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Stability in legged locomotion
Abstract
Stability is a key element in a gait synthesis. Static stability margins are widely adopted in crawlers, while no similar approach has been developed for dynamically stable systems. Utilizing an analytical approach, we developed a set of easy-to-calculate stability indices to describe instantaneous static and dynamic (In)stability for a certain group of walking systems. The analysis is based on a thorough analysis of the interaction between ground reaction forces and the walking system. The indices are applicable to walking systems regardless of the number of legs or mechanical/biological design. We show that static and dynamic stability are independent of each other. We suggest a possible categorization of gait modes based on stability. Stability characteristics are analyzed in a healthy and highly pathological human gait. Finally, we discuss the applicability of the proposed methods.
... According to Whittle [16], the gait cycle is divided in two main phases (see Figure 2 (g) Terminal swing. These phases are only presented for one leg, the other leg performs the same cycle but displaced in time. ...
... To be statically stable, a body should be able to stay in a given position without falling considering its current support. Additionally, dynamic stability can be defined as [16]: ...
... Thus, point is situated somewhere outside the support polygon. This point is termed FZMP [16]. ZMP carries two important roles: ...
From the time of Aristotle onward, there have been countless books written on the topic of movement in animals and humans. However, research of human motion, especially walking mechanisms, has increased over the last fifty years. The study of human body movement and its stability during locomotion involves both neuronal and mechanical aspect. The mechanical aspect, which is in the scope of this thesis, requires knowledge in the field of biomechanics. Walking is the most common maneuver of displacement for humans and it is performed by a stable dynamic motion. In this article it is introduced the bases of the human walking in biomechanical terms. Furthermore, two stability descriptive parameters during walking are also explained - Center of Pressure (CoP) and Zero-Moment Pint (ZMP).
... The traditional ZMP-based-stability criteria can only be applied to planar motion, and some researchers have made improvement to analyze the motion on irregular terrain by adjusting the support plane [11,13,14]. The stability criteria based on ZMP do not consider the influence of the robot's current speed on its stability, but speed is very important for dynamic stability [15]. ...
... The current velocity of the body, which can reflect the robot's current motion state, is not taken into account in the traditional ZMP-based stability criteria, however, the velocity is very important for maintaining balance [15], especially under some special condition. For example, when the current ground-reaction force cannot just offset the torque, the robot is made to tumble around a certain direction; however, if the robot's velocity is high enough to allow it to quickly enter a stable area, the robot can maintain its balance. ...
Dynamic-stability criteria are crucial for robot’s motion planning and balance recovery. Nevertheless, few studies focus on the motion stability of quadruped robots with dynamic gait, none of which have accurately evaluated the robots’ stability. To fill the gaps in this field, this paper presents a new stability criterion for the motion of quadruped robots with dynamic gaits running over irregular terrain. The traditional zero-moment point (ZMP) is improved to analyze the motion on irregular terrain precisely for dynamic gaits. A dynamic-stability criterion and measurement are proposed to determine the stability state of the robot and to evaluate its stability. The simulation results show the limitations of the existing stability criteria for dynamic gaits and indicate that the criterion proposed in this paper can accurately and efficiently evaluate the stability of a quadruped robot using such gaits.
... The platform's stability depends on the leg height, the terrain conditions, speed, contact point on the ground, and navigation control. The research community has been using the qualitative parameters, including the static stability margin, longitudinal margin, crab longitudinal margin, energy stability criterion, and tip over energy stability criterion [56][57][58][59][60], to evaluate the stability of the quadruped moving at low speed. ...
The inspection and maintenance of drains with varying heights necessitates a drain mapping robot with trained labour to maintain community hygiene and prevent the spread of diseases. For adapting to level changes and navigating in the narrow confined environments of drains, we developed a self-configurable hybrid robot, named Tarantula-II. The platform is a quadruped robot with hybrid locomotion and the ability to reconfigure to achieve variable height and width. It has four legs, and each leg is made of linear actuators and modular rolling wheel mechanisms with bi-directional movement. The platform has a fuzzy logic system for collision avoidance of the side wall in the drain environment. During level shifting, the platform achieves stability by using the pitch angle as the feedback from the inertial measuring unit (IMU) mounted on the platform. This feedback helps to adjust the accurate height of the platform. In this paper, we describe the detailed mechanical design and system architecture, kinematic models, control architecture, and stability of the platform. We deployed the platform both in a lab setting and in a real-time drain environment to demonstrate the wall collision avoidance, stability, and level shifting capabilities of the platform.
... Using a stable set of reference trajectories as a basis for the controller can reduce controller complexity (97), as well as reducing actuator demand and increasing energy efficiency by using the unforced system dynamics to partially drive the system (114). Gaiting and the transitions between gaits is also driven by stability measures (72). High-speed gaits are dynamically stable but are statically unstable, whereas walking gaits are the reverse. ...
This research quantitatively analyzes a multi-body dynamics quadrupedal model with an articulated spine to evaluate the effects of speed and stride frequency on the energy requirements of the system. The articulated model consists of six planar, rigid bodies with a single joint in the middle of the torso. All joints are frictionless and mass is equally distributed in the limbs and torso. A model with the mid-torso joint removed, denoted as the rigid model, is used as a baseline comparison. Impulsive forces and torques are used to instantaneously reset the velocities at the phase transitions, allowing for ballistic trajectories during flight phases. Active torques at the haunch and shoulder joints are used during the stance phases to increase the model robustness. Simulations were conducted over effective high-speed gaits from 6.0 - 9.0 m/s. Stride frequencies were varied for both models. An evolutionary algorithm was employed to find plausible gaits based on biologically realistic constraints and bounds. The objective function for the optimization was cost of transport.
Results show a decreasing cost of transport as speed increases for the articulated model with an optimal stride frequency of 3 s$^{-1}$ and an increasing cost of transport with increasing speed for the rigid model at an optimal stride frequency of 1.4 s$^{-1}$, with a crossover in the cost of transport between the two models occurring at 7.0 m/s. The rigid model favors low speeds and stride frequencies at the cost of a large impulsive vertical force, driving the system through a long, gathered flight phase used to cover the long distances at the low stride frequencies. The articulated model prefers higher speeds and stride frequencies at the cost of a large impulsive torque in the back joint, akin to the contraction of abdomen muscles, preventing the collapse of the back. Thus, it is demonstrated that the inclusion of back articulation enables a more energetically efficient high-speed gait than a rigid back system, as seen in biological systems. Detailed analysis is provided to identify the mechanics associated with the optimal gaits of both the rigid and the articulated systems to support this claim.
... Thus, stability assessment measures can be acquired, such as body center-of-mass (COM) position relative to the center-of-pressure (COP) under the foot, [3][4][5][6][7] COM sway angle, medial-lateral and anterior-posterior velocities and accelerations of the COM, 5 and combinations of COM position and velocity. 8,9 Unfortunately, these approaches are typically restricted to gait laboratories and do not permit patient point-of-contact assessment, which is of particular importance in a rehabilitation setting where mobility at home and in the community is a key component of quality of life. ...
Background: For people with lower extremity amputations, the decreased confidence and suboptimal gait associated with dynamic instability can negatively affect mobility and quality of life. Quantifying dynamic instability could enhance clinical decision making related to lower extremity prosthetics and inform future prosthetic research.
Objective: To quantitatively examine gait adaptations in transfemoral amputees across various walking conditions.
Study design: Cross-sectional study.
Methods: Plantar-pressure data were collected from 11 individuals with unilateral transfemoral amputations using an in-shoe plantar-pressure measurement system while navigating rigid and soft ground, ramp, and stair conditions. Six parameters were examined: anterior–posterior and medial–lateral center-of-pressure direction changes, sensor cell loading frequency (cell triggering), maximum lateral force position, double support time, and stride time. Paired t-tests and analyses of variance were used to examine differences between limbs and walking conditions, respectively.
Results: Values for medial–lateral center-of-pressure direction change, sensor cell loading frequency, and double support time were significantly greater on the intact limb than the prosthetic limb. Significant differences between conditions occurred only for anterior–posterior center-of-pressure direction change and double support time on the prosthetic limb.
Conclusion: Higher values on the intact limb suggest that it plays a key role in maintaining stability and optimizing body progression during different tasks. Differences between participants, limbs, and walking condition indicate parameter sensitivity to adaptive gait strategies.
... According to Karčnik (2004) walking systems are divided into two groups: systems that use static stability, and systems that use dynamic stability. In a static walking system, the center of mass (COM) projection is always inside the base of support (BOS) defined by the points of contact in the ground. ...
... Whereas many stability indices have been proposed for clinical application [8][9][10][11][12], there is still no commonly accepted way to define or quantify locomotor stability [13]. Recently, a systematic review of kinematic measures of gait stability [12] highlighted the limitations in assessing fall risk using motor performance tests and questionnaires and summarized the most common methods for assessing stability of walking in clinics and research, concluding that assessment methods designed to identify fall-prone individuals remain controversial. ...
Falls represent a heavy economic and clinical burden on society. The identification of individual chronic characteristics associated with falling is of fundamental importance for the clinicians; in particular, the stability of daily motor tasks is one of the main factors that the clinicians look for during assessment procedures. Various methods for the assessment of stability in human movement are present in literature, and methods coming from stability analysis of nonlinear dynamic systems applied to biomechanics recently showed promise. One of these techniques is orbital stability analysis via Floquet multipliers. This method allows to measure orbital stability of periodic nonlinear dynamic systems and it seems a promising approach for the definition of a reliable motor stability index, taking into account for the whole task cycle dynamics. Despite the premises, its use in the assessment of fall risk has been deemed controversial. The aim of this systematic review was therefore to provide a critical evaluation of the literature on the topic of applications of orbital stability analysis in biomechanics, with particular focus to methodologic aspects. Four electronic databases have been searched for articles relative to the topic; 23 articles were selected for review. Quality of the studies present in literature has been assessed with a customised quality assessment tool. Overall quality of the literature in the field was found to be high. The most critical aspect was found to be the lack of uniformity in the implementation of the analysis to biomechanical time series, particularly in the choice of state space and number of cycles to include in the analysis.
... The CoP is the point on the floor where the resultant ground reaction force vector is located; under the foot in one-legged standing and between the two feet in two-legged standing. In walking or other gross motor activities the CoM has a velocity which cannot be neglected in the analysis (Pai and Patton, 1997; Karcnik, 2004). It has been shown that this dependency can conveniently be described by introducing a new point, the 'extrapolated centre of mass', XcoM, defined as (Hof et al., 2005): ...
During walking on a treadmill 10 human subjects (mean age 20 years) were perturbed by 100 ms pushes or pulls to the left or the right, of various magnitudes and in various phases of the gait cycle. Balance was maintained by (1) a stepping strategy (synergy), in which the foot at the next step is positioned a fixed distance outward of the 'extrapolated centre of mass', and (2) a lateral ankle strategy, which comprises a medial or lateral movement of the centre of pressure under the foot sole. The extrapolated centre of mass is defined as the centre of mass position plus the centre of mass velocity multiplied by a parameter related to the subject's leg length. The ankle strategy is the fastest, with a mechanical delay of about 200 ms (20% of a stride), but it can displace the centre of pressure no more than 2 cm. The stepping strategy needs at least 300 ms (30% of a stride) before foot placement, but has a range of 20 cm. When reaction time is sufficient, the magnitude of the total response is in good agreement with our hypothesis: mean centre of pressure (foot) position is a constant distance outward of the extrapolated centre of mass. If the reaction time falls short, a further correction is applied in the next step. In the healthy subjects studied here, no further corrections were necessary, so balance was recovered within two steps (one stride).
... Existing balance measures are either too restrictive or too limited to quantify instability and balance performance accurately for large perturbations. Many attempts have been made to quantify human stability using heuristic metrics ( [29], [30], [31]) and more recently by examining orbital and local stability measures ( [29], [32]). Heuristic balance metrics are difficult to use because the regions of stability and validity have not been formally established, nor are they accompanied by a stability proof. ...
Foot placement has long been recognized as the primary mechanism that humans use to restore balance. Many biomechanists have examined where humans place their feet during gait, perturbations, and athletic events. Roboticists have also used foot placement as a means of control but with limited success. Recently, Wight et al. (2008, "Introduction of the Foot Placement Estimator: A Dynamic Measure of Balance for Bipedal Robotics," ASME J. Comput. Nonlinear Dyn., 3, p. 011009) introduced a planar foot placement estimator (FPE) algorithm that will restore balance to a simplified biped that is falling. This study tested the FPE as a candidate function for sagittal plane human-foot-placement (HFP) by recording the kinematics of 14 healthy subjects while they performed ten walking trials at three speeds. The FPE was highly correlated with HFP (rho>or=0.997) and its accuracy varied linearly from 2.6 cm to -8.3 cm as walking speed increased. A sensitivity analysis revealed that assumption violations of the FPE cannot account for the velocity-dependent changes in FPE-HFP error suggesting that this behavior is volitional.
... Various measures of instability or body adaptation to prevent instability have been reported. Upper-body motion measures include body center of mass (COM) position, COM position relative to the center of pressure (COP) under the foot (Buckley et al., 2005;Chang and Krebs, 1999;Hahn and Chou, 2004;Krebs et al., 1998;Lee and Chou, 2006); mediolateral (ML) and anterior-posterior (AP) velocities and accelerations of the COM (Hahn and Chou, 2004); and measures that combine COM position and velocity (Hof et al., 2005;Karcnik, 2004). However, the above COM-based measures require three-dimensional reconstruction of the whole body, and thereby restrict applicability to facilities capable of bilateral kinematic measurement such as gait laboratories (Hahn and Chou, 2003). ...
Stability during locomotion, or dynamic stability, is critical to ensure safe locomotion and a high quality of life. A dynamic stability measure should be easily applied in a clinical setting and must provide a quantitative index that can be used for comparisons over a range of tasks and environments. Plantar foot pressure data acquired by shoe-insole sensors have potential to provide such a measure. To generate a quantitative dynamic gait stability index, six gait parameters were extracted from a commercial plantar pressure measurement system (F-Scan): anterior-posterior (A/P) center of force (CoF) motion, medial-lateral (M/L) CoF motion, maximum lateral position, cell triggering, stride time (ST), and double support time (DST). A fuzzy logic controller combined these six parameters and generated the index. To validate the stability index, 15 healthy subjects performed four tasks intended to induce increasing levels of instability. Fifty-seven gait parameter combinations were assessed to determine the most effective index. A combination of A/P motion, M/L motion, maximum lateral position, and cell triggering parameters was the most consistently effective index across all subjects. However, small changes in ST and DST for able-bodied subjects may have reduced the effectiveness of these measures in the index calculation. The index combining all six parameters should be investigated further with populations with disabilities or pathological gait.
The focus of this chapter is the measure of dynamic stability during walking gait and the many variables studied in attempts to quantify it. In the search for the safest methods of load carriage for school children, dynamic stability has not been specifically addressed, possibly due to the need for a valid, reliable and clinically relevant set of variables which can identify a walking gait as "stable". The various measures which have been used in the research on human locomotion, both while carrying loads and carrying no load, are reviewed. Recent application of methods of non-linear analysis shows promise in identifying stability (or lack thereof) while walking. These methods have long been used to study various physiological rhythms, such as cardiac activity. While these methods are mathematically complex, a basic understanding of the concepts behind their use could propel the use of non-linear analysis into the realm of load carriage for children, and help identify important aspects of gait which may lead to increased risk of injury. School children will be carrying loads on the back. Identifying predisposition to risk of injury will aid in developing the safest methods and equipment to carry these loads
Currently there is no commonly accepted way to define, much less quantify, locomotor stability. In engineering, "orbital stability" is defined using Floquet multipliers that quantify how purely periodic systems respond to perturbations discretely from one cycle to the next. For aperiodic systems, "local stability" is defined by local divergence exponents that quantify how the system responds to very small perturbations continuously in real time. Triaxial trunk accelerations and lower extremity sagittal plane joint angles were recorded from ten young healthy subjects as they walked for 10 min over level ground and on a motorized treadmill at the same speed. Maximum Floquet multipliers (Max FM) were computed at each percent of the gait cycle (from 0% to 100%) for each time series to quantify the orbital stability of these movements. Analyses of variance comparing Max FM values between walking conditions and correlations between Max FM values and previously published local divergence exponent results were computed. All subjects exhibited orbitally stable walking kinematics (i.e., magnitudes of Max FM < 1.0), even though these same kinematics were previously found to be locally unstable. Variations in orbital stability across the gait cycle were generally small and exhibited no systematic patterns. Walking on the treadmill led to small, but statistically significant improvements in the orbital stability of mediolateral (p = 0.040) and vertical (p = 0.038) trunk accelerations and ankle joint kinematics (p = 0.002). However, these improvements were not exhibited by all subjects (p < or = 0.012 for subject x condition interaction effects). Correlations between Max FM values and previously published local divergence exponents were inconsistent and 11 of the 12 comparisons made were not statistically significant (r2 < or = 19.8%; p > or = 0.049). Thus, the variability inherent in human walking, which manifests itself as local instability, does not substantially adversely affect the orbital stability of walking. The results of this study will allow future efforts to gain a better understanding of where the boundaries lie between locally unstable movements that remain orbitally stable and those that lead to global instability (i.e., falling).
The main focus of the present investigation is the development of quantitative measures to assess the dynamic stability of human locomotion. The analytical methodology is based on Floquet theory, which was developed to investigate the stability of nonlinear oscillators. Here the basic approach is modified such that it accommodates the study of the complex dynamics of human locomotion and differences among various individuals. A quantitative stability index has been developed to characterize the ability of humans to maintain steady gait patterns. Floquet multipliers of twenty normal subjects were computed from the kinematic data at Poincaré sections taken at four instants of the gait cycle, namely heel strike, foot flat, heel off, and toe off. Then, an averaged stability index was computed for each subject. Statistical analysis was performed to demonstrate the utility of the stability indices as quantitative measures of dynamic stability of gait for the subject population tested during the present study.
We demonstrate that an irreducibly simple, uncontrolled, two-dimensional, two-link model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a point-mass at the hip, and infinitesimal point-masses at the feet. The feet have plastic (no-slip, no-bounce) collisions with the slope surface, except during forward swinging, when geometric interference (foot scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope gamma. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics. The analytic calculations find initial conditions and stability estimates for period-one gait limit cycles. The model exhibits two period-one gait cycles, one of which is stable when 0 < gamma < 0.015 rad. With increasing gamma, stable cycles of higher periods appear, and the walking-like motions apparently become chaotic through a sequence of period doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance angle is proportional to gamma 1/3, and that the gravitational power used is proportional to v4 where v is the velocity along the slope.
A triaxial accelerometer is placed at the back of the subject at
the height of the center of mass. Force plate data are collected
simultaneously. Subjects stand in a comfortable position with eyes open,
eyes closed and doing cognitive tasks; and with feet together with eyes
open and closed. The cognitive tasks are: mathematical, auditory Stroop
and memory. The force plate data are processed to obtain the center of
pressure and from it the parameters of: mean radius, speed and
frequency, and base of support. The same parameters are obtained from
the combined accelerations vector projection on the floor, found from
the triaxial accelerometer data. The mean angular velocity, angular
acceleration and accelerations in the horizontal plane at the level of
the accelerometer are calculated T-tests indicate that for most
parameters the accelerometer measurements are able to distinguish
between the different test conditions as well as the force plate
(p⩽0.05)
Five initiation and five termination plus three steady-state walking trials were collected for each of four subjects using three videos cameras and three force platforms. Data were analysed using a 13-segment three-dimensional biomechanical model. During initiation 90% of steady-state velo-city was achieved during the first step and 100% by the second step. During termination, 10% of the velocity was reduced in the first step and 90% in the last step. The interaction between the centre of mass (COM) and centre of pressure (COP) is tightly regulated to control the trajectory of the COM and thereby control total body balance. Coarse control of this balance is achieved by foot placement, with fine control during weight bearing by the ankle musculature.
The selection of vehicle and leg configuration and of power transmission and actuation system configuration for the adaptive suspension vehicle (ASV) are discussed. The ASV will be a proof-of-concept prototype of a proposed class of transportation vehicles for use in terrain that is not passable for conventional vehicles. It uses a legged locomotion princi ple. The machine will not be an autonomous "robot, " in the sense that it will carry an operator. It will, however, have a very high level of machine intelligence and environmental sensing capability. Much of the technology involved is unique and has potential for application to future robot systems. In this paper, major aspects of the vehicle and leg geometry, the on-board processing configuration, and the hydrostatic power transmission system are discussed.
The authors have developed five kinds of biped locomotive robots so far. They are named BIPER-1, 2, 3, 4, and 5. All of them are statically unstable but can perform a dynamically stable walk with suitable control. BIPER-1 and BIPER-2 walk only sideways. BIPER-3 is a stilt-type robot whose foot contacts occur at a point and who can walk sideways, back ward, and forward. BIPER-4's legs have the same degrees of freedom as human legs. BIPER-5 is similar to BIPER-3, but in the case of BIPER-5 all apparatus, such as the computer, are mounted on it.
This paper deals with the control theory used for BIPER-3 and BIPER-4. In both cases, basically the same control method is applied. The most important point is that the mo tion of either robot during the single-leg support phase can be approximated by the motion of an inverted pendulum. Ac cordingly, in this paper, dynamic walk is considered to be a series of inverted-pendulum motions with appropriate condi tions of connection.
The dynamic similarity hypothesis postulates that different mammals move in a dynamically similar fashion whenever they travel at speeds that give them equal values of a dimensionless parameter, the Froude number. Thus, given information about one species, it could be possible to predict for others relationships between size, speed and features of gait such as stride length, duty factor, the phase relationships of the feet and the patterns of force exerted on the ground.
Data for a diverse sample of mammals have been used to test the hypothesis. It is found to be tenable in many cases when comparisons are confined to quadrupedal mammals of the type described by Jenkins (1971) as “cursorial”. Most mammals of mass greater than 5 kg are of this type. Although the hypothesis applies less successfully to comparisons between cursorial and non-cursorial mammals it is shown to be a reasonable approximation even for such comparisons and for comparisons between quadrupedal mammals and bipedal mammals and birds.
Crab walking is as important as forward walking as applied to walking machine control. Crab walking is especially important to a quadruped since a quadruped has a similar leg geometric layout in both longitudinal and lateral directions. In the studies of forward walking gaits, the wave gait was found to be the optimally stable. In this article, the wave gait is applied to the crab walking of a quadruped and it is modified into four types of wave-crab gaits according to the range of crab angle. The stability formulae of these wave-crab gaits are then derived analytically based on the following three stability measurements: stability margin (Sm), body-longitudinal (or lateral) stability margin (Sbl or Sbt) and crab longitudinal stability margin (Scl). Sm is the true stability index under quasi-static walking condition. However, the equations are more complicated. Sbl (or Sbt) is simpler and can be used as a good approximation of Sm. Scl was commonly adopted as the stability index in the previous gait studies. Nevertheless, Scl is found to be misleading for a large portion of crab angle range. The analytical results derived in this paper are useful to the geometric design and to the real-time control of a quadruped.
A dynamic model of a quadrupedal walking machine is derived to
study the dynamic stability and energy efficiency during walking. The
legs are three-axis, cylindrical pantograph legs and the whole system
consists of twenty-nine links. The quadruped adopts a wave gait which
has at least three feet on the ground. Significant efforts are made to
improve the computational efficiency. The CPU time of the complete
inverse dynamics, including kinematics, is about 10 msec in an IBM 3090.
Dynamic stability and energy efficiency during walking with different
hip axis orientations, walking velocity, strokes and duty factors are
studied and discussed
While the total number of theoretically possible quadruped gaits is quite large, only six gaits have the property that they can be executed while keeping at least three feet on the ground at all times. These gaits, called creeping gaits, seem to be well suited for low-speed locomotion since they permit a quadruped to remain statically stable during most of a locomotion cycle. A mathematical analysis shows, however, that for only three of the six creeping gaits it is possible to place the feet of an animal or machine so that it is statically stable at all times. Furthermore, among these three, there exists a unique optimum gait that maximizes static stability. This gait corresponds to the normal quadruped crawl favored by most animals for very low-speed locomotion.
To plan safe, reliable walker motions, it is important to assess the stability of a walker. In this article, two basic modes of walker stability are defined and developed: stance stability and walker stability. For slowly moving, statically stable walkers, it is convenient to use the magnitude of the amount of the work required to destabilize a walker as a measure of the stability of that walker. Furthermore, as shown in this article, the com pliance of the walker and/or terrain can significantly affect the work necessary to destabilize the walker. Consideration of compliance and the two modes of walker stability leads to the definition and development of four energy-based stability mea sures : the rigid stance stability measure, the compliant stance stability measure, the rigid walker stability measure, and the compliant walker stability measure. (The rigid stance stability measure is identical to the energy stability margin reported in Messuri and Klein [1985].) Several examples are used to demonstrate the application and use of these stability measures in type selection, gait planning, and control of the walker. The outcome of the present work is a more complete approach to using stability measures to ensure reliable walker gait planning and control.
We have defined 2 indices describing gait kinematic and dynamic stability. We assessed their values in the gaits of 5 different paraparetic subjects. The indices are correlated to the gait velocity to prove the close relationship between overall gate velocity and stability. Based on stability analysis and certain kinematic parameters, some possible ways of increasing the average gait velocity are explained.
The authors have been using the ZMP (zero moment point) as a
criterion to distinguish the stability of walking for a biped walking
robot which has a trunk. The authors introduce a control method of
dynamic biped walking for a biped walking robot to compensate for the
three-axis (pitch, roll and yaw-axis) moment on an arbitrary planned ZMP
by trunk motion. The authors developed a biped walking robot and
performed a walking experiment with the robot using the control method.
The result was a fast dynamic biped walking at the walking speed of 0.54
s/step with a 0.3 m step on a flat floor. This walking speed is about
50% faster than that with the robot which compensates for only the
two-axis (pitch and roll-axis) moment by trunk motion
This paper discusses an algorithm to make a quadruped machine walk
dynamically and omnidirectionally following a real-time command from an
operator. To produce a smooth body motion at high speed locomotion, we
introduced a new gait, named the “intermittent trot gait”,
in which a four-leg-supporting phase and a two-diagonal-leg-supporting
phase appear in orders. In this gait, the pitching and rolling motion of
the body is suppressed to a lower level than that of the other gaits
because the dynamic effects of the swinging legs almost cancel each
other. To realize the intermittent trot gait, new algorithms to plan a
landing point and body motion are discussed. A landing point is decided
by considering an operator command and conversion to the standard leg
formation. A body motion is planned to produce dynamic stability and to
follow speed and direction commands. By using these algorithms, a
mechanical vehicle TITAN VI can walk omnidirectionally, smoothly
following a real-time operator command. The top speed is 1 m/sec on flat
terrain and 125 mm/sec on 105 mm up and down over rough terrain
Walk can be classified as "static walk" and "dynamic walk". It is said that dynamic walk is superior in both speed and energy consumption. This paper describes how a quadruped robot should walk dynamically to realize these advantages. Such consideration is lacking in past research. In this paper, three criteria are introduced to evaluate the walk -- `stability', `maximum speed' and `energy consumption'. The relations between these three criteria and the parameters (gait, speed, period, stride, length of the leg, joint angles, etc.) are formulated accordingly to the dynamics. The conclusions are as follows: (1) The shorter a period is, the more stably the quadruped can walk. (2) It is desirable to walk with a longer period and wider stride in order to increase the maximum speed. (3) There is a period which maximizes the speed. (4) There is a period which minimizes the energy consumption for a given speed. (5) Trot gait is desirable when the priority is placed on energy consumption...
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