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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,172 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "import matplotlib.pyplot as plt" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "def latex_label(text):\n", | ||
| " \"\"\"\n", | ||
| " Converts regular text to a LaTeX-compatible label, handling LaTeX math mode correctly.\n", | ||
| " \"\"\"\n", | ||
| " # Split text into math ($...$) and non-math segments\n", | ||
| " parts = re.split(r'(\\$.+?\\$)', text)\n", | ||
| " formatted_parts = []\n", | ||
| "\n", | ||
| " for part in parts:\n", | ||
| " if part.startswith('$') and part.endswith('$'):\n", | ||
| " # It's a math mode segment, add it as is\n", | ||
| " formatted_parts.append(part)\n", | ||
| " else:\n", | ||
| " # Replace spaces with ~ and wrap non-math text with \\mathrm{}\n", | ||
| " clean_fragment = part.replace(' ', '~')\n", | ||
| " if clean_fragment:\n", | ||
| " latex_command = r\"\\mathrm{\" + clean_fragment + \"}\"\n", | ||
| " formatted_parts.append(f'${latex_command}$')\n", | ||
| " # formatted_parts.append(f'${r\"\\mathrm{\" + clean_fragment + \"}\"}$')\n", | ||
| "\n", | ||
| " return ''.join(formatted_parts)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "def plot_mpc_trajectory(ts, z_ref, z_mpc, z_true, u_mpc, N, plot_controls=True):\n", | ||
| " \"\"\"\n", | ||
| " Plot the MPC trajectory for 2D or 3D data.\n", | ||
| " \"\"\"\n", | ||
| " # Determine the dimension (2D or 3D)\n", | ||
| " dim = z_true.shape[1]\n", | ||
| "\n", | ||
| " # Set up the plotting environment\n", | ||
| " if plot_controls:\n", | ||
| " if dim == 2:\n", | ||
| " fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n", | ||
| " else:\n", | ||
| " fig = plt.figure(figsize=(12, 5))\n", | ||
| " ax = [fig.add_subplot(1, 2, 1, projection='3d'), fig.add_subplot(1, 2, 2)]\n", | ||
| " else:\n", | ||
| " if dim == 2:\n", | ||
| " fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n", | ||
| " ax = [ax]\n", | ||
| " else:\n", | ||
| " fig = plt.figure(figsize=(6, 5))\n", | ||
| " ax = [fig.add_subplot(1, 1, 1, projection='3d')]\n", | ||
| "\n", | ||
| " # Plot the MPC trajectories\n", | ||
| " for t_idx in range(len(ts) - 2 * N):\n", | ||
| " if dim == 2:\n", | ||
| " ax[0].plot(z_mpc[t_idx, :, 0], z_mpc[t_idx, :, 1], '--*', color='k', markersize=3,\n", | ||
| " label=latex_label('MPC') if t_idx == 0 else None)\n", | ||
| " else:\n", | ||
| " ax[0].plot3D(z_mpc[t_idx, :, 0], z_mpc[t_idx, :, 1], z_mpc[t_idx, :, 2], '--*', color='k', markersize=3,\n", | ||
| " label=latex_label('MPC') if t_idx == 0 else None)\n", | ||
| "\n", | ||
| " # Plot the true trajectory, start point, and reference\n", | ||
| " if dim == 2:\n", | ||
| " ax[0].plot(z_true[:-N, 0], z_true[:-N, 1], '-o', label=latex_label('True'), markersize=3)\n", | ||
| " ax[0].plot(z_true[0, 0], z_true[0, 1], 'ro', label=latex_label('Start'), markersize=6)\n", | ||
| " ax[0].plot(z_ref[:-N, 0], z_ref[:-N, 1], 'y--', label=latex_label('Reference'))\n", | ||
| " ax[0].set_xlabel(latex_label('X [m]'))\n", | ||
| " ax[0].set_ylabel(latex_label('Y [m]'))\n", | ||
| " ax[0].axis('equal')\n", | ||
| " else:\n", | ||
| " ax[0].plot3D(z_true[:-N, 0], z_true[:-N, 1], z_true[:-N, 2], '-o', label=latex_label('True'), markersize=3)\n", | ||
| " ax[0].scatter(z_true[0, 0], z_true[0, 1], z_true[0, 2], color='r', label=latex_label('Start'), s=36)\n", | ||
| " ax[0].plot3D(z_ref[:-N, 0], z_ref[:-N, 1], z_ref[:-N, 2], 'y--', label=latex_label('Reference'))\n", | ||
| " ax[0].set_xlabel(latex_label('X [m]'))\n", | ||
| " ax[0].set_ylabel(latex_label('Y [m]'))\n", | ||
| " ax[0].set_zlabel(latex_label('Z [m]'))\n", | ||
| " ax[0].set_box_aspect([1, 1, 1])\n", | ||
| " ax[0].view_init(elev=115, azim=-115, roll=-25)\n", | ||
| " ax[0].legend()\n", | ||
| "\n", | ||
| " # Plot the control inputs\n", | ||
| " if plot_controls:\n", | ||
| " for u_idx in range(u_mpc.shape[-1]):\n", | ||
| " ax[1].plot(ts, u_mpc[:, 0, u_idx], label=latex_label(f'u_{u_idx+1}(t)'))\n", | ||
| " ax[1].set_xlabel(latex_label('t [s]'))\n", | ||
| " ax[1].set_ylabel(latex_label('U'))\n", | ||
| " ax[1].legend()\n", | ||
| " plt.tight_layout()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "def generate_ref_trajectory(T, dt, traj_type, size):\n", | ||
| " \"\"\"\n", | ||
| " Generate a 3D reference trajectory for the system to track.\n", | ||
| " \"\"\"\n", | ||
| " t = np.linspace(0, T, int(T/dt))\n", | ||
| " z_ref = np.zeros((len(t), 3))\n", | ||
| "\n", | ||
| " # Note that y is up\n", | ||
| " if traj_type == 'circle':\n", | ||
| " z_ref[:, 0] = size * (np.cos(2 * np.pi / T * t) - 1)\n", | ||
| " z_ref[:, 1] = size / 2 * np.ones_like(t)\n", | ||
| " z_ref[:, 2] = size * np.sin(2 * np.pi / T * t)\n", | ||
| " elif traj_type == 'figure_eight':\n", | ||
| " z_ref[:, 0] = size * np.sin(2 * np.pi / T * t)\n", | ||
| " z_ref[:, 1] = size / 2 * np.ones_like(t)\n", | ||
| " z_ref[:, 2] = size * np.sin(4 * np.pi / T * t)\n", | ||
| " elif traj_type == 'periodic_line':\n", | ||
| " m = -1\n", | ||
| " z_ref[:, 0] = size * np.sin(2 * np.pi / T * t)\n", | ||
| " z_ref[:, 1] = np.zeros_like(t)\n", | ||
| " z_ref[:, 2] = m * size * np.sin(2 * np.pi / T * t)\n", | ||
| " elif traj_type == 'arc':\n", | ||
| " m = 1\n", | ||
| " l_trunk = 0.35\n", | ||
| " R = l_trunk / 2\n", | ||
| " z_ref[:, 0] = size * np.sin(2 * np.pi / T * t)\n", | ||
| " z_ref[:, 2] = m * size * np.sin(2 * np.pi / T * t)\n", | ||
| " z_ref[:, 1] = R - np.sqrt(R**2 - z_ref[:, 0]**2 - z_ref[:, 0]**2)\n", | ||
| " else:\n", | ||
| " raise ValueError('Invalid trajectory type: ' + traj_type + '. Valid options are: \"circle\" or \"figure_eight\".')\n", | ||
| " return z_ref, t" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# Generate reference trajectory (check that it's the same as used in mpc_initializer_node.py)\n", | ||
| "z_ref, t = generate_ref_trajectory(10, 0.01, 'figure_eight', 0.1)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "language_info": { | ||
| "name": "python" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 2 | ||
| } |
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