From ba4046b6e26bdb34c97c25b7794c183c1a1ec376 Mon Sep 17 00:00:00 2001 From: 12345qiupeng Date: Wed, 23 Oct 2024 13:41:00 +0800 Subject: [PATCH] =?UTF-8?q?feat:=20=E7=BF=BB=E8=AF=91=E5=8F=82=E6=95=B0?= =?UTF-8?q?=E5=8C=96=E6=9B=B2=E7=BA=BF?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- notebooks/1.0-lti-system-modelling.ipynb | 90 +++--- notebooks/1.1-parametrized-path-curves.ipynb | 287 ++++++++++++++++--- 2 files changed, 294 insertions(+), 83 deletions(-) diff --git a/notebooks/1.0-lti-system-modelling.ipynb b/notebooks/1.0-lti-system-modelling.ipynb index 49b24a5..65d7e3b 100644 --- a/notebooks/1.0-lti-system-modelling.ipynb +++ b/notebooks/1.0-lti-system-modelling.ipynb @@ -11,22 +11,14 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 51, "metadata": { "ExecuteTime": { - "end_time": "2024-10-22T08:05:56.118290Z", - "start_time": "2024-10-22T08:05:46.550696Z" + "end_time": "2024-10-22T09:43:55.338138Z", + "start_time": "2024-10-22T09:43:55.319761Z" } }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Matplotlib is building the font cache; this may take a moment.\n" - ] - } - ], + "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", @@ -190,11 +182,11 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 52, "metadata": { "ExecuteTime": { - "end_time": "2024-10-22T09:21:29.100064Z", - "start_time": "2024-10-22T09:21:29.094806Z" + "end_time": "2024-10-22T09:43:55.339159Z", + "start_time": "2024-10-22T09:43:55.327823Z" } }, "outputs": [], @@ -238,11 +230,11 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 53, "metadata": { "ExecuteTime": { - "end_time": "2024-10-22T09:25:39.603454Z", - "start_time": "2024-10-22T09:25:39.598889Z" + "end_time": "2024-10-22T09:43:55.355431Z", + "start_time": "2024-10-22T09:43:55.333525Z" } }, "outputs": [ @@ -250,8 +242,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 2.66 ms, sys: 55 μs, total: 2.71 ms\n", - "Wall time: 2.77 ms\n" + "CPU times: user 1.37 ms, sys: 7 μs, total: 1.38 ms\n", + "Wall time: 1.42 ms\n" ] } ], @@ -273,18 +265,18 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 54, "metadata": { "ExecuteTime": { - "end_time": "2024-10-22T09:25:42.569050Z", - "start_time": "2024-10-22T09:25:42.507079Z" + "end_time": "2024-10-22T09:43:55.414551Z", + "start_time": "2024-10-22T09:43:55.354098Z" } }, "outputs": [ { "data": { "text/plain": "
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" 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" }, "metadata": {}, "output_type": "display_data" @@ -318,14 +310,23 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 55, "metadata": { "ExecuteTime": { - "end_time": "2024-10-22T09:30:50.489618Z", - "start_time": "2024-10-22T09:30:50.483390Z" + "end_time": "2024-10-22T09:43:55.415384Z", + "start_time": "2024-10-22T09:43:55.412871Z" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": "'\\n控制问题描述\\n'" + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "\"\"\"\n", "Control problem statement.\n", @@ -339,11 +340,11 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 56, "metadata": { "ExecuteTime": { - "end_time": "2024-10-22T09:30:50.962772Z", - "start_time": "2024-10-22T09:30:50.957952Z" + "end_time": "2024-10-22T09:43:55.419986Z", + "start_time": "2024-10-22T09:43:55.419039Z" } }, "outputs": [], @@ -388,11 +389,11 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 57, "metadata": { "ExecuteTime": { - "end_time": "2024-10-22T09:30:53.505536Z", - "start_time": "2024-10-22T09:30:53.502223Z" + "end_time": "2024-10-22T09:43:55.424811Z", + "start_time": "2024-10-22T09:43:55.422385Z" } }, "outputs": [ @@ -400,8 +401,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 3.48 ms, sys: 2.16 ms, total: 5.64 ms\n", - "Wall time: 4.17 ms\n" + "CPU times: user 1.81 ms, sys: 361 μs, total: 2.17 ms\n", + "Wall time: 576 μs\n" ] }, { @@ -452,18 +453,18 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 58, "metadata": { "ExecuteTime": { - "end_time": "2024-10-22T09:30:54.635354Z", - "start_time": "2024-10-22T09:30:54.569920Z" + "end_time": "2024-10-22T09:43:55.586059Z", + "start_time": "2024-10-22T09:43:55.425290Z" } }, "outputs": [ { "data": { "text/plain": "
", - "image/png": 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" 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" }, "metadata": {}, "output_type": "display_data" @@ -497,8 +498,13 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2024-10-22T09:43:55.586267Z", + "start_time": "2024-10-22T09:43:55.558478Z" + } + }, "outputs": [], "source": [] } diff --git a/notebooks/1.1-parametrized-path-curves.ipynb b/notebooks/1.1-parametrized-path-curves.ipynb index b99eb86..fb486b0 100644 --- a/notebooks/1.1-parametrized-path-curves.ipynb +++ b/notebooks/1.1-parametrized-path-curves.ipynb @@ -11,19 +11,31 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this notebook I try to reproduce the parmetrization of the track via curve-fitting like its done in Udacity MPC Course. " + "In this notebook I try to reproduce the parmetrization of the track via curve-fitting like its done in Udacity MPC Course. \n", + "在这篇笔记中,我试图通过曲线拟合来重现轨迹的参数化,就像在Udacity MPC课程中所做的那样。" ] }, { "cell_type": "code", - "execution_count": 10, - "metadata": {}, + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2024-10-23T04:21:58.444911Z", + "start_time": "2024-10-23T04:21:57.902473Z" + } + }, "outputs": [], "source": [ "import numpy as np\n", "from scipy.interpolate import interp1d\n", "\n", - "\n", + "# 函数 compute_path_from_wp 用于生成平滑的轨迹。\n", + "# 输入:start_xp 和 start_yp 分别是路径点的 x 和 y 坐标,step 是插值的步长。\n", + "# 作用:通过使用线性插值的方法,在每两个路径点之间生成一些中间点,使路径更加平滑。\n", + "# 细节:\n", + "# 计算每段路径的长度。\n", + "# 使用 interp1d 对每两个路径点进行线性插值,从而在每段路径之间生成更多的中间点。\n", + "# 最后返回平滑后的路径点集合。\n", "def compute_path_from_wp(start_xp, start_yp, step=0.1):\n", " final_xp = []\n", " final_yp = []\n", @@ -47,7 +59,13 @@ "\n", " return np.vstack((final_xp, final_yp))\n", "\n", - "\n", + "# 函数 get_nn_idx 用于找到车辆当前状态下,最接近的路径点索引。\n", + "# \n", + "# 输入:state 是车辆的当前位置和航向角信息,path 是轨迹点集合。\n", + "# 作用:找到车辆当前位置与轨迹的最近点,并根据路径点的方向矢量来决定目标点的位置。\n", + "# 细节:\n", + "# 计算车辆与路径点之间的欧氏距离,通过 np.argmin(dist) 找到最近的路径点索引。\n", + "# 然后根据路径点方向矢量,判断是否需要向前一个点继续行驶,最终返回目标路径点索引 target_idx。\n", "def get_nn_idx(state, path):\n", "\n", " dx = state[0] - path[0, :]\n", @@ -77,15 +95,20 @@ }, { "cell_type": "code", - "execution_count": 11, - "metadata": {}, + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2024-10-23T04:23:27.055937Z", + "start_time": "2024-10-23T04:23:27.047349Z" + } + }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/home/marcello/miniconda3/envs/jupyter/lib/python3.8/site-packages/IPython/core/interactiveshell.py:3331: RankWarning: Polyfit may be poorly conditioned\n", - " exec(code_obj, self.user_global_ns, self.user_ns)\n" + "/var/folders/hd/8kg_jtmd6svgg_sc384pbcdm0000gn/T/ipykernel_8828/1217459931.py:29: RankWarning: Polyfit may be poorly conditioned\n", + " coeff = np.polyfit(\n" ] } ], @@ -105,6 +128,7 @@ "lk_wp = track[:, nn_idx : nn_idx + LOOKAHED]\n", "\n", "# trasform lookahead waypoints to vehicle ref frame\n", + "# 转换前视路径点到车辆参考框架\n", "dx = lk_wp[0, :] - state[0]\n", "dy = lk_wp[1, :] - state[1]\n", "\n", @@ -116,6 +140,7 @@ ")\n", "\n", "# fit poly\n", + "# 拟合多项式\n", "coeff = np.polyfit(\n", " wp_vehicle_frame[0, :],\n", " wp_vehicle_frame[1, :],\n", @@ -154,22 +179,24 @@ " j = len(coeff)\n", " for k in range(j - 1):\n", " y += (j - k - 1) * coeff[k] * x ** (j - k - 2)\n", - " return y" + " return y\n" ] }, { "cell_type": "code", - "execution_count": 12, - "metadata": {}, + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2024-10-22T09:48:10.578934Z", + "start_time": "2024-10-22T09:48:10.573997Z" + } + }, "outputs": [ { "data": { - "text/plain": [ - "array([ 0.10275887, 0.03660033, -0.21750601, 0.03551043, -0.53861442,\n", - " -0.58083993])" - ] + "text/plain": "array([ 0.10275887, 0.03660033, -0.21750601, 0.03551043, -0.53861442,\n -0.58083993])" }, - "execution_count": 12, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -180,15 +207,66 @@ }, { "cell_type": "code", - "execution_count": 13, - "metadata": {}, + "execution_count": 9, "outputs": [ { "data": { - "image/png": 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" }, "metadata": {}, "output_type": "display_data" @@ -226,32 +304,40 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Error Formulation\n", + "## Error Formulation 误差公式\n", "\n", "So, the track can be represented by fitting a curve trough its waypoints, using the vehicle position as reference!\n", + "因此,可以通过拟合一条曲线穿过路径点来表示轨迹,并使用车辆位置作为参考!\n", "\n", "\n", "\n", "Recall A fitted cubic poly has the form:\n", + "回顾一下,拟合的三次多项式形式为:\n", "\n", "$\n", "f = K_0 * x^3 + K_1 * x^2 + K_2 * x + K_3\n", "$\n", "\n", "The derivative of a fitted cubic poly has the form:\n", + "拟合的三次多项式的导数形式为:\n", "\n", "$\n", "f' = 3.0 * K_0 * x^2 + 2.0 * K_1 * x + K_2\n", "$\n", "\n", "Then we can formulate\n", + "然后我们可以进行如下公式化\n", "\n", "* **crosstrack error** cte: desired y-position - y-position of vehicle -> this is the value of the fitted polynomial\n", + "* **横向误差** cte:期望的y位置 - 车辆的y位置 -> 这是拟合多项式的值\n", "\n", "* **heading error** epsi: desired heading - heading of vehicle -> is the inclination of tangent to the fitted polynomial\n", + "* **航向误差** epsi:期望航向 - 车辆航向 -> 是拟合多项式的切线的倾斜\n", "\n", "Becouse the reference is centered on vehicle the eqation are simplified!\n", "Then using the fitted polynomial representation in vehicle frame the errors can be easily computed as:\n", + "因为参考点是以车辆为中心的,方程得到了简化!\n", + "因此,使用车辆坐标系中的拟合多项式表示,可以很容易地计算误差:\n", "\n", "$\n", "cte = f(px) \\\\\n", @@ -264,7 +350,8 @@ "metadata": {}, "source": [ "### In Practice:\n", - "I use a **convex** mpc so non-linearities are not allowed (in Udacity they use a general-purpose nonlinear solver) -> so this solution does not really work well for my case..." + "I use a **convex** mpc so non-linearities are not allowed (in Udacity they use a general-purpose nonlinear solver) -> so this solution does not really work well for my case...\n", + "我使用了一个凸优化的 MPC,因此不允许非线性项(在 Udacity 的课程中,他们使用的是通用的非线性求解器) -> 因此这个解决方案对于我的情况并不太适用" ] }, { @@ -276,38 +363,156 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2024-10-22T09:59:44.820293Z", + "start_time": "2024-10-22T09:59:44.813407Z" + } + }, "outputs": [], "source": [ - "def spline_planning(qs, qf, ts, tf, dqs=0.0, dqf=0.0, ddqs=0.0, ddqf=0.0):\n", + "# 五次样条曲线\n", + "# def spline_planning(qs, qf, ts, tf, dqs=0.0, dqf=0.0, ddqs=0.0, ddqf=0.0):\n", + "# \n", + "# bc = np.array([ys, dys, ddys, yf, dyf, ddyf]).T\n", + "# \n", + "# C = np.array(\n", + "# [\n", + "# [1, xs, xs**2, xs**3, xs**4, xs**5], # f(xs)=ys\n", + "# [0, 1, 2 * xs**1, 3 * xs**2, 4 * xs**3, 5**xs ^ 4], # df(xs)=dys\n", + "# [0, 0, 1, 6 * xs**1, 12 * xs**2, 20**xs ^ 3], # ddf(xs)=ddys\n", + "# [1, xf, xf**2, xf**3, xf**4, xf**5], # f(xf)=yf\n", + "# [0, 1, 2 * xf**1, 3 * xf**2, 4 * xf**3, 5**xf ^ 4], # df(xf)=dyf\n", + "# [0, 0, 1, 6 * xf**1, 12 * xf**2, 20**xf ^ 3],\n", + "# ]\n", + "# ) # ddf(xf)=ddyf\n", + "# \n", + "# # To compute the polynomial coefficients we solve:\n", + "# # Ax = B.\n", + "# # Matrices A and B must have the same number of rows\n", + "# a = np.linalg.lstsq(C, bc)[0]\n", + "# return a" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "outputs": [], + "source": [ + "import numpy as np\n", "\n", - " bc = np.array([ys, dys, ddys, yf, dyf, ddyf]).T\n", + "def spline_planning(xs, xf, ys, yf, dys=0.0, dyf=0.0, ddys=0.0, ddyf=0.0):\n", + " \"\"\"\n", + " 计算五次多项式的系数,满足边界条件。\n", "\n", + " 参数:\n", + " - xs: 初始位置 x\n", + " - xf: 最终位置 x\n", + " - ys: 初始位置 y\n", + " - yf: 最终位置 y\n", + " - dys: 初始速度 (默认值为 0)\n", + " - dyf: 最终速度 (默认值为 0)\n", + " - ddys: 初始加速度 (默认值为 0)\n", + " - ddyf: 最终加速度 (默认值为 0)\n", + "\n", + " 返回:\n", + " - a: 五次多项式的系数\n", + " \"\"\"\n", + " # 定义边界条件矩阵 B\n", + " bc = np.array([ys, dys, ddys, yf, dyf, ddyf])\n", + "\n", + " # 定义系数矩阵 A\n", " C = np.array(\n", " [\n", " [1, xs, xs**2, xs**3, xs**4, xs**5], # f(xs)=ys\n", - " [0, 1, 2 * xs**1, 3 * xs**2, 4 * xs**3, 5**xs ^ 4], # df(xs)=dys\n", - " [0, 0, 1, 6 * xs**1, 12 * xs**2, 20**xs ^ 3], # ddf(xs)=ddys\n", + " [0, 1, 2 * xs, 3 * xs**2, 4 * xs**3, 5 * xs**4], # df(xs)=dys\n", + " [0, 0, 2, 6 * xs, 12 * xs**2, 20 * xs**3], # ddf(xs)=ddys\n", " [1, xf, xf**2, xf**3, xf**4, xf**5], # f(xf)=yf\n", - " [0, 1, 2 * xf**1, 3 * xf**2, 4 * xf**3, 5**xf ^ 4], # df(xf)=dyf\n", - " [0, 0, 1, 6 * xf**1, 12 * xf**2, 20**xf ^ 3],\n", + " [0, 1, 2 * xf, 3 * xf**2, 4 * xf**3, 5 * xf**4], # df(xf)=dyf\n", + " [0, 0, 2, 6 * xf, 12 * xf**2, 20 * xf**3], # ddf(xf)=ddyf\n", " ]\n", - " ) # ddf(xf)=ddyf\n", + " )\n", "\n", - " # To compute the polynomial coefficients we solve:\n", - " # Ax = B.\n", - " # Matrices A and B must have the same number of rows\n", - " a = np.linalg.lstsq(C, bc)[0]\n", + " # 计算多项式系数\n", + " a = np.linalg.solve(C, bc) # 使用线性方程组求解 A * a = B\n", " return a" - ] + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2024-10-22T10:01:56.052349Z", + "start_time": "2024-10-22T10:01:56.047486Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 11, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# 初始和最终位置及其条件\n", + "xs = 0 # 初始位置\n", + "xf = 10 # 最终位置\n", + "ys = 0 # 初始位置 y\n", + "yf = 5 # 最终位置 y\n", + "dys = 1.0 # 初始速度\n", + "dyf = 0.5 # 最终速度\n", + "\n", + "# 计算多项式系数\n", + "coefficients = spline_planning(xs, xf, ys, yf, dys, dyf)\n", + "\n", + "# 使用计算出的系数生成样条曲线\n", + "x_vals = np.linspace(xs, xf, 100)\n", + "y_vals = [\n", + " coefficients[0] * x**5 + coefficients[1] * x**4 + coefficients[2] * x**3 + coefficients[3] * x**2 + coefficients[4] * x + coefficients[5]\n", + " for x in x_vals\n", + "]\n", + "\n", + "# 绘制样条曲线\n", + "plt.figure(figsize=(10, 6))\n", + "plt.plot(x_vals, y_vals, label='Splined Path')\n", + "plt.xlabel('X position')\n", + "plt.ylabel('Y position')\n", + "plt.title('5th Order Spline Path')\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2024-10-22T10:02:42.157868Z", + "start_time": "2024-10-22T10:02:42.097737Z" + } + } + }, + { + "cell_type": "code", + "execution_count": null, + "outputs": [], + "source": [], + "metadata": { + "collapsed": false + } } ], "metadata": { "kernelspec": { - "display_name": "Python [conda env:.conda-jupyter] *", + "name": "python3", "language": "python", - "name": "conda-env-.conda-jupyter-py" + "display_name": "Python 3 (ipykernel)" }, "language_info": { "codemirror_mode": {