MATLAB, in which the proposed passive dynamic walking model could walk stably down a shallow slope, which proves that the derived walking dynamics are correct. A physical passive robot prototype was built finally, and the experiment results show that by only simple control scheme the passive dynamic robot could walk stably on level ground.

Common formation mechanism of basin of attraction for bipedal walking models by saddle hyperbolicity and hybrid dynamics

In this paper, we investigate the mathematical structures and mechanisms of bipedal walking from a dynamical viewpoint. Especially, we focus on the basin of attraction since it determines the stability of bipedal walking. We treat two similar but different bipedal walking models (passive and active dynamic walking models) and examine common mathematical structure between these models. We find that the saddle hyperbolicity and hybrid system play important roles for the shape of the basin of attraction in both models, which are quite common for more general bipedal models and important for understanding the stability mechanism of bipedal walking.

Effects of a Passive Dynamic Walker’s Mechanical Parameters on Foot-Ground Clearance

Unlike human beings, a robot will fall without a sufficient walking foot-ground clearance, which is essential to a success walking. However, to obtain less calculating time and simpler analysis, foot scuffing is ignored in most studies during numerical simulations of passive dynamic walkers which can walk down a gentle slope and are actuated only by their own gravity. So this paper initials a study on the effects of a passive dynamic walker’s mechanical parameters on foot-ground clearance and the results can be used to make a further parameters optimization based on walking stability analysis. A passive dynamic walking model with a hip joint, knee joints, ankle joints and an upper body and a prototype were built and numerical simulations were implemented to analyze the effects of mechanical parameters on foot-ground clearance. Finally, the results were validated in prototype experiments.

Bifurcation and chaos in the simple passive dynamic walking model with upper body.

We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.

The role of walking surface in enhancing the stability of the simplest passive dynamic biped

SUMMARYEmploying passive dynamics of the simplest point-foot walker, we have shown that the walking surface could have a great role in promoting the gait stability. In this regard, the stabilization of the simplest walking model,3 between the range of slopes greater than 0.0151 rad. and less than 0.26 rad., has been achieved. The walker like other passive dynamic walking models has no open or closed-loop control system; so, is only actuated by the gravity field. Moreover, no damper or spring is used. Obviously, according to the model's unstable behavior, it is unable to walk on an even flat ramp between the mentioned intervals.3 Here, instead of restraining the model, we let it explore other smooth surfaces, walking on which, will end in an equally inclined surface. To reach the objective, we employ a parallel series of fixed straight lines (local slopes) passing through contact points of an unstable cycling gait, which is generated by an ordinary ramp. To categorize, we have nicknamed those local slopes that guide the biped to a stable cyclic walking, “Ground Attractors,” and the other, leading it to a fall, “Repulsive Directions.” Our results reveal that for the slope <0.26 rad., a closed interval of ground attractors could be found. Stabilization of those unstable limit cycles by this technique makes obvious the key role of walking surface on bipedal gait. Furthermore, following our previous work,13 the results confirm that the two thoroughly similar walking trajectories can have different stability. All of these results strongly demonstrate that without considering the effects of a walking surface, we cannot establish any explicit relationship between the walker's speed and its stability.

1A1-J05 スリップ時における二足歩行ロボットの制御と回復性(進化・学習とロボティクス)

Passive Dynamic Walking is a technique that makes a robot walk naturally like a human adjusting to skews and slight slopes without active control or energy. It is energy efficient, but to set the initial condition for robots to walk stably is difficult. So when a Passive Dynamic Walking model is affected by a slip, it is not considered to walk stably. This paper analyzes how the gait stability of Passive Dynamic Walking robots is affected by a slip. The results of this study provide some ideas about how to apply such technique in a variety of environments or conditions.

A passive dynamic walking model with Coulomb friction at the hip joint

SUMMARYThis paper presents a modified passive dynamic walking model with hip friction. We add Coulomb friction to the hip joint of a two-dimensional straight-legged passive dynamic walker. The walking map is divided into two parts – the swing phase and the impact phase. Coulomb friction and impact make the model's dynamic equations nonlinear and non-smooth, and a numerical algorithm is given to deal with this model. We study the effects of hip friction on gait and obtain basins of attraction of different coefficients of friction.

Passive Dynamic Biped Walking—Part I: Development and Validation of an Advanced Model

Passive dynamic walking is a manner of walking developed, partially or in whole, by the energy provided by gravity. Studying passive dynamic walking provides insight into human walking and is an invaluable tool for designing energy-efficient biped robots. The objective of this research was to develop a continuous mathematical model of passive dynamic walking, in which the Hunt–Crossley contact model, and the LuGre friction model were used to represent the normal and tangential ground reactions continuously. A physical passive walker was built to validate the proposed mathematical model. A traditional impact-based passive walking model was also used as a reference to demonstrate the advancement of the proposed passive dynamic walking model. The simulated gait of the proposed model matched the gait of the physical passive walker exceptionally well, both in trend and magnitude.

A Passive Dynamic Walking Model Based on Knee-Bend Behaviour: Stability and Adaptability for Walking down Steep Slopes

This paper presents a passive dynamic walking model based on knee-bend behaviour, which is inspired by the way human beings walk. The length and mass parameters of human beings are used in the walking model. The knee-bend mechanism of the stance leg is designed in the phase between knee-strike and heel-strike. q* which is the angular difference of the stance leg between the two events, knee-strike and knee-bend, is adjusted in order to find a stable walking motion. The results show that the stable periodic walking motion on a slope of r <0.4 can be found by adjusting q*. Furthermore, with a particular q* in the range of 0.12< q*<0.18, the walker can walk down more steps before falling down on an arbitrary slope. The walking motion is more stable and adaptable than the conventional walking motion, especially for steep slopes.

Modeling and analysis of passive dynamic bipedal walking with segmented feet and compliant joints

Passive dynamic walking has been developed as a possible explanation for the efficiency of the human gait. This paper presents a passive dynamic walking model with segmented feet, which makes the bipedal walking gait more close to natural human-like gait. The proposed model extends the simplest walking model with the addition of flat feet and torsional spring based compliance on ankle joints and toe joints, to achieve stable walking on a slope driven by gravity. The push-off phase includes foot rotations around the toe joint and around the toe tip, which shows a great resemblance to human normal walking. This paper investigates the effects of the segmented foot structure on bipedal walking in simulations. The model achieves satisfactory walking results on even or uneven slopes.

Analysis of period doubling bifurcation and chaos mirror of biped passive dynamic robot gait

With a reasonable parameter configuration, the passive dynamic walking model has a stable, efficient, natural periodic gait, which depends only on gravity and inertia when walking down a slight slope. In fact, there is a delicate balance in the energy conversion in the stable periodic gait, making the gait adjustable by changing the model parameters. Poincare mapping is combined with Newton-Raphson iteration to obtain the numerical solution of the final state of the passive dynamic walking model. In addition, a simulation on the walking gait of the model is performed by increasing the slope step by step, thereby fixing the model’s parameters synchronously. Then, the gait features obtained in the different slope stages are analyzed and discussed, the intrinsic laws are revealed in depth. The results indicate that the gait can present features of a single period, doubling period, the entrance of chaos, merging of sub-bands, and so on, because of the high sensitivity of the passive dynamic walking to the slope. From a global viewpoint, the gait becomes chaotic by way of period doubling bifurcation, with a self-similar Feigenbaum fractal structure in the process. At the entrance of chaos, the gait sequence comprises a Cantor set, and during the chaotic stage, sub-bands in the final-state diagram of the robot system present as a mirror of the period doubling bifurcation.

Dynamic arm swinging in human walking

Humans tend to swing their arms when they walk, a curious behaviour since the arms play no obvious role in bipedal gait. It might be costly to use muscles to swing the arms, and it is unclear whether potential benefits elsewhere in the body would justify such costs. To examine these costs and benefits, we developed a passive dynamic walking model with free-swinging arms. Even with no torques driving the arms or legs, the model produced walking gaits with arm swinging similar to humans. Passive gaits with arm phasing opposite to normal were also found, but these induced a much greater reaction moment from the ground, which could require muscular effort in humans. We therefore hypothesized that the reduction of this moment may explain the physiological benefit of arm swinging. Experimental measurements of humans (n = 10) showed that normal arm swinging required minimal shoulder torque, while volitionally holding the arms still required 12 per cent more metabolic energy. Among measures of gait mechanics, vertical ground reaction moment was most affected by arm swinging and increased by 63 per cent without it. Walking with opposite-to-normal arm phasing required minimal shoulder effort but magnified the ground reaction moment, causing metabolic rate to increase by 26 per cent. Passive dynamics appear to make arm swinging easy, while indirect benefits from reduced vertical moments make it worthwhile overall.

The simplest passive dynamic walking model with toed feet: a parametric study

This paper presents a passive dynamic walking model with toed feet that can walk down a gentle slope under the action of gravity alone. The model is the simplest of its kind with a point mass at the hip and two rigid legs each hinged at the hip on the one end and equipped with toed foot on the other end. We investigate two cases of the model, one with massless legs and another with infinitesimal leg masses. Rotation of the stance foot about the toe joint is initiated by ankle-strike, which is caused by the inelastic collision of the stance leg with a stop mounted on the stance foot. Numerical simulations of walking show that larger step lengths, higher speeds, stability, and energy efficiency can be achieved than what is achievable by a point-feet walker of same hip mass and leg lengths. Period-two gait of a point-feet walker is compared with period-one gait of the toed-feet walker and the mechanism responsible for achieving longer step lengths is described. It is shown that the advantage of the proposed walker comes from its relation to arc-feet walker. The characteristics of deterministic gait with infinitesimal leg masses is compared with that of nondeterministic gait with zero leg masses. It is shown that deterministic gait does not give maximum speed and efficiency compared to nondeterministic gait with swing leg control. Finally, active dynamic walking of the proposed walker is discussed.