{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "wEFzPjzcL30B", "pycharm": {} }, "source": [ "# Path Planning for a Simple Car\n", "\n", "Keywords: optimal control, path planning, ipopt usage, rescaling time" ] }, { "cell_type": "markdown", "metadata": { "id": "LWw3RVx-_zmy" }, "source": [ "## Imports\n", "\n", "The following cell checks if pyomo is installed amd, if not, executes a \n", "\n", " !pip install -q pyomo\n", " \n", "command to install pyomo. The following statement attempts to install the ipopt solver. This code is not bullet proof. If installation errors occur, try to install manually before proceeding further." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "executionInfo": { "elapsed": 10657, "status": "ok", "timestamp": 1607290817611, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64", "userId": "09038942003589296665" }, "user_tz": 300 }, "id": "6JYrSJWD_zmy", "outputId": "1605ade6-3443-46bb-cc19-68af5bc91563" }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "import shutil\n", "import sys\n", "import os.path\n", "\n", "if not shutil.which(\"pyomo\"):\n", " !pip install -q pyomo\n", " assert(shutil.which(\"pyomo\"))\n", "\n", "if not (shutil.which(\"ipopt\") or os.path.isfile(\"ipopt\")):\n", " if \"google.colab\" in sys.modules:\n", " !wget -N -q \"https://ampl.com/dl/open/ipopt/ipopt-linux64.zip\"\n", " !unzip -o -q ipopt-linux64\n", " else:\n", " try:\n", " !conda install -c conda-forge ipopt \n", " except:\n", " pass\n", "\n", "assert(shutil.which(\"ipopt\") or os.path.isfile(\"ipopt\"))" ] }, { "cell_type": "markdown", "metadata": { "id": "U-BYc_td_zmz", "pycharm": {} }, "source": [ "## Mathematical model\n", "\n", "![Simple Car](https://github.com/jckantor/ND-Pyomo-Cookbook/blob/master/notebooks/figures/SimpleCar.png?raw=1)\n", "\n", "The following equations describe a simple model of a car at low speeds\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{dx}{dt} & = v \\cos(\\theta) \\\\\n", "\\frac{dy}{dt} & = v \\sin(\\theta) \\\\\n", "\\frac{d\\theta}{dt} & = \\frac{v}{L}\\tan(\\phi) \\\\\n", "\\frac{dv}{dt} & = a_v \\\\\n", "\\end{align}\n", "$$\n", "\n", "where $x$ and $y$ denote the position of the center of the rear axle, $v$ is velocity, $\\theta$ is the angle of the car axis to the horizontal, and $\\phi$ is the angle of the front steering wheels relative to the car axis. The car length $L$ is the distance between the front and rear axles. The car responds to acceleration input $a_v$ and and steering input $\\phi$.\n", "\n", "The lateral acceleration (or lateral \"g\" force) on the car is $v^2/R$ where $R = L/\\sin(\\phi)$ is the radius of curvature. Denoting lateral acceleration as $a_r$, \n", "\n", "$$\n", "\\begin{align}\n", "a_r & = \\frac{v^2 \\sin(\\phi)}{L} \\\\\n", "\\end{align}\n", "$$\n", "\n", "The path planning problem is to find values $a_v(t)$ and $\\phi(t)$ on an interval $0 \\leq t \\leq t_f$ which steer the car from an initial condition $\\left[x(0), y(0), \\theta(0), u(0)\\right]$ to a specified final condition $\\left[x(t_f), y(t_f), \\theta(t_f), u(t_f)\\right]$. The desired control inputs minimizes an objective function:\n", "\n", "$$\n", "\\begin{align}\n", "J = \\min \\int_0^{t_f} \\left( a_v(t)^2 + \\gamma a_r(t)^2 \\right)\\,dt\n", "\\end{align}\n", "$$\n", "\n", "subject to the following limits $a_v$, $\\phi$, and $v$.\n", "\n", "| variable | bound |\n", "| :---: | :---: |\n", "| $|a_r|$ | 2.8 $m/s$ |\n", "| $|a_v|$ | 2.8 $m/s$ |\n", "| $|\\phi|$ | 0.7 $rad$ |\n", "| $v$ | 30 $m/s$ |\n", "| $-v$ | 4 $m/s$ |\n", "\n", "The next cells implement the model using a fixed estimate for $t_f$, the time required to complete the desired maneuver." ] }, { "cell_type": "markdown", "metadata": { "id": "wSGzoRAJL30C", "pycharm": {} }, "source": [ "## Pyomo model" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 358 }, "executionInfo": { "elapsed": 588, "status": "error", "timestamp": 1607291001627, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64", "userId": "09038942003589296665" }, "user_tz": 300 }, "id": "VOsdtIxrL30E", "outputId": "915e3740-ca53-4a1f-f895-8c4ae15f13d6", "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# ==========================================================\n", "# = Solver Results =\n", "# ==========================================================\n", "# ----------------------------------------------------------\n", "# Problem Information\n", "# ----------------------------------------------------------\n", "Problem: \n", "- Lower bound: -inf\n", " Upper bound: inf\n", " Number of objectives: 1\n", " Number of constraints: 502\n", " Number of variables: 310\n", " Sense: unknown\n", "# ----------------------------------------------------------\n", "# Solver Information\n", "# ----------------------------------------------------------\n", "Solver: \n", "- Status: ok\n", " Message: Ipopt 3.13.4\\x3a Optimal Solution Found\n", " Termination condition: optimal\n", " Id: 0\n", " Error rc: 0\n", " Time: 2.47509503364563\n", "# ----------------------------------------------------------\n", "# Solution Information\n", "# ----------------------------------------------------------\n", "Solution: \n", "- number of solutions: 0\n", " number of solutions displayed: 0\n" ] } ], "source": [ "from pyomo.environ import *\n", "from pyomo.dae import *\n", "\n", "# parameters\n", "ar_max = 2.8\n", "av_max = 2.8\n", "phi_max = 0.7\n", "v_max = 30\n", "v_min = -4\n", "\n", "# time and length scales\n", "L = 5\n", "tf = 40\n", "\n", "# create a model object\n", "m = ConcreteModel()\n", "\n", "# define the independent variable\n", "m.t = ContinuousSet(bounds=(0, tf))\n", "\n", "# define control inputs\n", "m.av = Var(m.t)\n", "m.phi = Var(m.t, bounds=(-phi_max, phi_max))\n", "\n", "# define the dependent variables\n", "m.x = Var(m.t)\n", "m.y = Var(m.t)\n", "m.a = Var(m.t)\n", "m.v = Var(m.t)\n", "\n", "# define derivatives\n", "m.x_dot = DerivativeVar(m.x)\n", "m.y_dot = DerivativeVar(m.y)\n", "m.a_dot = DerivativeVar(m.a)\n", "m.v_dot = DerivativeVar(m.v)\n", "\n", "# define the differential equation as constrainta\n", "m.ode_x = Constraint(m.t, rule=lambda m, t: m.x_dot[t] == m.v[t]*cos(m.a[t]))\n", "m.ode_y = Constraint(m.t, rule=lambda m, t: m.y_dot[t] == m.v[t]*sin(m.a[t]))\n", "m.ode_a = Constraint(m.t, rule=lambda m, t: m.a_dot[t] == m.v[t]*tan(m.phi[t])/L)\n", "m.ode_v = Constraint(m.t, rule=lambda m, t: m.v_dot[t] == m.av[t])\n", "\n", "# path constraints\n", "m.path_x1 = Constraint(m.t, rule=lambda m, t: m.x[t] >= 0)\n", "m.path_y1 = Constraint(m.t, rule=lambda m, t: m.y[t] >= 0)\n", "m.path_v1 = Constraint(m.t, rule=lambda m, t: m.v[t] <= v_max)\n", "m.path_v2 = Constraint(m.t, rule=lambda m, t: m.v[t] >= v_min)\n", "m.path_a1 = Constraint(m.t, rule=lambda m, t: m.av[t] <= av_max)\n", "m.path_a2 = Constraint(m.t, rule=lambda m, t: m.av[t] >= -av_max)\n", "m.path_a3 = Constraint(m.t, rule=lambda m, t: m.v[t]**2*sin(m.phi[t])/L <= ar_max)\n", "m.path_a4 = Constraint(m.t, rule=lambda m, t: m.v[t]**2*sin(m.phi[t])/L >= -ar_max)\n", "\n", "# initial conditions\n", "m.pc = ConstraintList()\n", "m.pc.add(m.x[0]==0)\n", "m.pc.add(m.y[0]==0)\n", "m.pc.add(m.a[0]==0)\n", "m.pc.add(m.v[0]==0)\n", "\n", "# final conditions\n", "m.pc.add(m.x[tf]==0)\n", "m.pc.add(m.y[tf]==4*L)\n", "m.pc.add(m.a[tf]==0)\n", "m.pc.add(m.v[tf]==0)\n", "\n", "# final conditions on the control inputs\n", "m.pc.add(m.av[tf]==0)\n", "m.pc.add(m.phi[tf]==0)\n", "\n", "# define the optimization objective\n", "m.integral = Integral(m.t, wrt=m.t, rule=lambda m, t: m.av[t]**2 + (m.v[t]**2*sin(m.phi[t])/L)**2)\n", "m.obj = Objective(expr=m.integral)\n", "\n", "# transform and solve\n", "TransformationFactory('dae.finite_difference').apply_to(m, wrt=m.t, nfe=30)\n", "SolverFactory('ipopt').solve(m).write()" ] }, { "cell_type": "markdown", "metadata": { "id": "hK-zziSKL30L", "pycharm": {} }, "source": [ "## Accessing solution data" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "id": "BXNdMWvTL30M", "outputId": "54221ea1-8ca9-4a82-d5d5-aeccafd35d45", "pycharm": {} }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# access the results\n", "t = np.array([t for t in m.t])\n", "\n", "av = np.array([m.av[t]() for t in m.t])\n", "ar = np.array([(m.v[t]()**2 * np.sin(m.phi[t]()))/L for t in m.t])\n", "phi = np.array([m.phi[t]() for t in m.t])\n", "\n", "x = np.array([m.x[t]() for t in m.t])\n", "y = np.array([m.y[t]() for t in m.t])\n", "a = np.array([m.a[t]() for t in m.t])\n", "v = np.array([m.v[t]() for t in m.t])\n", "\n", "def plot_results(t, x, y, a, v, av, phi):\n", " fig, ax = plt.subplots(3,1, figsize=(10,8))\n", "\n", " ax[0].plot(t, av, t, v**2*np.sin(phi)/L)\n", " ax[0].legend(['Acceleration','Lateral Acceleration'])\n", "\n", " ax[1].plot(t, phi, t, a)\n", " ax[1].legend(['Wheel Position','Car Direction'])\n", "\n", " ax[2].plot(t, v)\n", " ax[2].legend(['Velocity'])\n", " ax[2].set_ylabel('m/s')\n", " for axes in ax:\n", " axes.grid(True)\n", " \n", "plot_results(t, x, y, a, v, av, phi)" ] }, { "cell_type": "markdown", "metadata": { "id": "3kdx9Xd9L30O", "pycharm": {} }, "source": [ "## Visualizing the car path" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 660 }, "id": "xEkwV3IxL30P", "outputId": "d724c46f-ef87-4b5b-be86-ba1ab2e9f92c", "pycharm": {} }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scl=0.3\n", "\n", "def draw_car(x=0, y=0, a=0, phi=0):\n", " R = np.array([[np.cos(a), -np.sin(a)], [np.sin(a), np.cos(a)]])\n", " car = np.array([[0.2, 0.5], [-0.2, 0.5], [0, 0.5], [0, -0.5],\n", " [0.2, -0.5], [-0.2, -0.5], [0, -0.5], [0, 0], [L, 0], [L, 0.5],\n", " [L + 0.2*np.cos(phi), 0.5 + 0.2*np.sin(phi)],\n", " [L - 0.2*np.cos(phi), 0.5 - 0.2*np.sin(phi)], [L, 0.5],[L, -0.5],\n", " [L + 0.2*np.cos(phi), -0.5 + 0.2*np.sin(phi)],\n", " [L - 0.2*np.cos(phi), -0.5 - 0.2*np.sin(phi)]])\n", " carz = scl*R.dot(car.T)\n", " plt.plot(x + carz[0], y + carz[1], 'k', lw=2)\n", " plt.plot(x, y, 'k.', ms=10)\n", " \n", "plt.figure(figsize=(10,10))\n", "for xs,ys,ts,ps in zip(x, y, a, phi): \n", " draw_car(xs, ys, ts, scl*ps)\n", "plt.plot(x, y, 'r--', lw=0.8)\n", "plt.axis('square')\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": { "id": "voaUGXRNL30W", "pycharm": {} }, "source": [ "## Rescaling to incorporate time into the optimization model\n", "\n", "While out initial formulation of the path planning problem leads to a solution, one unsatisfactory aspect of the formulation is the need to estimate the time necessary to complete the maneuver. Here we rescale the problem in such a way that the time horizon becomes part of the optimization calculation.\n", "\n", "The following equations describe a simple model of a car\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{dx}{dt'} & = t_f v \\cos(\\theta) \\\\\n", "\\frac{dy}{dt'} & = t_f v \\sin(\\theta) \\\\\n", "\\frac{d\\theta}{dt'} & = \\frac{t_f }{L}\\tan(\\phi) \\\\\n", "\\frac{dv}{dt'} & = t_f a_v \\\\\n", "\\end{align}\n", "$$\n", "\n", "subject to bounds on the manipulable variables.\n", "\n", "$$\n", "\\begin{align}\n", "| a_v | & \\leq a^{max}_v \\\\\n", "|\\frac{v^2\\sin(\\phi)}{L}| & \\leq a^{max}_r \\\\\n", "|\\phi | & \\leq \\phi^{max} \\\\\n", "| v | & \\leq v^{max} \\\\\n", "\\end{align}\n", "$$\n", "\n", "The objective function \n", "\n", "$$\n", "\\begin{align}\n", "J = t_f \\min \\int_0^{1} \\left( \\phi(t)^2 + \\alpha a(t)^2 + \\beta v(t)^2\\right)\\,dt'\n", "\\end{align}\n", "$$\n", "\n", "Introduce the natural scales\n", "\n", "$$\n", "\\begin{align}\n", "x' & = \\frac{x}{L} \\\\\n", "y' & = \\frac{y}{L} \\\\\n", "v' & = \\frac{t_f}{L} v \\\\\n", "a'_v & = \\frac{t_f^2}{L} a_v\\\\\n", "\\end{align}\n", "$$\n", "\n", "Resulting\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{dx'}{dt'} & = v' \\cos(\\theta) \\\\\n", "\\frac{dy'}{dt'} & = v' \\sin(\\theta) \\\\\n", "\\frac{d\\theta}{dt'} & = v' \\tan(\\phi) \\\\\n", "\\frac{dv'}{dt'} & = a'_v \\\\\n", "\\end{align}\n", "$$\n", "\n", "The bounds become\n", "\n", "$$\n", "\\begin{align}\n", "|a'_v| & \\leq \\frac{t_f^2}{L}a^{max}_v \\\\\n", "|v'^2\\sin(\\phi)| & \\leq \\frac{t_f^2}{L}a^{max}_r \\\\\n", "|\\phi | & \\leq \\phi^{max} \\\\\n", "| v' | & \\leq \\frac{t_f}{L}v^{max} \\\\\n", "\\end{align}\n", "$$\n", "\n", "In the rescaled variables, the objective function becomes\n", "\n", "$$\n", "\\begin{align}\n", "J = \\min \\left[ t_f + \\frac{L^2}{t_f^3} \\int_0^1 \\left(\\gamma_v a_v^2 + \\gamma_r v^4 \\sin^2(\\phi) \\right)\\,dt\\right]\n", "\\end{align}\n", "$$\n", "\n", "where an additional term $t_f$ has been included to incorporate a tradeoff between applied acceleration and corning forces and the time required to complete the maneuver.\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "id": "t5i8pmKV_zm0", "outputId": "71f6ad09-c041-4d8a-97a2-7e2d53bd5555" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# ==========================================================\n", "# = Solver Results =\n", "# ==========================================================\n", "# ----------------------------------------------------------\n", "# Problem Information\n", "# ----------------------------------------------------------\n", "Problem: \n", "- Lower bound: -inf\n", " Upper bound: inf\n", " Number of objectives: 1\n", " Number of constraints: 502\n", " Number of variables: 311\n", " Sense: unknown\n", "# ----------------------------------------------------------\n", "# Solver Information\n", "# ----------------------------------------------------------\n", "Solver: \n", "- Status: ok\n", " Message: Ipopt 3.13.4\\x3a Optimal Solution Found\n", " Termination condition: optimal\n", " Id: 0\n", " Error rc: 0\n", " Time: 1.4138092994689941\n", "# ----------------------------------------------------------\n", "# Solution Information\n", "# ----------------------------------------------------------\n", "Solution: \n", "- number of solutions: 0\n", " number of solutions displayed: 0\n" ] } ], "source": [ "# parameters\n", "ar_max = 2.8\n", "av_max = 2.8\n", "phi_max = 0.7\n", "v_max = 30\n", "v_min = -4\n", "\n", "# time and length scales\n", "L = 5\n", "\n", "# create a model object\n", "m = ConcreteModel()\n", "\n", "# define the independent variable\n", "m.tf = Var(domain=NonNegativeReals)\n", "m.t = ContinuousSet(bounds=(0, 1))\n", "\n", "# define control inputs\n", "m.av = Var(m.t)\n", "m.phi = Var(m.t, bounds=(-phi_max, phi_max))\n", "\n", "# define the dependent variables\n", "m.x = Var(m.t)\n", "m.y = Var(m.t)\n", "m.a = Var(m.t)\n", "m.v = Var(m.t)\n", "\n", "# define derivatives\n", "m.x_dot = DerivativeVar(m.x)\n", "m.y_dot = DerivativeVar(m.y)\n", "m.a_dot = DerivativeVar(m.a)\n", "m.v_dot = DerivativeVar(m.v)\n", "\n", "# define the differential equation as constrainta\n", "m.ode_x = Constraint(m.t, rule=lambda m, t: m.x_dot[t] == m.v[t]*cos(m.a[t]))\n", "m.ode_y = Constraint(m.t, rule=lambda m, t: m.y_dot[t] == m.v[t]*sin(m.a[t]))\n", "m.ode_a = Constraint(m.t, rule=lambda m, t: m.a_dot[t] == m.v[t]*tan(m.phi[t])/L)\n", "m.ode_v = Constraint(m.t, rule=lambda m, t: m.v_dot[t] == m.av[t])\n", "\n", "# path constraints\n", "m.path_x1 = Constraint(m.t, rule=lambda m, t: m.x[t] >= 0)\n", "m.path_y1 = Constraint(m.t, rule=lambda m, t: m.y[t] >= 0)\n", "m.path_v1 = Constraint(m.t, rule=lambda m, t: m.v[t] <= m.tf*v_max/L)\n", "m.path_v2 = Constraint(m.t, rule=lambda m, t: m.v[t] >= m.tf*v_min/L)\n", "m.path_a1 = Constraint(m.t, rule=lambda m, t: m.av[t] <= m.tf**2*av_max/L)\n", "m.path_a2 = Constraint(m.t, rule=lambda m, t: m.av[t] >= -m.tf**2*av_max/L)\n", "m.path_a3 = Constraint(m.t, rule=lambda m, t: m.v[t]**2*sin(m.phi[t]) <= m.tf**2*ar_max/L)\n", "m.path_a4 = Constraint(m.t, rule=lambda m, t: m.v[t]**2*sin(m.phi[t]) >= -m.tf**2*ar_max/L)\n", "\n", "# initial conditions\n", "m.pc = ConstraintList()\n", "m.pc.add(m.x[0]==0)\n", "m.pc.add(m.y[0]==0)\n", "m.pc.add(m.a[0]==0)\n", "m.pc.add(m.v[0]==0)\n", "\n", "# final conditions\n", "m.pc.add(m.x[1]==0)\n", "m.pc.add(m.y[1]==4)\n", "m.pc.add(m.a[1]==0)\n", "m.pc.add(m.v[1]==0)\n", "\n", "# final conditions on the control inputs\n", "m.pc.add(m.av[1]==0)\n", "m.pc.add(m.phi[1]==0)\n", "\n", "# define the optimization objective\n", "m.integral = Integral(m.t, wrt=m.t, rule=lambda m, t: m.av[t]**2 + (m.v[t]**2*sin(m.phi[t]))**2)\n", "m.obj = Objective(expr= m.tf + L**2*m.integral/m.tf**3)\n", "\n", "# transform and solve\n", "TransformationFactory('dae.finite_difference').apply_to(m, wrt=m.t, nfe=30)\n", "SolverFactory('ipopt').solve(m).write()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "id": "qECb3eA-_zm0", "outputId": "82ae1e66-e4e0-4db3-df7c-92327a5ade26" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# access the results\n", "t = np.array([t*m.tf() for t in m.t])\n", "\n", "av = np.array([m.av[t]()*L/(m.tf()**2) for t in m.t])\n", "phi = np.array([m.phi[t]() for t in m.t])\n", "\n", "x = np.array([m.x[t]()*L for t in m.t])\n", "y = np.array([m.y[t]()*L for t in m.t])\n", "a = np.array([m.a[t]() for t in m.t])\n", "v = np.array([m.v[t]()*L/m.tf() for t in m.t])\n", "\n", "ar = v**2 * np.sin(phi)/L\n", " \n", "plot_results(t, x, y, a, v, av, phi)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "id": "Iq7aCJ3c_zm0", "outputId": "c63949c8-8aaf-4ef8-c20d-503203db6cb4" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scl=0.2\n", "\n", "plt.figure(figsize=(10,10))\n", "for xs,ys,ts,ps in zip(x, y, a, phi): \n", " draw_car(xs, ys, ts, scl*ps)\n", "plt.plot(x, y, 'r--', lw=0.8)\n", "plt.axis('square')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "id": "PGr1tFV2_zm0", "outputId": "8147a2c5-21db-46a4-9df0-de9aa8fe0e02" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "37.569148444099255\n" ] } ], "source": [ "print(m.tf())" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "name": "06.03-Path-Planning-for-a-Simple-Car.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 4 }