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update docs
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PathTracking/model_predictive_speed_and_steer_control/notebook.ipynb renamed to PathTracking/model_predictive_speed_and_steer_control/Model_predictive_speed_and_steering_control.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Model predictive speed and steering control\n",
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"## Model predictive speed and steering control\n",
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"\n",
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"![Model predictive speed and steering control](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathTracking/model_predictive_speed_and_steer_control/animation.gif?raw=true)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"\n",
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"code:\n",
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"\n",
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"https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py\n",
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"[PythonRobotics/model\\_predictive\\_speed\\_and\\_steer\\_control\\.py at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py)\n",
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"\n",
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"This is a path tracking simulation using model predictive control (MPC).\n",
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"\n",
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# MPC modeling\n",
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"### MPC modeling\n",
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"\n",
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"State vector is:\n",
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"$$ z = [x, y, v,\\phi]$$ x: x-position, y:y-position, v:velocity, φ: yaw angle\n",
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"metadata": {},
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"source": [
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"subject to:\n",
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"\n",
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"- Linearlied vehicle model\n",
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"\n",
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"$$z_{t+1}=Az_t+Bu+C$$\n",
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"\n",
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"- Maximum steering speed\n",
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"\n",
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"$$|u_{t+1}-u_{t}|<du_{max}$$\n",
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"\n",
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"- Maximum steering angle\n",
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"\n",
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"$$|u_{t}|<u_{max}$$\n",
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"\n",
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"- Initial state\n",
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"\n",
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"$$z_0 = z_{0,ob}$$\n",
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"\n",
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"- Maximum and minimum speed\n",
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"\n",
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"$$v_{min} < v_t < v_{max}$$\n",
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"\n",
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"- Maximum and minimum input\n",
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"$$u_{min} < u_t < u_{max}$$\n"
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"\n",
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"$$u_{min} < u_t < u_{max}$$\n",
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"\n"
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]
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},
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{
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"source": [
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"This is implemented at \n",
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"\n",
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"https://github.com/AtsushiSakai/PythonRobotics/blob/f51a73f47cb922a12659f8ce2d544c347a2a8156/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py#L247-L301"
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"[PythonRobotics/model\\_predictive\\_speed\\_and\\_steer\\_control\\.py at f51a73f47cb922a12659f8ce2d544c347a2a8156 · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/f51a73f47cb922a12659f8ce2d544c347a2a8156/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py#L247-L301)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Vehicle model linearization\n",
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"### Vehicle model linearization\n",
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"\n",
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"\n",
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"\n",
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"source": [
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"where\n",
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"\n",
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"\\begin{equation*}\n",
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"$$\\begin{equation*}\n",
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"A' =\n",
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"\\begin{bmatrix}\n",
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"\\frac{\\partial }{\\partial x}vcos(\\phi) & \n",
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"0 & 0 & 0 & 0 \\\\\n",
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"0 & 0 &\\frac{tan(\\bar{\\delta})}{L} & 0 \\\\\n",
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"\\end{bmatrix}\n",
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"\\end{equation*}\n",
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"\\end{equation*}$$\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\\begin{equation*}\n",
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"$$\\begin{equation*}\n",
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"B' =\n",
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"\\begin{bmatrix}\n",
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"\\frac{\\partial }{\\partial a}vcos(\\phi) &\n",
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"1 & 0 \\\\\n",
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"0 & \\frac{\\bar{v}}{Lcos^2(\\bar{\\delta})} \\\\\n",
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"\\end{bmatrix}\n",
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"\\end{equation*}\n",
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"\\end{equation*}$$\n",
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"\n"
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]
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},
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"\n",
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"where,\n",
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"\n",
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"\\begin{equation*}\n",
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"$$\\begin{equation*}\n",
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"A = (I + dtA')\\\\\n",
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"=\n",
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"\\begin{bmatrix} \n",
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"0 & 0 & 1 & 0 \\\\\n",
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"0 & 0 &\\frac{tan(\\bar{\\delta})}{L}dt & 1 \\\\\n",
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"\\end{bmatrix}\n",
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"\\end{equation*}"
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"\\end{equation*}$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\\begin{equation*}\n",
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"$$\\begin{equation*}\n",
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"B = dtB'\\\\\n",
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"=\n",
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"\\begin{bmatrix} \n",
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"dt & 0 \\\\\n",
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"0 & \\frac{\\bar{v}}{Lcos^2(\\bar{\\delta})}dt \\\\\n",
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"\\end{bmatrix}\n",
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"\\end{equation*}"
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"\\end{equation*}$$"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\\begin{equation*}\n",
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"$$\\begin{equation*}\n",
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"C = (f(\\bar{z},\\bar{u})-A'\\bar{z}-B'\\bar{u})dt\\\\\n",
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"= dt(\n",
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"\\begin{bmatrix} \n",
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"0\\\\\n",
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"-\\frac{\\bar{v}\\bar{\\delta}}{Lcos^2(\\bar{\\delta})}dt\\\\\n",
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"\\end{bmatrix}\n",
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"\\end{equation*}"
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"\\end{equation*}$$"
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]
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},
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{
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"source": [
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"This equation is implemented at \n",
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"\n",
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"https://github.com/AtsushiSakai/PythonRobotics/blob/eb6d1cbe6fc90c7be9210bf153b3a04f177cc138/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py#L80-L102"
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"[PythonRobotics/model\\_predictive\\_speed\\_and\\_steer\\_control\\.py at eb6d1cbe6fc90c7be9210bf153b3a04f177cc138 · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/eb6d1cbe6fc90c7be9210bf153b3a04f177cc138/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py#L80-L102)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Reference\n",
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"### Reference\n",
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"\n",
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"- [Vehicle Dynamics and Control \\| Rajesh Rajamani \\| Springer](http://www.springer.com/us/book/9781461414322)\n",
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"\n",
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python [default]",
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.4"
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"version": "3.6.6"
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}
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},
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"nbformat": 4,

‎docs/conf.py‎

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'sphinx.ext.autodoc',
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'sphinx.ext.mathjax',
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'sphinx.ext.viewcode',
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'sphinx.ext.viewcode',
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]
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# Add any paths that contain templates here, relative to this directory.

‎docs/jupyternotebook2rst.py‎

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"""
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Jupyter notebook converter to rst file
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author: Atsushi Sakai
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"""
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NOTEBOOK_DIR = "../"
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import glob
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import os
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import os.path
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import subprocess
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def get_notebook_path_list(ndir):
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path = glob.glob(ndir + "**/*.ipynb", recursive=True)
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return path
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def generate_rst(npath):
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# print(npath)
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# generate dir
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dirpath = "./modules/" + os.path.dirname(npath)[3:]
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# print(dirpath)
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if not os.path.exists(dirpath):
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os.makedirs(dirpath)
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rstpath = os.path.abspath("./modules/" + npath[3:-5] + "rst")
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print(rstpath)
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cmd = "jupyter nbconvert --to rst "
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cmd += npath
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cmd += " --output "
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cmd += rstpath
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print(cmd)
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subprocess.call(cmd, shell=True)
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def main():
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print("start!!")
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notebook_path_list = get_notebook_path_list(NOTEBOOK_DIR)
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# print(notebook_path_list)
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for npath in notebook_path_list:
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generate_rst(npath)
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print("done!!")
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if __name__ == '__main__':
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main()

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