Passive Dynamic Walking Research Articles

Legged walking robot design applying the adaptive behavior of passive dynamic walking and interconnections among the different dynamics

In this paper, the authors propose a new design methodology for legged walking robots with dynamic characteristics suitable for walking motions by applying the unique properties of Passive Dynamic Walking as design criteria. The authors have identified the ‘adaptive behaviour’, in which the passive dynamic walking robot automatically adjusts its gait to keep walking in response to variations in physical parameters, such as the slope angle or mass, that constitute its mechanics. Furthermore, the authors discovered that this adaptive behaviour enables the transition of the structure and degrees of freedom of the passive dynamic walking robot to different mechanical systems through the application of ‘interconnections among different dynamics’. This paper introduces new mechanical design approach for legged robots that applies these unique properties, with its validity verified through the computer simulations.

Piezoelectric energy harvesting from walking motion of a passive biped robot model with flexible legs

Passive dynamic walking biped robots utilize the inherent dynamics of their structure to achieve walking motion without continuous actuation, enhancing energy efficiency and stability. Replacing conventional rigid legs with flexible elastic beams in the simplest passive walker will be associated with undesirable vibrations. Despite the positive effect of the damper in reducing vibrations, the current research has used the piezoelectric energy harvesting with the aim of reducing the wasted energy of the gait cycle and improving its stability range. For this purpose, the electromechanical Lagrange equations are determined by applying Hamilton's principle and the assumed mode method and then, the new definition of the step function is obtained through numerical methods, solving a boundary value problem to establish proper initial conditions for stable walking. Numerical simulations indicate that the piezoelectric energy harvester can create a stable period-one gait cycle by optimizing the length of the piezo layers attached to the undamped elastic legs despite the presence of small vibrations. Additional results are presented in bifurcation diagrams, investigating the effect of important physical and structural parameters such as slope angle, length and thickness of the piezo layer.

The Role of Knee Joint in Passive Dynamic Walking

The Role of Knee Joint in Passive Dynamic Walking

Stability analysis for passive robots walking on inclined surfaces with local angles

For common-legged robots with a kind of stiff joints, the human-like and consecutive gait shown by passive walking robots is a bit difficult to achieve because of varying degrees of control, which is usually accompanied by computational cost. Of course, passive dynamic walking undoubtedly has its inevitable disadvantages because of the lack of control, which is stability. At the same time, the significant nonlinearity of the passive gait increases the difficulty of realizing the walking stability of the passive robot. Therefore, the passive robot still needs certain control to achieve stable walking even on the natural plane or smooth slope. In this paper, a passive robot model walking on an inclined plane with a local angle is studied. First of all, the approximate solution of the nonlinear dynamic equation is given by the perturbation method, and the conditions for the robot to achieve stable walking without external forces are obtained. Further, the input-output feedback linearization control based on hybrid zero dynamics is employed to carry out virtual constraints on the passive robot during the swing stage of walking, facilitating the transition from the unstable state to the stable periodic state. From the result of the experiments, the walking stability of the passive robot is improved over a larger range of walking status values compared with the condition without external force control, and the use of this method reduces the complicated work of solving the fixed point. These findings possibly have reference value in passive walking stabilization control. Meanwhile, the simulation results obtained by designing and studying the minimum controlled walking model show that human walking is based on the uncontrolled mechanical process. The exploration of the mechanism of passive gait can provide some enlightenment to the research of human texture and the application of exoskeleton.

Towards Humanlike Passive Dynamic Walking with Physical and Dynamic Gait Resemblance

Towards Humanlike Passive Dynamic Walking with Physical and Dynamic Gait Resemblance

Analysis of Velocity Variation during Collision for Passive Dynamic Walking via Non-elastic and Elastic Models

Analysis of Velocity Variation during Collision for Passive Dynamic Walking via Non-elastic and Elastic Models

Sharp changes in fractal basin of attraction in passive dynamic walking

A passive dynamic walker is a mechanical system that walks down a slope without any control, and gives useful insights into the dynamic mechanism of stable walking. This system shows specific attractor characteristics depending on the slope angle due to nonlinear dynamics, such as period-doubling to chaos and its disappearance by a boundary crisis. However, it remains unclear what happens to the basin of attraction. In our previous studies, we showed that a fractal basin of attraction is generated using a simple model over a critical slope angle by iteratively applying the inverse image of the Poincaré map, which has stretching and bending effects. In the present study, we show that the size and fractality of the basin of attraction sharply change many times by changing the slope angle. Furthermore, we improved our previous analysis to clarify the mechanisms for these changes and the disappearance of the basin of attraction based on the stretching and bending deformation in the basin formation process. These findings will improve our understanding of the governing dynamics to generate the basin of attraction in walking.

Complex dynamics of the passive biped robot with flat feet: Gait bifurcation, intermittency and crisis

During the past decades, the walking dynamics of different types of passive biped robots have garnered significant attention. This paper investigates the complex dynamics of a passive flat-footed robot, encompassing both the local bifurcation of limit cycles and global bifurcation, resulting in significant changes in the system’s walking pattern. To identify the robot’s dynamic behavior, the Lyapunov Exponents (LEs) are calculated using the small orthogonal perturbation vectors method. The obtained LEs diagram also unveils several subtle periodic windows scattered within the chaotic region, where interior crisis and intermittency occur. Moreover, two new kinds of gaits that coexist with the traditional period-1 ones are found. Of particular significance is the discovery of the double boundary crisis that caused by the critical period-3 unstable periodic orbit, and this crisis serves as the fundamental reason to the falling down on slopes of the flat-footed robots. By gaining a better understanding of the nature of passive dynamic walking, it becomes possible to design more efficient controllers that impose less stringent torque requirements on biped walking robots.

Study on human-SRL synchronized walking based on coupled impedance.

Supernumerary robotic limbs (SRL) is a novel category of wearable robotics. Unlike prostheses (compensation for human limbs) and exoskeletons (augmentation of human limbs), SRL focuses on expanding human limbs and enhancing human activities, perception, and operation through the mutual collaboration of mechanical limbs and human limbs. The SRL of lower limbs are attached to the human waist, synchronized with the human walking in the forward direction, and can carry weight independently in the vertical direction. In order to enhance the synchronization performance of the human-machine system during walking and minimize interference with human gait, it is essential to investigate the coupling dynamics within the human-SRL system. To facilitate our research, this paper focuses on relatively ideal working conditions: level road surfaces, no additional weight-bearing on the SRL, and humans walking in a straight line without any turns. We build upon the passive dynamic walking theory and utilize the human-SRL system model established by MIT to develop a coupling system model. Through numerical simulations, we identify the optimal values for the stiffness and damping coefficients of the human-machine connection. Additionally, we have designed the wheel-legged SRL structure and constructed the SRL control system for experimental validation. It is found that a better synchronization of the human-machine walking process can be achieved by configuring suitable spring and damping units in the human-machine connection part. In this study, we explored the concept of SRL and its potential benefits for enhancing human motion, conducting simulations and experiments based on the coupled dynamics of human-SRL systems. The results indicate that by equipping the human-machine connection component with suitable spring and damping units, synchronization during the walking process can be improved.

Multistability of gaits, the basin of attraction and its external topology in the simplest passive walking model on stairs

For the passive walking robot, the basin of attraction is very small and thin, and thus makes it a great challenge to produce stable passive dynamic walking. This paper reports systematically the effect of initial conditions on gait dynamics of the simplest passive walking model on stairs. We find two new gaits with period-3 and period-4, and they both lead to higher periodic gaits and chaos by period-doubling bifurcations. The critical period-3 unstable orbit generated via the cyclic-fold bifurcation takes part in the annihilation of chaotic attractors twice, and this double boundary crisis becomes the main cause to the falling down on stairs of the passive walker. In particular, we compute the Lyapunov exponents to verify the effectiveness of the bifurcation process of these new gaits. More importantly, through analyzing the topology of phase space, the external domain of basin of attraction is classified in detail and marked precisely with different falling patterns. We believe such findings to add significantly to the knowledge of the selection of initial values and to be potentially helpful in the design and optimization of passive walking robots.

3-D Passive Dynamic Bipedal Walking and its Extension to Active Dynamic Walking

3-D Passive Dynamic Bipedal Walking and its Extension to Active Dynamic Walking

Effective of Constraing Foot Shape for Fall-down Phenomena on Bipedal Passive Dynamic Walk

Effective of Constraing Foot Shape for Fall-down Phenomena on Bipedal Passive Dynamic Walk

Low-speed Passive Dynamic Walking of Rimless Wheel Based on Antigravity Effect of Semicircular Feet

Low-speed Passive Dynamic Walking of Rimless Wheel Based on Antigravity Effect of Semicircular Feet

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.

A hybrid chaotic controller integrating hip stiffness modulation and reinforcement learning-based torque control to stabilize passive dynamic walking

Implementation of bipedal stable walking has attracted a lot of interest. Passive dynamic walking (PDW) is one promising manner to generate natural bipedal walking with high energy efficiency. However, how to improve stability and versatility of PDW-based robot against disturbance and time varying environments is still a big challenge in robotics. Chaos and bifurcations are intrinsic features of biped dynamic walking, which are important reasons for the failure of PDW. Thus a hybrid chaotic controller to stabilize chaos and bifurcations of PDW was proposed in this paper. At first, the dynamics model of compliant biped robot was set up, and routine to bipedal chaotic motions was found through parameter study. Then one hybrid chaotic controller integrating hip stiffness modulation and hip impulse torque control was developed, where hip impulse torque control based on reinforcement learning was trained to get state variables close to fixed point of PDW, and then hip stiffness modulation was conducted based on Ott-Grebogi-Yorke method to stabilize unstable motions of fixed point. Simulation results showed that period-1 stable walking could be gained for biped robots from chaotic motions, against original value disturbance, force disturbance and in time varying environments. The proposed hybrid chaotic controller could be used to stabilize bipedal chaotic motions and make the passivity-based robot become robust and versatile to disturbed and time changing environments.

A necessary and sufficient condition for conservation of angular momentum at foot strike during passive dynamic walking

A necessary and sufficient condition for conservation of angular momentum at foot strike during passive dynamic walking

Motion analysis of passive dynamic walking with a rigorously constraint model: A necessary condition for maintaining period-1 gait

The friction force is an important environmental factor that influences dynamic walking. While most of the related works simply assume static friction or Coulomb friction, we use the LuGre friction, which accounts for both static and dynamic effects, to model the horizontal ground reaction force of passive dynamic walking. We present a detailed mathematical modeling method and perform numerical simulations using it. Furthermore, we analyze the ground surface cases of the Coulomb friction condition and static friction condition to verify the model’s generalization. We discover the required condition for the existence of the period-1 gait through investigation. Our mathematical model and theoretical analysis add to our understanding of passive dynamic walking, which helps to positively utilize the natural dynamics of the legged locomotion system in control design.

Passive Dynamic Walking of Rimless Wheel Formed by Four Rigid Frames and Eight Springs

This paper proposes a novel rimless-wheel type legged robot that can be made by adding the constraint of the rotation axis to the tensegrity structure formed by four rigid frames and eight springs. First, we introduce a planar 12-DOF robot model for passive-dynamic walking on a gentle downhill, and develop the equations of motion, constraint conditions and inelastic collision. Second, we numerically show that the generated passive-dynamic gait is not always asymptotically stable due to the variable impact posture, and that it is possible to generate a passive-dynamic gait that is faster than a normal rimless wheel by appropriately setting the spring coefficient.

Passive Dynamic Walking of Combined Rimless Wheels Formed by Two Cross-shaped Frames and Eight Viscoelastic Elements

Passive Dynamic Walking of Combined Rimless Wheels Formed by Two Cross-shaped Frames and Eight Viscoelastic Elements