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. 2017 Mar;25(3):265-278.
doi: 10.1109/TNSRE.2016.2569019. Epub 2016 May 13.

A Robust Parameterization of Human Gait Patterns Across Phase-Shifting Perturbations

Dario J Villarreal, Hasan A Poonawala, Robert D Gregg

A Robust Parameterization of Human Gait Patterns Across Phase-Shifting Perturbations

Dario J Villarreal et al. IEEE Trans Neural Syst Rehabil Eng. 2017 Mar.

Abstract

The phase of human gait is difficult to quantify accurately in the presence of disturbances. In contrast, recent bipedal robots use time-independent controllers relying on a mechanical phase variable to synchronize joint patterns through the gait cycle. This concept has inspired studies to determine if human joint patterns can also be parameterized by a mechanical variable. Although many phase variable candidates have been proposed, it remains unclear which, if any, provide a robust representation of phase for human gait analysis or control. In this paper we analytically derive an ideal phase variable (the hip phase angle) that is provably monotonic and bounded throughout the gait cycle. To examine the robustness of this phase variable, ten able-bodied human subjects walked over a platform that randomly applied phase-shifting perturbations to the stance leg. A statistical analysis found the correlations between nominal and perturbed joint trajectories to be significantly greater when parameterized by the hip phase angle (0.95+) than by time or a different phase variable. The hip phase angle also best parameterized the transient errors about the nominal periodic orbit. Finally, interlimb phasing was best explained by local (ipsilateral) hip phase angles that are synchronized during the double-support period.

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Figures

Fig. 1
Fig. 1
Body diagram of the leg coordinates px, py, θp, θh, θk, and θa corresponding to the horizontal hip position, vertical hip position, pelvic tilt, hip angle, knee angle, and ankle angle, respectively. The first three are global variables and the last three are relative variables. Additional global variables include the tibia angle θt and the thigh angle Θ, i.e., global hip angle. The horizontal hip position px and the polar coordinate of the thigh’s phase portrait are evaluated as phase variables.
Fig. 2
Fig. 2
The natural and modified global hip kinematics used to compute the phase angle (i.e., polar coordinate of the phase portrait) are shown in the first two rows. The corresponding phase portrait and phase angle (φ) are shown in the last two rows.
Fig. 3
Fig. 3
Top view of the experimental setup. The subject walked along an 8 m walkway, stepping on the force plate in the center. The force plate randomly translated forward or backward 5 cm over 100 ms at different times after heel contact, moving the stance leg ahead or behind the body, respectively. The subject was asked to walk naturally from the starting position to the final position, after which the subject turned around and repeated.
Fig. 4
Fig. 4
The hip, knee, and ankle joint angles (top, middle, and bottom rows) for the initiating leg (i.e., leg contacting the perturbation platform) are shown parameterized over time (left), hip position (center), and hip phase angle (right) for 100 ms onset condition. The blue solid line represents the non-perturbed trajectories, whereas the red dashed and green dash-dot lines represent the joint trajectories perturbed backward (i.e., moving stance leg behind the body) and forward (i.e., moving stance leg ahead of the body). The black dashed vertical line represents the onset time of the perturbation.
Fig. 5
Fig. 5
The hip, knee, and ankle joint angles (top, middle, and bottom rows) for the initiating leg (i.e., leg contacting the perturbation platform) are shown parameterized over time (left), hip position (center), and hip phase angle (right) for 250 ms onset condition. The blue solid line represents the non-perturbed trajectories, whereas the red dashed and green dash-dot lines represent the joint trajectories perturbed backward (i.e., moving stance leg behind the body) and forward (i.e., moving stance leg ahead of the body). The black dashed vertical line represents the onset time of the perturbation.
Fig. 6
Fig. 6
Hip phase angle over time with and without perturbations at 100 ms (top) and 250 ms (bottom) after initial contact with the platform. The dashed red line shows the backward perturbation condition (i.e., moving stance leg behind the body), whereas the dash-dot green line shows the forward perturbation condition (i.e., moving stance leg ahead of the body). The dashed black vertical line represents the onset time of the perturbation.
Fig. 7
Fig. 7
Observed errors between perturbed and nominal joint trajectories in the time parameterization (et) vs. the hip phase angle parameterization (ep) for the initiating leg with the 250 ms onset condition. The observed errors of the phase parameterization tend toward zero. The last 10% of the gait cycle was excluded because ground impact prevents strict monotonicity, preventing the interpolation of joint trajectories to compute the phase-based error.
Fig. 8
Fig. 8
Contralateral (left) vs. ipsilateral (right) hip phase angle parameterizations of the non-initiating (i.e., swing) leg during the perturbation step for the 250 ms onset condition. The blue solid line represents the non-perturbed trajectories, whereas the red dashed and green dash-dot lines represent the backward and forward perturbation conditions, respectively. The black dashed vertical line represents the onset time of the perturbation. Note that the ranges of the contralateral and ipsilateral phase variables differ by 0.5 because of the anti-phasic relationship between the stance and swing legs.
Fig. 9
Fig. 9
The swing-to-stance transition of the non-initiating leg (i.e., contralateral to the stance leg in contact with the force plate) shown parameterized over time for the 250 ms onset condition. The blue solid line represents the non-perturbed trajectories, whereas the red dashed and green dash-dot lines represent the backward and forward perturbation conditions, respectively. The black dashed vertical line represents the onset time of the perturbation whereas the blue solid, red dashed, and dash-dot green vertical lines represent the stance-to-swing transition of the contralateral (initiating) leg.
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