# Using Inertial measurements to quantify and classify movements for health care analysis.

## 21 March 2018

The ability to control and maintain force between robots and people remains a major problem in assistive robotics. This talk will review some past work in assistive robotics and machine mediated stroke rehabilitation as well as explore the challenges in designing effective force control for rehabilitation applications.

# Robot equations

$\underline\tau= M(\underline{q})\ddot{\underline{q}}+C(\underline{q},\dot{\underline{q}})\dot{\underline{q}} +G(\underline{q})$

i.e. $F=m\ddot{x}$

or

$\ddot{x}=\frac{F}{m}$

 http://www.cybernetia.co.uk/LN/Inertia.html An adventure game with gravity

# Accelerations of lower leg

$~^1\dot{\vec\omega}_1=\begin{bmatrix} 0\\ 0\\ {\ddot\theta}_{1} \end{bmatrix}$ $~^1\dot{\vec{v}}_{cog_1}=\begin{bmatrix} g\,\sin\left(\theta _{1}\right)-{{\dot\theta}_{1}}^2\,\mathrm{lcog}_{1}\\ {\ddot\theta}_{1}\,\mathrm{lcog}_{1}+g\,\cos\left(\theta _{1}\right)\\ 0 \end{bmatrix}$

# Accelerations of the thigh

$~^2\dot{\vec\omega}_2=\begin{bmatrix} 0\\ 0\\ {\ddot\theta}_{1}+{\ddot\theta}_{2} \end{bmatrix}$ $~^2\dot{\vec{v}}_{cog_2}=\begin{bmatrix} \sin\left(\theta _{2}\right)\,\left({\ddot\theta}_{1}\,l_{1}+g\,\cos\left(\theta _{1}\right)\right)-\mathrm{lcog}_{2}\,{\left({\dot\theta}_{1}+{\dot\theta}_{2}\right)}^2-\cos\left(\theta _{2}\right)\,\left({{\dot\theta}_{1}}^2\,l_{1}-g\,\sin\left(\theta _{1}\right)\right)\\ \cos\left(\theta _{2}\right)\,\left({\ddot\theta}_{1}\,l_{1}+g\,\cos\left(\theta _{1}\right)\right)+\sin\left(\theta _{2}\right)\,\left({{\dot\theta}_{1}}^2\,l_{1}-g\,\sin\left(\theta _{1}\right)\right)+\mathrm{lcog}_{2}\,\left({\ddot\theta}_{1}+{\ddot\theta}_{2}\right)\\ 0 \end{bmatrix}$

# Accelerations of the trunk

$~^3\dot{\vec\omega}_3=\begin{bmatrix} 0\\ 0\\ {\ddot\theta}_{1}+{\ddot\theta}_{2}+{\ddot\theta}_{3} \end{bmatrix}$ $~^3\dot{\vec{v}}_{cog_3}=\begin{bmatrix} \sin\left(\theta _{3}\right)\,\left({\ddot\theta}_{1}\,l_{2}+\cos\left(\theta _{2}\right)\,\left({\ddot\theta}_{1}\,l_{1}+g\,\cos\left(\theta _{1}\right)\right)+\sin\left(\theta _{2}\right)\,\left({{\dot\theta}_{1}}^2\,l_{1}-g\,\sin\left(\theta _{1}\right)\right)\right)-\cos\left(\theta _{3}\right)\,\left(l_{2}\,{\left({\dot\theta}_{1}+{\dot\theta}_{2}\right)}^2-\sin\left(\theta _{2}\right)\,\left({\ddot\theta}_{1}\,l_{1}+g\,\cos\left(\theta _{1}\right)\right)+\cos\left(\theta _{2}\right)\,\left({{\dot\theta}_{1}}^2\,l_{1}-g\,\sin\left(\theta _{1}\right)\right)\right)-\mathrm{lcog}_{3}\,{\left({\dot\theta}_{1}+{\dot\theta}_{2}+{\dot\theta}_{3}\right)}^2\\ \cos\left(\theta _{3}\right)\,\left({\ddot\theta}_{1}\,l_{2}+\cos\left(\theta _{2}\right)\,\left({\ddot\theta}_{1}\,l_{1}+g\,\cos\left(\theta _{1}\right)\right)+\sin\left(\theta _{2}\right)\,\left({{\dot\theta}_{1}}^2\,l_{1}-g\,\sin\left(\theta _{1}\right)\right)\right)+\sin\left(\theta _{3}\right)\,\left(l_{2}\,{\left({\dot\theta}_{1}+{\dot\theta}_{2}\right)}^2-\sin\left(\theta _{2}\right)\,\left({\ddot\theta}_{1}\,l_{1}+g\,\cos\left(\theta _{1}\right)\right)+\cos\left(\theta _{2}\right)\,\left({{\dot\theta}_{1}}^2\,l_{1}-g\,\sin\left(\theta _{1}\right)\right)\right)+\mathrm{lcog}_{3}\,\left({\ddot\theta}_{1}+{\ddot\theta}_{2}+{\ddot\theta}_{3}\right)\\ 0 \end{bmatrix}$

# Sphere:

Sensor Platform for HEalth in a Residential Environment

• Funded by the EPSRC
• University of Bristol
• University of Southampton
• Knowle West Media Centre
• Toshiba
• Bristol City Council
• IBM

• Video sensing
• Activity monitoring
• Social interaction
• Wearable technology
• Activity monitoring
• Quality of movement
• Environmental sensors
• Temperature, light, air quality, humidity
• Water and electricity consumption

Move to PPT

# Sit to stand

• Video shows Baysian classifier of sittting, standing sit-to-stand and stand-to-sit
• Left classifier uses acceleration mean and variance
• Right classifier uses angular velocity

# Sit to stand Study

• Data gathering in the lab and in unstructured environments
• Data sets that include