A Simple Model for Estimating the Kinematics of Tape-like Unstable Bases from Angular Measurements near Anchor Points

Abstract

Sensorimotor training on an unstable base of support is considered to lead to improvements in balance and coordination tasks. Here, we intend to lay the groundwork for generating cost-effective real-time kinematic feedback for coordination training on devices with an unstable base of support, such as Sensopros or slacklines, by establishing a model for estimating relevant tape kinematic data from angle measurements alone. To assess the accuracy of the model in a real-world setting, we record a convenience sample of three people performing ten exercises on the Sensopro Luna and compare the model predictions to motion capture data of the tape. The measured accuracy is reported for each target measure separately, namely the roll angle and XYZ-position of the tape segment directly below the foot. After the initial assessment of the model in its general form, we also propose how to adjust the model parameters based on preliminary measurements to adapt it to a specific setting and further improve its accuracy. The results show that the proposed method is viable for recording tape kinematic data in real-world settings, and may therefore serve as a performance indicator directly or form the basis for estimating posture and other measures related to human motor control in a more intricate training feedback system.

Keywords: augmented feedback; balance training; dynamic exercise; inertial measurement unit; kinematics; sensor-based; unstable surface.

Figure 1

The tapes of the Sensopro Luna during a sideways exercise (a) and at rest (b), with green markings indicating the IMU positions. Blue plastic covers are screwed onto the tape, hiding the springs. The anchor points are below the black platforms at the front and back.

Figure 2

The general model for the X-position and Z-displacement $d_M$ compared to the actual tape displacement approximated by $d_R$. The black and purple arrows correspond to the front and back tape segments that determine the input angles $\alpha$ and $\beta$, respectively.

Figure 3

Reflective marker on the tapes (with the front on the right hand side). The plastic covers on the right tape have been loosened to partially expose the metal springs.

Figure 4

One data point of the left and right tapes in the sagittal plane (as seen from the side).

Figure 5

One data point of the left and right tapes in the transversal plane (as seen from above).

Figure 6

Variation in roll angle along tape axis compared to non-parameterized ($R_M$) and parameterized ($R_S$) model outputs.

Figure 7

Modified box plots of the prediction errors in all samples. The whiskers range from the 2nd to the 98th percentile, and the boxes cover the 25th to 75th percentile. The median is shown as an orange line, and all outliers (highest and lowest two percentiles) are marked in blue.

Figure 8

Effect of X-position on prediction error for X, Y, $Z_{R85}$, and $R_{WS}$. The green line is the median, the dark green area covers the 25th to 75th percentiles, and the light green area covers the 2nd to 98th percentiles ($96\%$ of all data points). The blue, orange, red, and purple lines correspond to the 98th, 75th, 25th, and 2nd percentiles, respectively.

Figure 9

Effect of Z-position on prediction error for X, Y, $Z_{R85}$, and $R_{WS}$. The green line is the median, the dark green area covers the 25th to 75th percentiles, and the light green area covers the 2nd to 98th percentiles ($96\%$ of all data points). The blue, orange, red, and purple lines correspond to the 98th, 75th, 25th, and 2nd percentiles, respectively.

Figure 10

Comparison between IMU angles and reference motion capture data for a single trial (C02).

Figure 11

Modified box plots of prediction errors using IMU input data. The whiskers range from the 2nd to the 98th percentile.