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Atsushi Sakai
2018-11-15 21:11:00 +09:00
parent 620a0488f3
commit 274bfda8e6
12 changed files with 993 additions and 30 deletions
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PathTracking/model_predictive_speed_and_steer_control/notebook.ipynb → PathTracking/model_predictive_speed_and_steer_control/Model_predictive_speed_and_steering_control.ipynb
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@@ -4,11 +4,20 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"# Model predictive speed and steering control\n",
"## Model predictive speed and steering control\n",
"\n",
"![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"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"code:\n",
"\n",
"https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py\n",
"[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",
"\n",
"This is a path tracking simulation using model predictive control (MPC).\n",
"\n",
@@ -23,7 +32,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"# MPC modeling\n",
"### MPC modeling\n",
"\n",
"State vector is:\n",
"$$ z = [x, y, v,\\phi]$$ x: x-position, y:y-position, v:velocity, φ: yaw angle\n",
@@ -49,18 +58,31 @@
"metadata": {},
"source": [
"subject to:\n",
"\n",
"- Linearlied vehicle model\n",
"\n",
"$$z_{t+1}=Az_t+Bu+C$$\n",
"\n",
"- Maximum steering speed\n",
"\n",
"$$|u_{t+1}-u_{t}|<du_{max}$$\n",
"\n",
"- Maximum steering angle\n",
"\n",
"$$|u_{t}|<u_{max}$$\n",
"\n",
"- Initial state\n",
"\n",
"$$z_0 = z_{0,ob}$$\n",
"\n",
"- Maximum and minimum speed\n",
"\n",
"$$v_{min} < v_t < v_{max}$$\n",
"\n",
"- Maximum and minimum input\n",
"$$u_{min} < u_t < u_{max}$$\n"
"\n",
"$$u_{min} < u_t < u_{max}$$\n",
"\n"
]
},
{
@@ -69,14 +91,14 @@
"source": [
"This is implemented at \n",
"\n",
"https://github.com/AtsushiSakai/PythonRobotics/blob/f51a73f47cb922a12659f8ce2d544c347a2a8156/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py#L247-L301"
"[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)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Vehicle model linearization\n",
"### Vehicle model linearization\n",
"\n",
"\n",
"\n",
@@ -106,7 +128,7 @@
"source": [
"where\n",
"\n",
"\\begin{equation*}\n",
"$$\\begin{equation*}\n",
"A' =\n",
"\\begin{bmatrix}\n",
"\\frac{\\partial }{\\partial x}vcos(\\phi) & \n",
@@ -134,7 +156,7 @@
"0 & 0 & 0 & 0 \\\\\n",
"0 & 0 &\\frac{tan(\\bar{\\delta})}{L} & 0 \\\\\n",
"\\end{bmatrix}\n",
"\\end{equation*}\n",
"\\end{equation*}$$\n",
"\n"
]
},
@@ -142,7 +164,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation*}\n",
"$$\\begin{equation*}\n",
"B' =\n",
"\\begin{bmatrix}\n",
"\\frac{\\partial }{\\partial a}vcos(\\phi) &\n",
@@ -162,7 +184,7 @@
"1 & 0 \\\\\n",
"0 & \\frac{\\bar{v}}{Lcos^2(\\bar{\\delta})} \\\\\n",
"\\end{bmatrix}\n",
"\\end{equation*}\n",
"\\end{equation*}$$\n",
"\n"
]
},
@@ -190,7 +212,7 @@
"\n",
"where,\n",
"\n",
"\\begin{equation*}\n",
"$$\\begin{equation*}\n",
"A = (I + dtA')\\\\\n",
"=\n",
"\\begin{bmatrix} \n",
@@ -199,14 +221,14 @@
"0 & 0 & 1 & 0 \\\\\n",
"0 & 0 &\\frac{tan(\\bar{\\delta})}{L}dt & 1 \\\\\n",
"\\end{bmatrix}\n",
"\\end{equation*}"
"\\end{equation*}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation*}\n",
"$$\\begin{equation*}\n",
"B = dtB'\\\\\n",
"=\n",
"\\begin{bmatrix} \n",
@@ -215,14 +237,14 @@
"dt & 0 \\\\\n",
"0 & \\frac{\\bar{v}}{Lcos^2(\\bar{\\delta})}dt \\\\\n",
"\\end{bmatrix}\n",
"\\end{equation*}"
"\\end{equation*}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation*}\n",
"$$\\begin{equation*}\n",
"C = (f(\\bar{z},\\bar{u})-A'\\bar{z}-B'\\bar{u})dt\\\\\n",
"= dt(\n",
"\\begin{bmatrix} \n",
@@ -253,7 +275,7 @@
"0\\\\\n",
"-\\frac{\\bar{v}\\bar{\\delta}}{Lcos^2(\\bar{\\delta})}dt\\\\\n",
"\\end{bmatrix}\n",
"\\end{equation*}"
"\\end{equation*}$$"
]
},
{
@@ -262,14 +284,14 @@
"source": [
"This equation is implemented at \n",
"\n",
"https://github.com/AtsushiSakai/PythonRobotics/blob/eb6d1cbe6fc90c7be9210bf153b3a04f177cc138/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py#L80-L102"
"[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"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Reference\n",
"### Reference\n",
"\n",
"- [Vehicle Dynamics and Control \\| Rajesh Rajamani \\| Springer](http://www.springer.com/us/book/9781461414322)\n",
"\n",
@@ -279,7 +301,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python [default]",
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
@@ -293,7 +315,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
"version": "3.6.6"
}
},
"nbformat": 4,