 Estimating Lower Limb Kinematics using Distance Measurements with a Reduced Wearable Inertial Sensor Count

Luke Wicent Sy, Nigel Lovell, Stephen Redmond

Gait Analysis Osteoarthritis Cerebral Palsy Surgery Parkinson's Disease Perform. Improvement Fall risk assessment Real Time Feedback

Motion Capture Systems Camera based

Very accurate but limited to a small space Inertial Measurement Unit (IMU)

Miniaturization. Track position and orientation (albeit with drift). IMU based (one sensor per seg)

Can capture almost everywhere. Can be conspicuous for everyday use  Wearable based

More comfortable

• Soft stretch sensors
• More & smaller IMUs
• Sparse sensors

Wearable based

More comfortable

• Soft stretch sensors
• More & smaller IMUs
• Sparse sensors

Sparse Wearable Challenge

Goal: Comfortable, Fast, and Accurate Motion Capture System  One sensor per segment.

Less sensor = Missing info Infer through biomechanical constraints Sparse Constrained KF (CKF)

Algorithm overview of prior work  Body Model: Pred. Meas. Cstr. Sparse CKF - Sample Sparse CKF - Weakness

To make it work, we need to make assumptions that may not be practical for certain movements (e.g., Activities of Daily Living or ADLs).  Sparse CKF + Distance

Overview

Distance measurement which can be obtained through ultrasonic or ultra-wide band radio (UWB). Body Model: Sparse CKF + Distance

Remove pelvis related assumptions. Additional measurement model. $$\mathbf{H}(\mathbf{x}) = \tau_{k}^{pla} ( \hat{\theta}_{lk} ) \\ \tau_{k}^{pla} ( \theta_{lk} ) = \overbrace{\tfrac{d^{p}}{2} \mathbf{r}^p_y - d^{ls} \mathbf{r}^{ls}_{z}}^{\psi, \text{ hip + shanks}} + \overbrace{d^{lt} \mathbf{r}_x^{ls} \sin{(\theta_{lk})} -d^{lt} \mathbf{r}^{ls}_z \cos{(\theta_{lk})} }^{\Lambda, \text{ thigh}} \\ (\hat{d}^{pla})^2 = \tau_{k}^{pla}(\theta_{lk})^2 = \psi^2 + 2 \psi \cdot \Lambda + (d^{lt})^2 \\ \alpha \cos{(\theta_{lk})} + \beta \sin{(\theta_{lk})} = \gamma \\ \alpha = - 2 d^{lt} \psi \cdot \mathbf{r}^{ls}_z, \quad \beta = 2 d^{lt} \psi \cdot \mathbf{r}^{ls}_x \\ \gamma = (\hat{d}^{pla})^2 - \psi^2 - (d^{lt})^2 \\ \hat{\theta}_{lk} = \cos^{-1}\left( \tfrac{\alpha \gamma \pm \beta \sqrt{\alpha^2+\beta^2-\gamma^2}}{\alpha^2+\beta^2} \right)$$

Sparse CKF+D - Sample

Tested on actual IMU data + simulated distance measurement from Sparse CKF dataset (walking, jumping jacks, speedskater, TUG, jog). Most deviation is at the turning motion ($t=3.5 - 5$s).  Sparse CKF+D - Sample

Dramatic increase in performance in dynamic movements. Captures Sagitall knee angles better.  Sparse CKF+D - Sample

Is able to locate relative position better. Note: TUG = Timed Up and Go.  Sparse CKF+D - Varying $\sigma$

Simulated at different levels of distance measurement noise $\sigma$ (assumed gaussian). Useful from $\sigma \leq 0.1$ m for walking. Useful from $\sigma \leq 0.2$ m for dynamic movements. Conclusion & Future Work

• Adding distance measurement is indeed a promising approach
• Can be implemented using ultrasound or Ultrawideband (UWB) based sensors.
• Simulated distance measurement needs actual validation.
• Code at https://git.io/JvLCF
• Interesting to try with better models and tracking more segments.  Infer from distance.   Lie Group based 7 segment

Appendix - CKF+D Quant. Results

Tested on actual IMU data + simulated distance measurement from Sparse CKF dataset (walking, jumping jacks, speedskater, TUG, jog). 