Passive Walking Research Articles

Additional Complex Behaviors, Bifurcations and Chaos, in the Passive Walk of the Compass-Type Bipedal Robot

Abstract The compass-type bipedal robot is an impulsive hybrid mechanical system that can produce complex behaviors, chaos and bifurcations. In this work, we analyze the passive dynamic walking of the compass robot to further explore its complexity and these nonlinear phenomena while descending inclined surfaces. The bifurcation diagrams are mainly adopted to investigate the complex walking behaviors by varying the slope angle and the length of the lower-leg segment. We show exhibition of the period-doubling bifurcation, the Neimark-Sacker bifurcation, the period-remerging phenomenon, bubbles and chaos. The Poincare map and the state space are also used to further analyze these complex behaviors.

Simulation and optimization of materials used for prosthetic leg for above-knee amputees using MR fluid

The lower limb amputees are increasing day by day. This has led to an increase in research in the field of prosthetic legs. Prosthetic legs can be either active or passive. The active ones can behave very closely to the human leg. This means that they can provide adequate torques and forces for the ease of movement of the amputee. The downside of such prostheses is that they are too expensive thus being unaffordable for a lot of people. The passive type of prosthetic legs are very cheap as compared to the active ones, but they can’t provide the torque required for walking. Thus, the amputees with a passive prosthetic leg walk awkwardly. A semi-active prosthetic leg can behave closely like a natural leg and is also not very expensive. This can be achieved using MR Damper, which operates only in the stance phase. The MR Damper consists of an MR fluid, a smart material that changes its behaviour according to the magnetic field around it. It can be controlled using a PID controller, to produce the required current and hence the magnetic field. Apart from this, an ankle joint with 2 DOF can be provided for further ease of movement for a potential application. The choice of the material for MR Damper and the ankle for their effective working as well as to make a lighter prosthesis is an important decision. MR Damper needs to have a magnetic core. Iron and steel core has been simulated to see the variation of magnetic flux density and the magnetic contour lines. The most important factor for this analysis is the relative permeability of the material. For the ankle to work properly, it should be able to withstand the stresses and also have a factor of safety more than 1 at all points. Aluminium alloy, being a lighter material than steel can be used.

Abnormal Gait for Walking Robot Based on Passive Dynamical Mechanism and Walking Assistance

Abnormal Gait for Walking Robot Based on Passive Dynamical Mechanism and Walking Assistance

Elementary School Students' Inquiry Activities Related to the Creation of Quadrupedal Passive Walking Paper Toys

Elementary School Students' Inquiry Activities Related to the Creation of Quadrupedal Passive Walking Paper Toys

Development and Basic Experiments of Tensegrity Passive Walking Robot

Development and Basic Experiments of Tensegrity Passive Walking Robot

Study on 2D Passive Walking with Heels

Study on 2D Passive Walking with Heels

Walking Wheel

A hypothesis was proposed that during the bipedal walking, there appear stable periodic movements in certain variables (self-oscillations). In this case, it is possible to easily change parameters of this periodic locomotion using open (without feedback) control loops with respect to some of the variables. As the first stage in testing this hypothesis, dynamics of the walking wheel downward movement along an inclined plane was analytically studied. Walking wheel is the simplest model of passive bipedal walking. When it moves, energy is supplied to the system due to the force of gravity action. It is shown that point mapping of the wheel angular speed alteration per step (Poincare map) in the overwhelming majority of cases has one fixed point. This fixed point corresponds either to stable periodic solution (self-oscillation), which is the wheel rolling down an inclined plane, or to the wheel movement ending with its termination as a result of the endless series of impacts with swinging on two legs. In the degenerate case, the Poincare map has two fixed points. One of them corresponds to the unstable limiting cycle matching the wheel rolling, and the second corresponds to a wheel stop. In this case, the limiting cycle is stable outside and unstable inside itself

Transient contact-impact behavior for passive walking of compliant bipedal robots

When bipedal robots walk, the compliance of local contact zone and whole structure usually causes high amplitude contact force and wave propagation excited by impact. The object of this paper is to analyze the transient contact-impact behavior during the walking of compliant bipedal robots (CBR) using a completely flexible body model (CFBM) and obtain its fine contact modes. The applicability of the traditional method based on completely rigid body model (CRBM) to the compliant bipedal robots is also discussed. In CFBM, the structural deformation field and inertial field are discretized by finite element theory, and the penalty function method is adopted to account for the unilateral contact constraint. The dynamic equations, strain and stress equations for the CFBM are derived. The contact forces, impact-induced wave propagation and total mechanical energy of the CBR are calculated. The results show that the relative contact motions between the foot and the slope experience two phases: (1) macroscopic oblique impact phase (duration time is 0.1∼0.2 s) and (2) rolling phase (duration time is 0.6∼0.7 s). Phase 1 consists of a series of fast normal contact-separation switches and tangential stick–slip switches. Phase 2 means there are continuous normal compression and tangential stick. Since the traditional method neglects the first phase, it is not comprehensive for investigating the CBR with impact-induced waves and vibration, especially for the case of lower coefficient of friction (COF) μ. In addition, a ‘dynamic self-locking’ phenomenon is found as μ>0.9, which will lead to the walking unstable.

Stabilization of the passive walking dynamics of the compass-gait biped robot by developing the analytical expression of the controlled Poincaré map

The compass-gait biped robot is a two-DoF legged mechanical system that has been known by its passive dynamic walking. This kind of passive biped robot is modeled by an impulsive hybrid nonlinear system that exhibits complex behaviors. This paper is concerned with the stabilization of the passive dynamic walking of the compass-gait biped robot by designing an analytical expression of the controlled Poincare map. The suggested analytical method starts with the time-piecewise linearization of the impulsive system augmented with the controller, around a desired one-periodic passive hybrid limit cycle. By virtue of the first-order Taylor series, we design an explicit expression of the controlled Poincare map. We present also a simplified expression of the controlled Poincare map having a reduced dimension. In order to accomplish our goal concerned with the stabilization of the passive walking dynamics of the compass-gait biped robot, we develop first the linearized Poincare map around the period-1 fixed point of the Poincare map and we adopt a state-feedback control law to stabilize it. Furthermore, in order to enhance the effectiveness and robustness of the stabilization process, we adopt an LMI-based optimization approach by considering the controlled Poincare map to design the feedback gain. In the end of this work, we provide some numerical and graphical simulation results, to show the validity of the designed control law by means of the controlled Poincare map in the stabilization of the passive dynamic walking of the compass-gait biped robot.

Environmental and behavioral controls on juvenile Chinook salmon migration pathways in the Columbia River estuary

Juvenile Chinook salmon population dynamics in the Columbia River estuary are influenced by physical processes, hatchery practices, and behavioral decision-making. To better understand how environmental forcing and swimming behavior influence estuarine migration and travel times, we developed an individual-based model (IBM) that uses 3-D outputs from a hydrodynamic model to simulate Lagrangian transport as well as swimming and bioenergetics sub-models to simulate active swimming and growth. Simulations were run in 2010 during the migration seasons for yearling and subyearling Chinook salmon. For both life history types, alternative behaviors were simulated, from random walks to behaviors that optimized efficient system migration for yearling Chinook salmon and growth for subyearling Chinook salmon. Simulation results compared well against observed data on travel times and common migration pathways; the simulated travel times for both yearling and subyearling Chinook salmon were within several hours of the observed travel times. In general, residence times and pathways were largely driven by river discharge and the phase of the tide. During periods of greater river discharge, simulated estuarine residence times were reduced and variability across individuals was minimal. The timing of estuarine exit was closely tied to the phase of the tide, with most simulated individuals exiting the system during the ebb phase. While travel times were largely driven by flow velocities, swimming behavior was likewise important. Simulated yearling Chinook salmon behaviors that optimized movement with surrounding flows resulted in reduced estuarine residence times when compared to passive and random walk behaviors. Similarly, simulated subyearling Chinook salmon behaviors that optimized growth directed individuals to shallow peripheral habitats, resulting in longer residence times and higher growth rates. Even if potentially important factors such as predator avoidance were not included, this IBM provides an informative tool to model migration pathways, growth, and residence times of juvenile salmon in an estuarine environment and could be used to inform management decisions by evaluating various scenarios.

Development of an Improved Rotational Orthosis for Walking With Arm Swing and Active Ankle Control.

Based on interlimb neural coupling, gait robotic systems should produce walking-like movement in both upper and lower limbs for effective walking restoration. Two orthoses were previously designed in our lab to provide passive walking with arm swing. However, an active system for walking with arm swing is desirable to serve as a testbed for investigation of interlimb neural coupling in response to voluntary input. Given the important function of the ankle joint during normal walking, this work aimed to develop an improved rotational orthosis for walking with arm swing, which is called ROWAS II, and especially to develop and evaluate the algorithms for active ankle control. After description of the mechanical structure and control schemes of the overall ROWAS II system, the closed-loop position control and adjustable admittance control algorithms were firstly deduced, then simulated in Matlab/Simulink and finally implemented in the ROWAS II system. Six able-bodied participants were recruited to use the ROWAS II system in passive mode, and then to estimate the active ankle mechanism. It was showed that the closed-loop position control algorithms enabled the ROWAS II system to track the target arm-leg walking movement patterns well in passive mode, with the tracking error of each joint <0.7°. The adjustable admittance control algorithms enabled the participants to voluntarily adjust the ankle movement by exerting various active force. Higher admittance gains enabled the participants to more easily adjust the movement trajectory of the ankle mechanism. The ROWAS II system is technically feasible to produce walking-like movement in the bilateral upper and lower limbs in passive mode, and the ankle mechanism has technical potential to provide various active ankle training during gait rehabilitation. This novel ROWAS II system can serve as a testbed for further investigation of interlimb neural coupling in response to voluntary ankle movement and is technically feasible to provide a new training paradigm of walking with arm swing and active ankle control.

Nonlinear predictive control applied to a biped walker with adjustable step length using a passive walking‐based reference generator

SummaryThis paper presents the use of passive dynamics to generate the sagittal plane references for a biped walker. In order to achieve an adjustable gait width, a neural network reference generator, trained with passive walking data on different slopes, was applied. The control algorithm was implemented with an Nonlinear Model Predictive Control (NMPC) strategy, in order to perform multiple‐input multiple‐output reference tracking while maintaining balance. The main contributions of the present work are using a kneed passive walker model for reference generation, which creates gait profiles that are more natural than the compass gait model, presenting a low computational cost, since only the forward kinematic model is used, and enabling adjustable gait width, due to the use of a neural network trained with data from the passive walker. Simulation results using V‐REP (Virtual Robot Experimentation Platform) are presented, using a sagittal kneed walker with a torso and arms, demonstrating the effectiveness of the proposed method.

The InSight Crutches: Analyzing the Role of Arm Support During Robot-Assisted Leg Movements

To complement the assistance of a wearable robot, users with leg weakness often rely on balance and body-weight support (BWS) through their arms and passive walking aids. A precise quantification of this arm support is crucial to better understand real-world robot dynamics, human-robot interaction, and human user performance.

Existence and stability of limit cycles in the model of a planar passive biped walking down a slope.

We consider the simplest model of a passive biped walking down a slope given by the equations of switched coupled pendula (McGeer T. 1990 Passive dynamic walking. Int. J. Robot. Res. 9, 62-82. (doi:10.1177/027836499000900206)). Following the fundamental work by Garcia (Garcia et al. 1998 J. Biomech. Eng. 120, 281. (doi:10.1115/1.2798313)), we view the slope of the ground as a small parameter γ ≥ 0. When γ = 0, the system can be solved in closed form and the existence of a family of cycles (i.e. potential walking cycles) can be computed in closed form. As observed in Garcia et al. (Garcia et al. 1998 J. Biomech. Eng. 120, 281. (doi:10.1115/1.2798313)), the family of cycles disappears when γ increases and only isolated asymptotically stable cycles (walking cycles) persist. However, no mathematically complete proofs of the existence and stability of walking cycles have been reported in the literature to date. The present paper proves the existence and stability of a walking cycle (long-period gait cycle, as termed by McGeer) by using the methods of perturbation theory for maps. In particular, we derive a perturbation theorem for the occurrence of stable fixed points from 1-parameter families in two-dimensional maps that can be of independent interest in applied sciences.

Development of a Bipedal Passive Walking Paper Toy as a Teaching Material

Development of a Bipedal Passive Walking Paper Toy as a Teaching Material

Possibility of walking assistance from the viewpoint of passive walking robot

Possibility of walking assistance from the viewpoint of passive walking robot

Robust Control of Semi-passive Biped Dynamic Locomotion based on a Discrete Control Lyapunov Function

SUMMARYThis paper focuses on robust control of a simplest passive model, which is established on a DCLF (discrete control Lyapunov function) -based control system, and presents gait transition method based on the study of purely passive walker. Firstly, the DCLF is introduced to stabilize walking process between steps exponentially by modulating the length of next step. Next, the swing leg trajectory from mid-stance position to foot-strike can be planned. Then the control law is calculated to resist external disturbance. Besides, an impulse is added just before foot-strike to realize a periodic walking pattern on flat or uphill ground. With walking terrain varying, the robot can transit to an adaptive walking gait in a few steps. With different push or pull disturbances acting on hip joint and the robot gait transiting on a continuously slope-changing downhill, the effectiveness of the presented DCLF-based method is verified using simulation experiments. The ability to walk on a changing environment is also presented by simulation results. The insights of this paper can help to develop a robust control method and adaptive walking of dynamic passive locomotion robots.

Simulation verification for the robustness of passive compass gait with a joint stiffness adjustment

ABSTRACTA passive walking robot can achieve a smooth gait without any sensory feedback while walking down a slope. This phenomenon is based on the transformation of potential energy into kinetic energy in the legs. Although the entrainment is observed in a passive gait motion, there is a possibility that the passive gait cannot be achieved in the case of variations in physical parameters, initial conditions, and disturbances. To realize a robust passive gait against variations in physical parameters, this paper proposes a passive gait system that possesses a joint stiffness adjustment. Targeting a compass model, this paper investigates the effectiveness of the proposed method for a passive gait against variations in slope angle and hip joint mass through simulation. As a result, the simulation results show that this method especially has strong robustness against the slope angle variation.

Development and testing of a passive ankle exoskeleton

Walking Assist Exoskeletons are a class of assistive devices intended to restore a person’s independence. Current powered Exoskeletons suffer from limited usability due to power demands. Furthermore, motors and battery packs are often cumbersome and heavy. A passive walking assist device is one that does not rely on an external power source, instead drawing energy out of the gait cycle itself. This study proposes the development and initial testing of a passive ankle exoskeleton intended to provide a plantarflexion torque assist during the push off phase of gait. The design incorporates a Pneumatic Artificial Muscle as a non-linear elastic element to store and release energy during walking. The device also integrates a novel clutch mechanism design to engage and disengage the spring element about the ankle joint during walking such that it does not impede the ankle motion during swing phase. Mechanical testing demonstrated the prototypes ability to function adequately over the natural range of an ankle joint and generate an ankle torque equal to at least 25% of natural ankle torque during normal walking. Using motion capture and electromyography systems, human testing was performed to examine the gait kinematic and muscle activation when the device is worn, unilaterally. The preliminary results show that the exoskeleton is able to reduce the activation of the calf muscles on the limb wearing the device. However, a decrease in ankle joint range of motion is noted in the limb with the device, and, to a much lesser extent the leg without the exoskeleton.

A modified passive walking biped model with two feasible switching patterns of motion to resemble multi-pattern human walking

In this paper, a modified passive walking biped with two distinct feasible patterns of motion is presented. The biped has sole foot, and flexible elements are considered to model the muscles. The hip joint and the ankles are considered with flexible elements, springs and dampers, to model passive joint moments. The governing equations of motion are derived and transition rules are obtained by geometric constraints at impacts. The nonlinear coupled equations are investigated to detect stable periodic motions. The stability of motion patterns is verified by studying the eigenvalues of Jacobian matrix of Poincare’ map. Switching conditions between these stable patterns are determined to complete the governing equations of motion. One of the motion patterns have four phases and the other has three phases in each gait. Bifurcation diagrams are plotted to investigate the effect of various model parameters on dynamic behavior of the system. It is shown that the model is chaotic for a certain range of parameters. Because of systems switching, jumping in bifurcation diagrams is reported. Emergence of two feasible patterns of motion would enhance the resemblance of passive biped to multi-pattern human walking.