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Research Papers

Mechanical Analysis of the Preferred Strategy Selection in Human Stumble Recovery

[+] Author and Article Information
T. de Boer1

Department of BioMechanical Engineering, Faculty of Mechanical Engineering, Delft University of Technology, 2628 CD Delft, The Netherlandstomas.deboer@tudelft.nl

M. Wisse, F. C. T. van der Helm

Department of BioMechanical Engineering, Faculty of Mechanical Engineering, Delft University of Technology, 2628 CD Delft, The Netherlands

1

Corresponding author.

J Biomech Eng 132(7), 071012 (Jun 02, 2010) (8 pages) doi:10.1115/1.4001281 History: Received May 12, 2009; Revised February 05, 2010; Posted February 17, 2010; Published June 02, 2010; Online June 02, 2010

We use simple walking models, based on mechanical principles, to study the preferred strategy selection in human stumble recovery. Humans typically apply an elevating strategy in response to a stumble in early swing and midswing, for which the perturbed step is lengthened in a continuation of the original step. A lowering strategy is executed for stumbles occurring at midswing or late swing, for which the perturbed swing foot is immediately placed on the ground and the recovery is executed in the subsequent step. There is no clear understanding of why either strategy is preferred over the other. We hypothesize that the human strategy preference is the result of an attempt to minimize the cost of successful recovery. We evaluate five hypothesized measures for recovery cost, focusing on the energetic cost of active recovery limb placement. We determine all hypothesized cost measures as a function of the chosen recovery strategy and the timing of the stumble during gait. Minimization of the cost measures based on the required torque, impulse, power and torque/time results in a humanlike strategy preference. The cost measure based on swing work does not predict a favorable strategy as a function of the gait phase.

FIGURES IN THIS ARTICLE
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Copyright © 2010 by American Society of Mechanical Engineers
Topics: Torque , Simulation
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Figures

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Figure 1

Three dynamic walking models capable of showing passive cyclic gait on slope γ. All models are extended with hip and knee (if applicable) actuation to recover from a stumble. Hip actuation produces a torque that acts on the swing and stance leg. Knee actuation produces a torque that acts on the swing leg thigh and shank. (a) The simplest walking model by Garcia (24). All variables are described in nondimensional terms, with the leg length L, hip mass M, and gravitational constant g as base units. Foot mass m is infinitesimally small compared with the hip mass. (b) The straight-legged equivalent of the kneed anthropomorphic model in (c), adopted from McGeer (29). Both models have anthropomorphically distributed mass and a point mass at the hip that represent the torso. See Table 1 for the model parameter descriptions and values.

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Figure 2

For all three models, the segment angles are shown for one step as a function of the step time. The angles are measured counterclockwise with respect to the slope normal. During a step, only one foot is in contact with the ground at any time; double support occurs instantaneously at heelstrike. The gait of the simplest walking model is a result of a slope angle γ of 0.004, following the work of Wisse (30). For the anthropomorphic models, a slope angle γ of 0.0075 is selected that results in stable gait for both models. The graphs are scaled with respect to the gait phase, expressed as a percentage of the total step time.

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Figure 3

A graphical representation of three recovery scenarios for the kneed anthropomorphic model. Angles versus time are shown for each recovery scenario together with a cartoon showing an impression of the walker’s behavior. The data is generated for an induced stumble occurring at 58% of the step time, at which time the forward swing foot motion is blocked for a duration of 15% of the total step time. (a) A recovery action is required to prevent a fall. (b) The lowering strategy consists of two phases: The first phase consists of rapid placement of the perturbed step. In this phase, the kneed walking model requires a knee torque to extend the leg prior to heelstrike (in this example, Tknee=0.001). The second phase consists of a powered recovery step of the new swing leg. Hip and knee actuations can be used to ensure proper foot placement with a fully extended leg. The illustrated example requires only hip actuation. (c) The elevating strategy consists of a powered elongated perturbed step. Hip and knee actuations are used for recovery.

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Figure 4

The Poincaré section for the simplest walking model just after heelstrike, for a slope angle of γ=0.004(30). The failure modes, BoA and fixed point (star at (θ,θ̇)=(0.1534,−0.1516)) are shown. The right graph shows an enlarged and sheared section, which better visualizes the basin of attraction. A single lowering recovery is shown. Swing foot blockage results in a shortened step: The state of the model can now be represented by point number 1. The walker would fall forward if no recovery step would be performed. Recovery torques can place the state back toward the fixed point (point 3) or just within the basin of attraction (points 2 and 4), or lead to a fall if the torque magnitude is too large (point 5) or small. After a successful recovery, the model will passively converge back to its cyclic gait in the subsequent steps.

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Figure 5

Stumble recovery for the simplest walking model (slope angle γ=0.004) using an elevating and lowering strategy. Both contour maps indicate the torque magnitudes that result in successful recovery from an instantaneous swing foot blockage. The horizontal axis shows the timing of the induced stumble during a step, from swing initiation (at 0% of the step time) to heelstrike (at 100% of the step time). Just before heelstrike, no stumbles can be induced by swing foot blockage because the model shows a negative foot velocity. The vertical axis shows the applied constant hip recovery torque. The solid black lines represent recoveries where the recovered state ends up onto (or closest to) the fixed point. To explain the graph, five points are shown that represent different lowering recoveries in response to a stumble at approximately 65% of the step. All recoveries employ different recovery torque magnitudes. (Corresponding points can be found in Fig. 4). If the applied recovery torque is too low (1) or too high (5), the model will fall within the current or the consecutive steps. Minimal (2) or maximal (4) successful recovery torque will just result in recovery. If the applied recovery torque is just right (3), the model state returns onto (or closest to) the fixed point.

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Figure 6

Stumble recovery for the anthropomorphic walking models (slope angle γ=0.0075) using an elevating and lowering strategy. The two superimposed contour maps indicate the torque magnitudes that result in successful recovery from an instantaneous swing foot blockage, as in Fig. 5. (a) For the straight-legged model, the minimal amount of ground clearance of the swing foot frequently lead to failed stumble recovery due to foot-scuffing. (b) For the kneed model, knee actuation may be required to stretch the leg prior to heelstrike. Patches, bounded by white isocurves, indicate the recoveries that have equal knee torque requirements. The numbers in white indicate the magnitude of the required knee torque. The lowering phase of the lowering strategy required a constant torque of (Tknee=0.001).

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Figure 7

Example recovery scenario in response to a swing foot obstruction applied for a duration of 15% of the step time. (a) For the simplest walking model, as Fig. 5. The effect of the delay between the perturbation onset and recovery initiation is shown in comparison to an instantaneous blockage. For clarity, we only present torque magnitudes for recovery toward the fixed point. (b) For the kneed anthropomorphic model, as Fig. 6.

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Figure 8

Multiple-step recovery for the simplest walking model (a and b). The contour map of a two-step strategy is superimposed on the contour map of the corresponding single-step strategy from Fig. 5. The vertical axis shows the applied constant torque that is applied to the hip during the first recovery step and the following step. The contour map has different branches, for recoveries that have a higher or lower torque requirement compared with the single-step recoveries.

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Figure 9

Hypothetical measures for cost of recovery for the simplest walking model, as a function of the strategy and timing of the stumble. Cost of recovery hypothetically proportional to (a) the absolute magnitude of peak recovery torque; (b) the torque divided by a the duration of the recovery Δt; (c) the torque integrated over the duration of the recovery step, i.e., the impulse; (d) the peak recovery torque multiplied by the maximum of the recovery leg angular velocity θ̇; and (e) the amount of swing work performed: the torque multiplied by the angular displacement of the swing leg.

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