Estimating Stair Running Performance Using Inertial Sensors

Abstract

Stair running, both ascending and descending, is a challenging aerobic exercise that many athletes, recreational runners, and soldiers perform during training. Studying biomechanics of stair running over multiple steps has been limited by the practical challenges presented while using optical-based motion tracking systems. We propose using foot-mounted inertial measurement units (IMUs) as a solution as they enable unrestricted motion capture in any environment and without need for external references. In particular, this paper presents methods for estimating foot velocity and trajectory during stair running using foot-mounted IMUs. Computational methods leverage the stationary periods occurring during the stance phase and known stair geometry to estimate foot orientation and trajectory, ultimately used to calculate stride metrics. These calculations, applied to human participant stair running data, reveal performance trends through timing, trajectory, energy, and force stride metrics. We present the results of our analysis of experimental data collected on eleven subjects. Overall, we determine that for either ascending or descending, the stance time is the strongest predictor of speed as shown by its high correlation with stride time.

Keywords: human performance; inertial measurement units; motion tracking; stair running; wearable sensors.

Figure 1

IMU data logger setup: (a) APDM IMU device showing the IMU sensor axes; (b) IMU attached to the shoe showing the IMU frame axes convention used in this paper; and (c) video stills showing the IMUs mounted on a subject's shoe climbing stairs ascent.

Figure 2

Angular velocity components measured by the gyroscope are integrated once to obtain orientation estimates $\mathit{x}$. The accelerometer components are used to estimate tilt (roll and pitch) during stationary periods $t_s$. The Kalman filter bounds the tilt errors by fusing the gyro-based orientation and accelerometer-based tilt to establish the “corrected orientation” $\widehat{\mathit{x}}$.

Figure 3

The accelerometer measurements are resolved in the world coordinate frame using the corrected orientation. The resultant accelerations are integrated twice to determine velocity and position. During stationary periods $t_s$, any remaining velocity is considered an error and its value is used to reset the position and acceleration errors.

Figure 4

A Kalman filter makes foot elevation corrections using the known step height (riser), during each stationary time $t_s$.

Figure 5

Estimated foot trajectory and speed for running over three treads during ascending (a) and descending (b). Close up of a steady state running gait showing the major stride events times: toe-off $t_{off}$ (green dots), foot strike $t_{strike}$ (red dots), maximum elevation $t_{max}$ (black dots), minimum elevation $t_{min}$ (yellow dots); and gait phases: stance phase $t_{stance}$ (blue curves) and swing phase $t_{swing}$ (red curves).

Figure 6

Foot trajectory (black curve) and pitch angle $\theta$ (colored lines) for ascending (a) and descending (b) stairs. The colors distinguish the distinct gait cycles across successive treads.

Figure 7

Stance $t_{stance}$ and stride time $t_{stride}$ relationship for ascending (a) and descending (b) stairs. Each dot represents one stride, and each color represents one subject. Overall speed is largely determined by the stance phase.

Figure 8

Swing $t_{swing}$ and stride time $t_{stride}$ relationship for ascending (a) and descending (b) stairs. The greater correlation during stair descent indicates that subjects likely generate speed gains during the swing phase.

Figure 9

Foot clearance $c$ and stride time $t_{stride}$ relationship for ascending (a) and descending (b) stairs. Descent is accomplished with an overall smaller clearance relative to ascent.

Figure 10

Kinetic energy per unit of mass $kem$ and stride time $t_{stride}$ relationship for ascending (a) and descending (b) stairs. In stair ascent, a fraction of the kinetic energy is consumed in order to safely clear the nose of the treads.

Figure 11

Bounce angle ${\theta }_{bounce}$ and stride time $t_{stride}$ correlation for ascending (a) and descending (b) stairs. Lower bounce angle during stair ascent is related to impulsive motion.

Figure 12

Vertical ground reaction force per unit of mass $gfm$ and stride time $t_{stride}$ relationship for ascending (a) and descending (b) stairs. Stair ascent employs significantly larger impulses relative to descent.