Passive Dynamic Walking Research Articles

Passive turning motion of 3D rimless wheel: novel periodic gaits for bipedal curved walking

Passive dynamic walking originally was introduced to describe some natural stable periodic gaits in straight walking. However, in this research, we have extended this notion to curved walking, wherein some novel three-dimensional (3D) periodic gaits with natural stability have been realized. For this aim, the simplest bipedal walking model, i.e. a rimless spoked-wheel, in its general 3D form, has been considered on a straight slope surface. Then, two kinds of stable passive turning, i.e. limited and circular continuous have been discussed. The first kind is actually a transfer among two-dimensional (2D) periodic motions and can be implemented on such straight slope surface. It is shown that the second kind is related to novel 3D periodic motions and can be just recognized on a special surface profile namely ‘helical slope’. The latter are interpreted as 3D fixed points of a Poincare return map. Results not only show asymptotical stability of such periodic motions, but also surprisingly indicate that the stability of a 3D periodic gait (turning) is higher than 2D one (straight walking). Furthermore, the characteristics of passive turning are shown to be firmly connected with the value of the state variables such as the lean angle in each case.

Perception of gait patterns that deviate from normal and symmetric biped locomotion.

This study examines the range of gait patterns that are perceived as healthy and human-like with the goal of understanding how much asymmetry is allowable in a gait pattern before other people start to notice a gait impairment. Specifically, this study explores if certain abnormal walking patterns can be dismissed as unimpaired or not uncanny. Altering gait biomechanics is generally done in the fields of prosthetics and rehabilitation, however the perception of gait is often neglected. Although a certain gait can be functional, it may not be considered as normal by observers. On the other hand, an abnormally perceived gait may be more practical or necessary in some situations, such as limping after an injury or stroke and when wearing a prosthesis. This research will help to find the balance between the form and function of gait. Gait patterns are synthetically created using a passive dynamic walker (PDW) model that allows gait patterns to be systematically changed without the confounding influence from human sensorimotor feedback during walking. This standardized method allows the perception of specific changes in gait to be studied. The PDW model was used to produce walking patterns that showed a degree of abnormality in gait cadence, knee height, step length, and swing time created by changing the foot roll-over-shape, knee damping, knee location, and leg masses. The gait patterns were shown to participants who rated them according to separate scales of impairment and uncanniness. The results indicate that some pathological and asymmetric gait patterns are perceived as unimpaired and normal. Step time and step length asymmetries less than 5%, small knee location differences, and gait cadence changes of 25% do not result in a change in perception. The results also show that the parameters of a pathologically or uncanny perceived gait can be beneficially altered by increasing other independent parameters, in some sense masking the initial pathology.

2A1-L09 足裏曲率の制御による三次元受動歩行

To design a 3D biped robot, we should consider both of sagittal and lateral planes. Since the 3D biped robot involves two swings in the lateral and sagittal planes, passive dynamic walker in the lateral plane for synchronizing the swinging in the two planes and walks stably in three dimensions. -First, we designed a lateral model that can change radius of curvature of a foot. By changing a cycle of walking steps in the lateral can be controlled. Second, we developed a method of synchronizing two cycles of walking steps in the two planes by changing the radius of the foot. We performed numerical experiment for the model.

B-14 足関節背屈角制限による歩行安定靴の開発(シューズ)

It is known that a passive dynamic walk for a biped robot is stabilized by limiting its angle ofthe ankle of the stance leg. Since the passive dynamic walk has a similarity with a relaxed human walking, it is anticipated that the ankle angle limitation also contributes to stabilize a human walk. The purpose of this research is to realize this ankle angle limitation mechanism into human shoes, and investigate the effect of this shoes with the stabilization of human walk. In this paper, a simple configuration of the stabilized shoes is shown. In the shows, an angle of the ankle is limited by the attachment on a shin and a heel which are pulled together by a rubber sheet. A series of experiments were conducted to measure the stability of walking by recording integral EMG signals at the muscles that are known to posture control of a leg. The results showed that the muscles were less active during wearing the shoes with ankle angle limitation.

Energy Dissipation Rate Control Via a Semi-Analytical Pattern Generation Approach for Planar Three-Legged Galloping Robot based on the Property of Passive Dynamic Walking

In this paper an Energy Dissipation Rate Control (EDRC) method is introduced, which could provide stable walking or running gaits for legged robots. This method is realized by developing a semi-analytical pattern generation approach for a robot during each Single Support Phase (SSP). As yet, several control methods based on passive dynamic walking have been proposed by researchers to provide an efficient human-like biped walking robot. For most of these passive based controllers the main idea is to shape the robot’s energy level during each SSP to restore the mechanical energy which has been lost in the previous Impact Phases (IP); however, the EDRC method provides stable gaits for legged robots just by controlling the robot’s energy level during each IP. In this paper EDRC is applied to a Six-Link Three-Point Foot (6L3PF) model, to realize an active dynamic galloping gait on level ground. As the point-foot contact assumption for the 6L3PF imposes one degree of under-actuation in the ankle joint, it is not clear how to specify the forward kinematic defining the swing leg position and velocity as a function of actuated joint angles. So, a new strategy for solving the dynamic and kinematic equations of the robot is introduced for deriving suitable joint trajectories during each SSP. Simulation results show that the proposed methods in this paper are effective and the robot exhibits a stable dynamic galloping gait on level ground.

2P1-T10 対称構造を有する受動的動歩行ロボットを用いた適応的なふるまいの実験的検証

The passive dynamic walking's adaptive behavior is well known. It is behavior that changes gait for adaptation to environment. In previous studies have been performed to verify by experiment. However, previous robot has problem that has asymmetric parameters. Therefore two-period gait is appearing by the structure. This is not good for analysis the gait. So, we do experimental validation using a robot that has symmetric parameters for passive dynamic walking's adaptive behavior. This robot has symmetric parameters and one-period gait. This experiment is using slope can change slope angle. The robot walking on this slope. This slope is changing slope angle when robot walking. Then the robot will trying keep walking. A result, we verified the adaptive behavior of the robot with a symmetric parameters.

受動的動歩行の性質を利用した脚歩行ロボットの一設計方法

受動的動歩行の性質を利用した脚歩行ロボットの一設計方法

Dynamic Bipedal Walking under Stick-Slip Transitions

This paper studies the hybrid dynamics of bipedal robot walking under stick-slip transitions. We focus on two simple planar models with point feet: the rimless wheel and the compass biped. Unlike most of the existing works in the literature that assume sticking contact between the foot and the ground, we explore the case of insufficient friction, which may induce foot slippage. Numerical simulations of passive dynamic walking reveal the onset of stable periodic solutions involving stick-slip transitions. In the case of the compass biped with controlled joint torque actuation, we demonstrate how one can exploit kinematic trajectories of passive walking in order to induce and stabilize gaits with slipping impact.

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.

Stabilization and Walking Control for a Simple Passive Walker Using Computed Torque Method

The simple passive dynamic walker can walk down a shallow downhill slope with no external control or energy input. Nevertheless, the period-one gait stability is only possible over a very narrow range of slopes. Since the passive gaits are extremely sensitive to slope angles, it is important to use a control strategy in order to achieve a wide range of stable walking. The computed torque method is proposed here to produce stable period-one gait cycles for different slopes. In present method, the unstable walking gait is stabilized by a stable period-one gait pattern on a small specific slope. The proposed approach is illustrated by the simplest passive walkers with point and curved feet. Simulation results reveal the usefulness of this control method for improvement in stability properties of the models. doi: 10.5829/idosi.ije.2014.27.11b.16

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.

Finite difference method to find period-one gait cycles of simple passive walkers

Passive dynamic walking refers to a class of bipedal robots that can walk down an incline with no actuation or control input. These bipeds are sensitive to initial conditions due to their style of walking. According to small basin of attraction of passive limit cycles, it is important to start with an initial condition in the basin of attraction of stable walking (limit cycle). This paper presents a study of the simplest passive walker with point and curved feet. A new approach is proposed to find proper initial conditions for a pair of stable and unstable period-one gait limit cycles. This methodology is based on finite difference method which can solve the nonlinear differential equations of motion on a discrete time. Also, to investigate the physical configurations of the walkers and the environmental influence such as the slope angle, the parameter analysis is applied. Numerical simulations reveal the performance of the presented method in finding two stable and unstable gait patterns.

Modeling, control and analysis of limit cycle walking on slippery road surface

This paper investigates the feasibility and fundamental gait properties of active and passive limit-cycle walkers that walk on slippery road surface. First, we introduce the model of an underactuated spoked walker with a torso and mathematically analyze the collision model on the assumption of sliding contact with the ground to identify the condition for achieving instantaneous stance-leg exchange. Second, we develop the equation of motion incorporating sliding friction acting on the stance-leg-end and numerically show that the walker can generate a stable walking gait by applying a simple control of the torso. Furthermore, we discuss the case of passive dynamic walking on slippery slope using the same model but without considering the torso dynamics.

Legged Robot design applying the behavior of Passive Dynamic Walking

Legged Robot design applying the behavior of Passive Dynamic Walking

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.

Bifurcations and chaos in passive dynamic walking: A review

Irrespective of achieving certain success in comprehending Passive Dynamic Walking (PDW) phenomena from a viewpoint of the chaotic dynamics and bifurcation scenarios, a lot of questions still need to be answered. This paper provides an overview of the previous literature on the chaotic behavior of passive dynamic biped robots. A review of a broad spectrum of chaotic phenomena found in PDW in the past is presented for better understanding of the chaos detection and controlling methods. This paper also indicates that the bulk of literature on PDW robots is focused on locomotion on slope, but there is a thriving trend towards bipedal walking in more challenging environments.

Painlevé’s paradox and dynamic jamming in simple models of passive dynamic walking

Painleve’s paradox occurs in the rigid-body dynamics of mechanical systems with frictional contacts at configurations where the instantaneous solution is either indeterminate or inconsistent. Dynamic jamming is a scenario where the solution starts with consistent slippage and then converges in finite time to a configuration of inconsistency, while the contact force grows unbounded. The goal of this paper is to demonstrate that these two phenomena are also relevant to the field of robotic walking, and can occur in two classical theoretical models of passive dynamic walking — the rimless wheel and the compass biped. These models typically assume sticking contact and ignore the possibility of foot slippage, an assumption which requires sufficiently large ground friction. Nevertheless, even for large friction, a perturbation that involves foot slippage can be kinematically enforced due to external forces, vibrations, or loose gravel on the surface. In this work, the rimless wheel and compass biped models are revisited, and it is shown that the periodic solutions under sticking contact can suffer from both Painleve’s paradox and dynamic jamming when given a perturbation of foot slippage. Thus, avoidance of these phenomena and analysis of orbital stability with respect to perturbations that include slippage are of crucial importance for robotic legged locomotion.

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.

胴体の傾きによる推力を利用した2足歩行について

An attempt to extend passive dynamic walking from a slope to a horizontal surface have begun since the late 80's about the same time as the research on passive dynamic walking. A method using inclination of an upper body has been originally examined by McGeer, which enables a biped with the upper body to walk on the horizontal surface using counter torque of the torque generating to maintain the body inclination. However there are no deep insight into properties of the method such as stability against the inclination and robustness. Moreover, no researchers could achieve a real biped using the body inclination, and then the method would be sensitive against uncertainties (e.g., the ground undulation and small obstacles), accordingly. In this paper, we introduce an upper body and circular arc feet to a compass model biped and achieve various dynamic walking gait using thrust via the upper body inclination through numerical simulations. Stability of the walking gait is also analyzed using the Poincaré method. Moreover, a geometric tracking control using a cyclic motion of the biped walking is introduced in order to achieve more robust gait. Stability of the controlled walking is also analyzed using a Poincaré map of HZD. In addition, we discuss the difference between the walking using the upper body inclination and the geometric tracking controlled walking.

2A1-H06 対称構造を有する受動的動歩行ロボット(受動歩行ロボット(1))

Passive Dynamic Walking robots' structures which are used in previous researches usually generate different gaits for every step because of the robots' structures. However, general system model of Passive Dynamic Walking which is used for the research generates uniform gait for every step, of course. For this reason, it is desirable for the real prototyped legged walking robots to generate uniform gaits which are used for Passive Dynamic Walking research. For this reason, we proposed a new symmetric structure of Passive Dynamic Walking robot which generates uniform gait for every step. In this paper we describe the robot's structure and walking behavior in detail.