Figure 3 - uploaded by Sujatha Srinivasan
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6: Stick figure animation of one step of the example model. Note the rolling motion of the stance foot. The swing leg is shown with dashed lines.
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Abstract: This dissertation uses a robotics-inspired approach to develop a low-dimensional forward dynamic model of normal human walking. The analytical model captures the dynamics of walking over a complete gait cycle in the sagittal plane. The model for normal walking is extended to model asymmetric gait. The asymmetric model is applied to study...
Citations
... Robotic bipedal models [9,10] were recently presented for study of human walking gait [11,12], for design of prosthetic devices for lower-limbs [11] and control of robotic walkers. In Ref. [13], a bipedal model is proposed to study human gaits with fixed ankle joints. Both the single-and double-stance phases are included in the model and a hybrid zero dynamic (HZD) control is designed to track the human gait profile. ...
... The models in Refs. [12] and [13] use the circular curved foot-floor contact that was developed in Ref. [14]. However, all of the above-mentioned bipedal models are built on the assumption that the foot-floor contact friction forces are large enough to prevent the foot from slipping, and thus, cannot be directly used to study slip-and-fall walking gaits. ...
... Bipedal walking is commonly described by a hybrid dynamics framework with continuous dynamics during the single-or double-stance periods with discrete mappings to capture the foot contact impacts. Using the HZD concept [15], a low-dimensional normal human walking model is presented in Ref. [13] and a state feedback control is designed to track the gait profile parameterized by the stance phase variable, rather than time [9]. The repetitive human walking gait is captured by the HZD when the gaits follow the desired profiles. ...
Foot slip is one of the major causes of falls in human locomotion. Analytical bipedal models provide an insight into the complex slip dynamics and reactive control strategies for slip-induced fall prevention. Most of the existing bipedal dynamics models are built on no foot slip assumption and cannot be used directly for such analysis. We relax the no-slip assumption and present a new bipedal model to capture and predict human walking locomotion under slip. We first validate the proposed slip walking dynamic model by tuning and optimizing the model parameters to match the experimental results. The results demonstrate that the model successfully predicts both the human walking and recovery gaits with slip. Then, we extend the hybrid zero dynamics (HZD) model and properties to capture human walking with slip. We present the closed-form of the HZD for human walking and discuss the transition between the nonslip and slip states through slip recovery control design. The analysis and design are illustrated through human walking experiments. The models and analysis can be further used to design and control wearable robotic assistive devices to prevent slip-and-fall.
... Researchers have evaluated this design approach by conducting experimental and theoretical studies to measure or compute the metabolic and/or mechanical energy expended by amputees using prostheses with different inertial properties [9][10][11][12][13][14][15][16]. However, these studies have had two major limitations. ...
We quantify how the hip energetics and knee torque required for an above-knee prosthesis user to walk with the kinematics of able-bodied humans vary with the inertial properties of the prosthesis. We also select and optimize passive mechanical components for a prosthetic knee to accurately reproduce the required knee torque.
Previous theoretical studies have typically investigated the effects of prosthesis inertial properties on energetic parameters by modifying both mass and mass distribution of the prosthesis and computing kinetic and energetic parameters only during swing. Using inverse dynamics, we determined the effects of independently modifying mass and mass distribution of the prosthesis, and we computed parameters during both stance and swing. Results showed that reducing prosthesis mass significantly affected hip energetics, whereas reducing mass distribution did not. Reducing prosthesis mass to 25% of the mass of a physiological leg decreased peak stance hip power by 26%, average swing hip power by 74%, and absolute hip work over the gait cycle by 22%.
Previous studies have also typically optimized prosthetic knee components to reproduce the knee torque generated by able-bodied humans walking with normative kinematics. However, because the prosthetic leg of an above-knee prosthesis user weighs significantly less than a physiological leg, the knee torque required for above-knee prosthesis users to walk with these kinematics may be significantly different. Again using inverse dynamics, it was found that changes in prosthesis mass and mass distribution significantly affected this required torque. Reducing the mass of the prosthesis to 25% of the mass of the physiological leg increased peak stance torque by 43% and decreased peak swing torque by 76%.
The knee power required for an above-knee prosthesis user to walk with the kinematics of able-bodied humans was analyzed to select passive mechanical components for the prosthetic knee. The coefficients of the components were then optimized to replicate the torque required to walk with the kinematics of able-bodied humans. A prosthetic knee containing a single linear spring and two constant-force dampers was found to accurately replicate the targeted torque (R[superscript 2]=0.90 for a typical prosthesis). Optimal spring coefficients were found to be relatively insensitive to mass alterations of the prosthetic leg, but optimal damping coefficients were sensitive. In particular, as the masses of the segments of the prosthetic leg were altered between 25% and 100% of able-bodied values, the optimal damping coefficient of the second damper varied by 330%, with foot mass alterations having the greatest effect on its value.
... Second, the effects of prosthesis inertial properties on energy expenditure have not yet been completely determined. Researchers aiming to experimentally or theoretically quantify the effects of prosthesis inertial alterations on energy expenditure have typically applied mass perturbations (i.e., physical or simulated masses) to the prosthesis and determined metabolic or mechanical energy expenditure [22], [23], [24], [25], [26], [27]. Mass perturbations alter both mass and mass distribution (which in turn affects moment of inertia), confounding the effects of these parameters. ...
... Comparison of our work with experimental studies examining the effects of prosthesis alterations on joint kinetics and energetics of above-knee amputees [41], [42], [43], [26] is challenging, as these studies typically applied mass perturbations to the prostheses of amputees that do not walk with able-bodied kinematics. However, the results agree with the theoretical study of Srinivasan [27], who evaluated the effects of mass added or removed at various locations along the shank of a below-knee prosthesis on total knee moment cost (i.e., the integral of the absolute value of knee moment over the gait cycle) for an anthropomorphic forward dynamic model of a transtibial amputee. Srinivasan's study was modeled for a below-knee prosthesis and no equivalent study for an aboveknee prosthesis was found in literature. ...
... Numerical values could not be compared because the cited study considered adding and removing mass at the combined COM of the shank and foot while simultaneously altering moments of inertia in a non-proportional manner, whereas the present study considered decreasing masses of the segments separately and altered moments of inertia in proportion to masses. Our results also align with the theoretical work of Srinivasan [27], who evaluated the effects of mass added or removed at various locations along the shank of a below-knee prosthesis on total joint power cost (a quantity proportional to absolute joint work, but summed over multiple joints) for an anthropomorphic forward dynamic model of a transtibial amputee. Srinivasan determined that, for an optimal prosthesis alignment, removing mass near the COM of a prosthesis significantly decreased total joint power cost. ...
There is a major need in the developing world for a low-cost prosthetic knee that enables users to walk with able-bodied kinematics and low energy expenditure. To efficiently design such a knee, the relationship between the inertial properties of a prosthetic leg and joint kinetics and energetics must be determined. In this paper, using inverse dynamics, the theoretical effects of varying the inertial properties of an above-knee prosthesis on the prosthetic knee moment, hip power, and absolute hip work required for walking with ablebodied kinematics were quantified. The effects of independently varying mass and moment of inertia of the prosthesis, as well as independently varying the masses of each prosthesis segment, were also compared. Decreasing prosthesis mass to 25% of physiological leg mass increased peak late-stance knee moment by 43% and decreased peak swing knee moment by 76%. In addition, it reduced peak stance hip power by 26%, average swing hip power by 76%, and absolute hip work by 22%. Decreasing upper leg mass to 25% of its physiological value reduced absolute hip work by just 2%, whereas decreasing lower leg and foot mass reduced work by up to 22%, with foot mass having the greater effect. Results are reported in the form of parametric illustrations that can be utilized by researchers, designers, and prosthetists. The methods and outcomes presented have the potential to improve prosthetic knee component selection, facilitate ablebodied kinematics, and reduce energy expenditure for users of low-cost, passive knees in developing countries, as well as for users of advanced active knees in developed countries.
... Researchers have evaluated this design approach by conducting experimental and theoretical studies to measure or compute the metabolic and/or mechanical energy expended by amputees using prostheses with different inertial properties [9][10][11][12][13][14][15][16]. However, these studies have had two major limitations. ...
We quantify how the hip energetics and knee torque required for an above-knee prosthesis user to walk with the kinematics of able-bodied humans vary with the inertial properties of the prosthesis. We also select and optimize passive mechanical components for a prosthetic knee to accurately reproduce the required knee torque.
Previous theoretical studies have typically investigated the effects of prosthesis inertial properties on energetic parameters by modifying both mass and mass distribution of the prosthesis and computing kinetic and energetic parameters only during swing. Using inverse dynamics, we determined the effects of independently modifying mass and mass distribution of the prosthesis, and we computed parameters during both stance and swing. Results showed that reducing prosthesis mass significantly affected hip energetics, whereas reducing mass distribution did not. Reducing prosthesis mass to 25% of the mass of a physiological leg decreased peak stance hip power by 26%, average swing hip power by 74%, and absolute hip work over the gait cycle by 22%.
Previous studies have also typically optimized prosthetic knee components to reproduce the knee torque generated by able-bodied humans walking with normative kinematics. However, because the prosthetic leg of an above-knee prosthesis user weighs significantly less than a physiological leg, the knee torque required for above-knee prosthesis users to walk with these kinematics may be significantly different. Again using inverse dynamics, it was found that changes in prosthesis mass and mass distribution significantly affected this required torque. Reducing the mass of the prosthesis to 25% of the mass of the physiological leg increased peak stance torque by 43% and decreased peak swing torque by 76%.
The knee power required for an above-knee prosthesis user to walk with the kinematics of able-bodied humans was analyzed to select passive mechanical components for the prosthetic knee. The coefficients of the components were then optimized to replicate the torque required to walk with the kinematics of able-bodied humans. A prosthetic knee containing a single linear spring and two constant-force dampers was found to accurately replicate the targeted torque (R2=0.90 for a typical prosthesis). Optimal spring coefficients were found to be relatively insensitive to mass alterations of the prosthetic leg, but optimal damping coefficients were sensitive. In particular, as the masses of the segments of the prosthetic leg were altered between 25% and 100% of able-bodied values, the optimal damping coefficient of the second damper varied by 330%, with foot mass alterations having the greatest effect on its value.
... The initial portion of the modified proof is given by Srinivasan (2007) and presented below. C N is related to the inertia matrix (Spong and Vidyasagar, 1989) by ...
... Thus, Equation (33) for point feet reduces to the equation forξ 2 given in Westervelt et al. (2007). The proof in Srinivasan (2007) stops here. ...
This paper extends the use of virtual constraints and hybrid zero dynamics (HZD), a successful control strategy for point-foot bipeds, to the design of controllers for planar curved foot bipeds. Although the rolling contact constraint at the foot-ground interface increases complexity somewhat, the measure of local stability remains a function of configuration only, and a closed-form solution still determines the existence of a periodic orbit. The formulation is validated in experiment using the planar five-link biped ERNIE. While gaits designed for point feet yielded stable walking when ERNIE was equipped with curved feet, errors in both desired speed and joint tracking were significantly larger than for gaits designed for the correct radius curved feet. Thus, HZD-based control of this biped is shown to be robust to some modeling error in the foot radius, but at the same time, to require consideration of foot radius to achieve predictably reliable walking gaits. Additionally, under HZD-based control, this biped walked with lower specific energetic cost of transport and joint tracking errors for matched curved foot gait design and hardware compared to matched point-foot gait design and hardware.
... representan ángulos, velocidades angulares y aceleraciones respectivamente. Así, considerando nuevamente modelos mecánicos basados en el péndulo invertido (41), fue posible describir características dinámicas de marcha patológicas que afectan directamente el sub-sistema ósteo-articular, como por ejemplo las lesiones y amputaciones de miembros inferiores, caso en el cual se consideran las prótesis como cuerpos rígidos y de masa variable (42)(43)(44). ...
The human gait is the result of complex interactions between several sub-systems: neuromuscular, musculo-tendinous and osteo-articular, which work together to generate the body dynamics necessary to describe the bipedal movement. In the clinical routine, the gait analysis is the main element for identifying pathological disorders, supporting the diagnosis and facilitating a proper follow up. Traditionally, this analysis aims to establish the set of patterns that describe the dynamics of the system. However, this analysis is insufficient for some movements, especially for early stages of almost every pathological movement. The development of normal and pathological models has allowed to demostrate objective differences for each of these situations. In this article we present a summary of the models that describe the dynamics of the normal and pathological human gait, inspired by the morpho-physiology of the locomotor system. Furthermore, we perform an analysis of the effectiveness of the proposed models in the literature.
... representan ángulos, velocidades angulares y aceleraciones respectivamente. Así, considerando nuevamente modelos mecánicos basados en el péndulo invertido (41), fue posible describir características dinámicas de marcha patológicas que afectan directamente el sub-sistema ósteo-articular, como por ejemplo las lesiones y amputaciones de miembros inferiores, caso en el cual se consideran las prótesis como cuerpos rígidos y de masa variable (42)(43)(44). ...
La marcha humana es el resultado de la compleja interacción entre varios subsistemas: neuromuscular, músculo-tendinoso y osteoarticular, que trabajan coordinadamente para generan la dinámica corporal necesaria para el desplazamiento bípedo. En la rutina clínica, el estudio de la marcha es la base de la identificación de trastornos patológicos, facilitando su diagnóstico, tratamiento y seguimiento. Tradicionalmente este análisis determina el conjunto de patrones que describen la dinámica del sistema. Sin embargo, éste análisis es insuficiente para evaluar algunos movimientos, sobre todo para los estadios tempranos de casi todos los movimientos patológicos. El desarrollo de diferentes modelos normales y patológicos ha permitido establecer diferencias objetivas para cada una de estas situaciones. En este artículo se hace una revisión de los modelos que describen la dinámica de la marcha humana normal y patológica, inspirados en la morfo-fisiología del sistema locomotor. Además, se hace un análisis sobre la efectividad de los modelos propuestos en la literatura para describir comportamientos patológicos.
... The total joint power cost results given in Figure 8 The modeling approach assumes that posture control is the mechanism used by humans 360 to accomplish forward progression while walking. Using the parsimony hypothesis in fact captures the dynamic behavior in a forward dynamic simulation (Srinivasan et al., 2008; 362 Srinivasan, 2007). It is reasonable to assume that coordination of posture is also dependent 363 on walking speeds. ...
... one step). Applying the parsimony hypothesis enables the derivation of a one-DOF hybrid 110 model to describe the dynamics of walking in the sagittal plane over a complete gait cycle 111(Srinivasan et al., 2008;Srinivasan, 2007).112 In asymmetric gait, the anthropometric parameters of the left and right legs may be113 unequal. ...
This paper presents an extension of a recently developed low-dimensional modeling approach for normal human gait to the modeling of asymmetric gait. The asymmetric model is applied to analyze the gait dynamics of a transtibial prosthesis user, specifically the changes in joint torque and joint power costs that occur with variations in sagittal-plane alignment of the prosthesis, mass distribution of the prosthesis, and roll-over shape of the prosthetic foot being used. The model predicts an increase in cost with addition of mass and a more distal location of the mass, as well as the existence of an alignment at which the costs are minimized. The model's predictions also suggest guidelines for the selection of prosthetic feet and suitable alignments. The results agree with clinical observations and results of other gait studies reported in the literature. The model can be a useful analytical tool for more informed design and selection of prosthetic components, and provides a basis for making the alignment process systematic.
... In general, prosthetists appear to align different kinds of prosthetic feet (having different roll-over shapes) toward a similar rocker shape, perhaps an 'ideal' rocker for the prosthesis user. The use of roll-over shapes to describe the function of prosthetic feet can simplify walking models aimed at testing effects of feet and alignment (Srinivasan 2007;Srinivasan et al. 2008;Srinivasan et al. [in press]). ...
Recent work suggests that a prosthetic ankle-foot component's roll-over shape - the effective rocker it conforms to between initial contact and opposite initial contact (the 'roll-over' interval of walking) - is closely linked to its final alignment in the prosthesis (as determined by a skilled prosthetist using heuristic techniques). If true, this information may help to determine the appropriate alignment for a lower limb prosthesis before it is built, or a priori. Knowledge is needed for future models that will incorporate the roll-over shape including the relative effect of alignment on the roll-over shape's radius of curvature and arc length. The purpose of this study was to evaluate the hypotheses that: (i) Changes in prosthesis alignment alter the position and orientation of a foot's roll-over shape in prosthesis-based coordinates, and (ii) these changes occur without changing the radius of curvature or arc length of the roll-over shape. To examine the hypotheses, this study examined the effects of nine alignment settings on the roll-over shapes of two prosthetic feet. The idea that alignment changes move and rotate roll-over shapes of prosthetic feet in prosthesis coordinates is supported by this work, but the hypothesis that the radius of curvature and arc length do not change for different alignments is not strongly supported by the data. A revised approach is presented that explains some of the changes to the roll-over shape parameters due to changes in rotational alignment.
Background: Selection of prosthesis mechanical characteristics to restore function of persons with lower limb loss can be framed as an optimization problem to satisfy a given performance objective. However, the choice of a particular objective is critical, and considering only device and generalizable outcomes across users without accounting for inherent motor performance likely restricts a given patient from fully realizing the benefits of a prosthetic intervention.
Objectives: This review presents methods for optimizing passive below-knee prosthesis designs to maximize rehabilitation outcomes and how considerations on patient motor performance may enhance these outcomes.
Major Findings: Available literature supports that considering patient-specific variables pertaining to motor performance permits a multidimensional landscape relating device characteristics and user function, which may yield more accurate predictions of rehabilitation outcomes for individual patients. Moreover, the addition of targeted physical therapeutic interventions that encourage user self-organization may further improve these outcomes. We note the potential of existing paradigms to address these additional dimensions, and we encourage investigators to consider the many different performance objectives available for prosthesis optimization.
Conclusions: By considering user motor performance in combination with prosthesis mechanical characteristics, a staged optimization approach can be formulated which acknowledges that device modifications may only improve outcomes to a certain extent and user self-organization is a critical component to complete rehabilitation. An iterative process that can be integrated within existing rehabilitative practices accounts for changes in patient status through combined targeted prosthetic solutions and physical therapeutic techniques, and embodies the concept of personalized intervention for patients with lower limb loss.
