tactile_ergodic_control.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "    Copyright (c) 2024 Idiap Research Institute, http://www.idiap.ch/\n",
    "    Written by Cem Bilaloglu <cem.bilaloglu@idiap.ch>\n",
    "\n",
    "    This file is part of tactileErgodicExploration.\n",
    "\n",
    "    tactileErgodicExploration is free software: you can redistribute it and/or modify\n",
    "    it under the terms of the GNU General Public License version 3 as\n",
    "    published by the Free Software Foundation.\n",
    "\n",
    "    tactileErgodicExploration is distributed in the hope that it will be useful,\n",
    "    but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
    "    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n",
    "    GNU General Public License for more details.\n",
    "\n",
    "    You should have received a copy of the GNU General Public License\n",
    "    along with tactileErgodicExploration. If not, see <http://www.gnu.org/licenses/>.\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "np.set_printoptions(formatter={\"float\": lambda x: \"{0:0.3e}\".format(x)})\n",
    "\n",
    "import scipy.sparse.linalg as sla\n",
    "\n",
    "import robust_laplacian\n",
    "import time\n",
    "\n",
    "\n",
    "from plotting_utils import *\n",
    "from pointcloud_utils import *\n",
    "from virtual_agents import FirstOrderAgent, SecondOrderAgent\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "point_cloud_dir = \"point_clouds/\"\n",
    "data_dir = \"data/\"  # for saving the experiment data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspired from the work \n",
    "\n",
    "Heat Equation Driven Area Coverage (HEDAC):\n",
    "\n",
    "Ivić, S., Crnković, B., & Mezić, I. (2017). Ergodicity-Based Cooperative Multiagent Area Coverage via a Potential Field. IEEE Transactions on Cybernetics, 47(8), 1983–1993. https://doi.org/10.1109/TCYB.2016.2634400\n",
    "\n",
    "Spectral acceleration using eigenbasis:\n",
    "\n",
    "Sharp, N., Attaiki, S., Crane, K., & Ovsjanikov, M. (2022). DiffusionNet: Discretization Agnostic Learning on Surfaces. ACM Transactions on Graphics, 41(3), 27:1-27:16. https://doi.org/10.1145/3507905\n",
    "\n",
    "Heat method: \n",
    "\n",
    "Crane, K., Weischedel, C., & Wardetzky, M. (2013). Geodesics in heat: A new approach to computing distance based on heat flow. ACM Transactions on Graphics, 32(5), 152:1-152:11. https://doi.org/10.1145/2516971.2516977\n",
    "\n",
    "Discrete Laplacian of the point cloud:\n",
    "\n",
    "Sharp, N., & Crane, K. (2020). A Laplacian for Nonmanifold Triangle Meshes. \n",
    "Computer Graphics Forum, 39(5), 69–80. https://doi.org/10.1111/cgf.14069"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Select the object to explore\n",
    "\n",
    "# obj_name = \"bun270_X\" # Stanford bunny with X projected as the target\n",
    "obj_name = \"plate_shapes\"  # random IKEA plate with hand-drawn shapes\n",
    "# obj_name = \"cup_X\" # random cup that we scanned with X projected as the target\n",
    "\n",
    "experiment_index = 2  # choose which initial position to use from x0_arr_10.npz\n",
    "\n",
    "class param:\n",
    "    pass  # c-style struct\n",
    "\n",
    "\n",
    "param.timesteps = 500  # total simulation timesteps\n",
    "\n",
    "# tuning: [1,100] increasing alpha result in global exploration closer to SS\n",
    "# decreasing alpha result in local exploration lower limited\n",
    "param.alpha = 100\n",
    "# tuning: [25, 300] increasing the value bring more flexibility in selecting\n",
    "# the pairing alpha. Lowering the value results in faster computation\n",
    "param.nb_eigen = 200\n",
    "\n",
    "# eigen corresponds to using Laplacian eigenbasis and using spectral acceleration\n",
    "# when integrating the diffusion (heat) equation\n",
    "# exact corresponds to using implicit time stepping for integrating\n",
    "param.method = \"eigen\"\n",
    "# param.method = \"exact\"\n",
    "\n",
    "# voxel filter size for downsampling the point cloud\n",
    "param.voxel_size = 0.003\n",
    "# radius for the agent footprint that'd be used in coverage\n",
    "param.agent_radius = 2.5 * param.voxel_size # for the cup and the bunny\n",
    "# param.agent_radius = 5 * param.voxel_size  # for the plate\n",
    "# define speed and acceleration in terms of voxel size\n",
    "param.max_velocity = 1 * param.voxel_size\n",
    "param.max_acceleration = 1 * param.max_velocity\n",
    "\n",
    "# tuning: doesn't have much effect on exploration so we keep it at 1\n",
    "param.source_strength = 1\n",
    "\n",
    "# number of iterations for the non-stationary heat equation\n",
    "# we kept it at 1 in this work to decrease the computational cost and\n",
    "# it was enough for the exploration task\n",
    "param.ndt = 1\n",
    "# max. num. of neighbors to consider for computing the neighbors in agent radius\n",
    "param.nb_max_neighbors = 500\n",
    "# num. of neighbors to consider for tangent space and gradient computation\n",
    "param.nb_minimum_neighbors = 20\n",
    "# num. of neighbors to consider for implicitly determining the boundary\n",
    "# setting this lower in bunny resutls in right ear considered as a seperate body\n",
    "# setting this higher in bunny results in the right ear being considered as part\n",
    "# of the main body\n",
    "param.nb_boundary_neighbors = 40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original Point cloud with 7876 points is downsampled with voxel size 0.003\n",
      " resulted in 6228 points\n",
      "dt: 6.668e-04, h: 2.582e-03, s: 3.000e-03\n"
     ]
    }
   ],
   "source": [
    "# Select the object and load the point cloud\n",
    "# ==========================================\n",
    "filename = f\"{point_cloud_dir}{obj_name}.ply\"\n",
    "pcloud = process_point_cloud(filename, param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Process finished --- 1.163e-01 seconds ---\n"
     ]
    }
   ],
   "source": [
    "# Get the discrete Laplacian on the point cloud\n",
    "# =============================================\n",
    "\"\"\"\n",
    "Sharp, N., & Crane, K. (2020). A Laplacian for Nonmanifold Triangle Meshes. \n",
    "Computer Graphics Forum, 39(5), 69–80. https://doi.org/10.1111/cgf.14069\n",
    "compute the Laplacian of the point cloud\n",
    "\"\"\"\n",
    "start_time = time.time()\n",
    "n = 1  # number of iterations !1 only if we want to measure the time complexity\n",
    "for _ in range(n):  # only for measuring the time complexity\n",
    "    C, M = robust_laplacian.point_cloud_laplacian(\n",
    "        pcloud.vertices, n_neighbors=param.nb_boundary_neighbors\n",
    "    )\n",
    "print(f\"Process finished --- {((time.time() - start_time)/n):.3e} seconds ---\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to use other methods for solving the heat equation, but here we use Laplacian eigengunctions.\n",
    "\n",
    "$$L\\phi_i=\\lambda_iM\\phi_i$$\n",
    "\n",
    "$\\lambda_i$ corresponding to first $k$ smallest eigenvalues and $\\phi_i$ is the i'th eigenvector , $M$ is the mass matrix and $L$ is weak laplacian then heat equation approximation becomes @sharpDiffusionNetDiscretizationAgnostic2022\n",
    "\n",
    "$$h_t(u)=\\Phi \\left[\n",
    "    {\\begin{array}{c}\n",
    "        e^{-\\lambda_1 t}\\\\\n",
    "        e^{-\\lambda_2 t}\\\\\n",
    "\t\t\\vdots\n",
    "    \\end{array}}\n",
    "\\right]\n",
    "\\odot (\\Phi^TMu)\n",
    "$$\n",
    "\n",
    "right side of Hadamard Product is spectral weights, left side of Hadamard Product is projecting back to vertices\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First 5 eigenvalues: [-5.774e-13 2.205e+02 2.287e+02 6.219e+02 6.290e+02]\n",
      "Process finished in --- 2.472e+00 seconds ---\n"
     ]
    }
   ],
   "source": [
    "# Preprocessing step for solving diffusion\n",
    "# only needs to be done once the point cloud changes\n",
    "# ================================================================\n",
    "start_time = time.time()\n",
    "n = 1  # number of iterations !1 only if we want to measure the time complexity\n",
    "for _ in range(n):  # only for measuring the time complexity\n",
    "    if param.method == \"exact\":\n",
    "        A_inv = sla.inv(M + pcloud.dt * C)\n",
    "        A_invM = A_inv @ M\n",
    "    elif param.method == \"eigen\":\n",
    "        # Laplacian eigenfunctions\n",
    "        # compute the eigenvalue decomposition of Laplace-Beltrami\n",
    "        evals, evecs = sla.eigsh(C, param.nb_eigen, M, sigma=1e-12)\n",
    "        Phi = evecs\n",
    "        exp_vector = np.zeros(param.nb_eigen)\n",
    "        for i in range(param.nb_eigen):\n",
    "            exp_vector[i] = np.exp(-evals[i] * pcloud.dt)\n",
    "        first_term = Phi @ exp_vector\n",
    "        PhiT_M = Phi.T @ M\n",
    "        print(f\"First 5 eigenvalues: {(evals[:5])}\")\n",
    "print(f\"Process finished in --- {((time.time() - start_time)/n):.3e} seconds ---\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Process finished --- 0.006429910659790039 seconds ---\n"
     ]
    }
   ],
   "source": [
    "# Integration step for solving diffusion\n",
    "# called at each timestep during the runtime\n",
    "# ================================================================\n",
    "\"\"\"\n",
    "Spectral acceleration using eigenbasis:\n",
    "Sharp, N., Attaiki, S., Crane, K., & Ovsjanikov, M. (2022). \n",
    "DiffusionNet: Discretization Agnostic Learning on Surfaces. \n",
    "ACM Transactions on Graphics, 41(3), 27:1-27:16. https://doi.org/10.1145/3507905\n",
    "\"\"\"\n",
    "start_time = time.time()\n",
    "n = 1  # number of iterations !1 only if we want to measure the time complexity\n",
    "for _ in range(n):  # only for measuring the time complexity\n",
    "    if param.method == \"exact\":\n",
    "        ut = A_invM @ pcloud.u0\n",
    "    elif param.method == \"eigen\":\n",
    "        ut = pcloud.u0\n",
    "        second_term = PhiT_M @ ut\n",
    "        third_term = exp_vector * second_term\n",
    "        ut = Phi @ third_term\n",
    "print(f\"Process finished --- {(time.time() - start_time)/n} seconds ---\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "FigureWidget({\n",
       "    'data': [{'line': {'width': 0.1},\n",
       "              'marker': {'color': 'rgb(0,255,0)', 'size': 8},\n",
       "              'name': 'Agent',\n",
       "              'type': 'scatter3d',\n",
       "              'uid': 'e4342c4b-15ca-4f46-91a9-81b8013aaf85',\n",
       "              'x': [0.5957466661930084],\n",
       "              'y': [0.3105558007955551],\n",
       "              'z': [0.08647464960813522]},\n",
       "             {'marker': {'color': array([0.000e+00, 0.000e+00, 0.000e+00, ..., 0.000e+00, 0.000e+00, 2.550e+02]),\n",
       "                         'colorscale': [[0.0, 'rgb(0,0,255)'], [1.0,\n",
       "                                        'rgb(255,0,0)']],\n",
       "                         'opacity': 1,\n",
       "                         'size': 1},\n",
       "              'mode': 'markers',\n",
       "              'name': 'Point Cloud',\n",
       "              'type': 'scatter3d',\n",
       "              'uid': '46916c79-6b4d-4bb8-af4e-aa0dba862a45',\n",
       "              'x': array([5.143e-01, 5.307e-01, 5.237e-01, ..., 4.702e-01, 5.210e-01, 4.641e-01]),\n",
       "              'y': array([4.150e-01, 4.125e-01, 4.124e-01, ..., 3.833e-01, 3.128e-01, 2.846e-01]),\n",
       "              'z': array([1.092e-01, 1.091e-01, 1.089e-01, ..., 8.435e-02, 7.508e-02, 7.177e-02])}],\n",
       "    'layout': {'coloraxis': {'showscale': True},\n",
       "               'scene': {'aspectmode': 'data',\n",
       "                         'camera': {'center': {'x': 0, 'y': 0, 'z': 0},\n",
       "                                    'eye': {'x': 0.0, 'y': 0.0, 'z': 2.0},\n",
       "                                    'up': {'x': 0, 'y': 1, 'z': 0}},\n",
       "                         'xaxis': {'visible': False},\n",
       "                         'yaxis': {'visible': False},\n",
       "                         'zaxis': {'visible': False}},\n",
       "               'showlegend': True,\n",
       "               'template': '...'}\n",
       "})"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  Initialize the agent and visualize the initial position and the point cloud\n",
    "# ===============================\n",
    "nb_experiments = 10\n",
    "\n",
    "x0_arr = np.load(f\"{data_dir}{obj_name}/x0_arr_{nb_experiments}.npz\")[\"x0_arr\"]\n",
    "# agent = FirstOrderAgent(\n",
    "#     x=np.zeros(3), dim_t=param.timesteps, max_velocity=param.max_velocity\n",
    "# )\n",
    "\n",
    "agent = SecondOrderAgent(\n",
    "    x=np.zeros(3), dim_t=param.timesteps, max_velocity=param.max_velocity,max_acceleration=param.max_acceleration*2\n",
    ")\n",
    "agent.x = x0_arr[experiment_index - 1, :]\n",
    "agent.radius = param.agent_radius\n",
    "\n",
    "plots = []\n",
    "# visualize the agents' initial position\n",
    "x = agent.x\n",
    "scatter = go.Scatter3d(\n",
    "    x=[x[0]],\n",
    "    y=[x[1]],\n",
    "    z=[x[2]],\n",
    "    name=\"Agent\",\n",
    "    marker=dict(\n",
    "        size=8,\n",
    "        color=\"rgb(0,255,0)\",\n",
    "    ),\n",
    "    line=dict(width=0.1),\n",
    ")\n",
    "plots.append(scatter)\n",
    "visualize_point_cloud(pcloud.vertices, colors=pcloud.u0, plots=plots, is_show_plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hedac(agent, param, pcloud):\n",
    "    \"\"\"\n",
    "    Perform HEDAC exploration using the agent and the point cloud.\n",
    "\n",
    "    Original implementation on a 2-D rectangular grid by Ivic et al.\n",
    "    Ivić, S., Crnković, B., & Mezić, I. (2017). Ergodicity-Based Cooperative \n",
    "    Multiagent Area Coverage via a Potential Field. IEEE Transactions on \n",
    "    Cybernetics, 47(8), 1983–1993. https://doi.org/10.1109/TCYB.2016.2634400\n",
    "\n",
    "    Args:\n",
    "        agent (Agent): The agent object representing the virtual exploration agent.\n",
    "        param (Parameters): The parameters for the HEDAC algorithm.\n",
    "        pcloud (PointCloud): The point cloud object representing the exploration\n",
    "             domain and target\n",
    "\n",
    "    Returns:\n",
    "        tuple: A tuple containing the agent's trajectory, heat array,\n",
    "            coverage array, and time array.\n",
    "    \"\"\"\n",
    "    coverage_arr = np.zeros((len(pcloud.vertices), param.timesteps))\n",
    "    heat_arr = np.zeros_like(coverage_arr)\n",
    "\n",
    "    # we normalize the goal because it should be a probability distribution\n",
    "    goal_density = normalize_mat(pcloud.u0)\n",
    "\n",
    "    # we keep this and add coverage at each timestep on top of it\n",
    "    coverage = np.zeros_like(goal_density)\n",
    "    ut = np.array(goal_density)\n",
    "\n",
    "    # for keeping the runtime of each timestep\n",
    "    time_arr = np.zeros(param.timesteps)\n",
    "\n",
    "    agent.t = 0  # reset the agent's time\n",
    "    # do absolute minimum inside the main loop\n",
    "    for t in range(param.timesteps):\n",
    "        dists, neighbor_ids, neighbor_coords = get_pcloud_neighbors(\n",
    "            pcloud.pcd_tree,\n",
    "            pcloud.vertices,\n",
    "            np.copy(agent.x),\n",
    "            agent.radius,\n",
    "            param.nb_max_neighbors,\n",
    "            param.nb_minimum_neighbors,\n",
    "        )\n",
    "\n",
    "        # Compute the coverage using RBF kernel\n",
    "        kernel_vals = np.exp(-(1 / agent.radius) * dists**2)\n",
    "        coverage[neighbor_ids] += kernel_vals\n",
    "\n",
    "        neighbor_ids = neighbor_ids[: param.nb_minimum_neighbors]\n",
    "        dists = dists[: param.nb_minimum_neighbors]\n",
    "        neighbor_coords = pcloud.vertices[neighbor_ids, :]\n",
    "        coverage_density = normalize_mat(coverage)\n",
    "        source = np.maximum(goal_density - coverage_density, 0) ** 2\n",
    "        source = normalize_mat(source)\n",
    "\n",
    "        start_time = time.time()\n",
    "        # Integrate the heat takes around ~ 2ms\n",
    "        if param.method == \"eigen\":\n",
    "            second_term = PhiT_M @ ut\n",
    "            third_term = exp_vector * second_term\n",
    "            ut = Phi @ third_term\n",
    "        elif param.method == \"exact\":\n",
    "            ut = A_invM @ source\n",
    "\n",
    "        time_arr[t] = time.time() - start_time\n",
    "\n",
    "        ut += param.source_strength * source\n",
    "        (\n",
    "            agent.x,\n",
    "            gradient,\n",
    "            _,\n",
    "        ) = get_gradient(\n",
    "            np.copy(agent.x),\n",
    "            neighbor_coords,\n",
    "            neighbor_ids,\n",
    "            ut,\n",
    "        )\n",
    "        agent.update(gradient)\n",
    "\n",
    "        coverage_arr[..., t] = coverage\n",
    "        heat_arr[..., t] = np.copy(ut)\n",
    "    return agent.x_arr, heat_arr, coverage_arr, time_arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Average Frequency: 1462.209470553989 Hz ---\n",
      "255.0053032062016\n"
     ]
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    "# Run and visualize a single experiment\n",
    "# =================================================\n",
    "x_arr, heat_arr, coverage_arr, time_arr = hedac(agent, param, pcloud)\n",
    "print(f\"Average Frequency: {1/np.mean(time_arr)} Hz ---\")\n",
    "val = 255-(normalize_mat(pcloud.u0)-normalize_mat(coverage_arr[:, 50]))\n",
    "print(np.max(val))\n",
    "# plots = visualize_point_cloud(\n",
    "#     pcloud.vertices[val>50], colors=val[val>50], is_show_plot=False, point_size=3\n",
    "# )\n",
    "plots = visualize_point_cloud(\n",
    "    pcloud.vertices, \n",
    "    colors=heat_arr[...,0], \n",
    "    # colors=heat_arr[...,-1], \n",
    "    is_show_plot=False, point_size=2\n",
    ")\n",
    "fig = visualize_trajectory(x_arr[:,:], plots, color=\"black\")\n",
    "\n",
    "fig.show()\n",
    "\n",
    "# Compute and plot the coverage error\n",
    "# ==========================\n",
    "normalized_residual = compute_coverage_residual(heat_arr[..., 0], coverage_arr)\n",
    "\n",
    "# plot the coverage error\n",
    "fig = go.Figure()\n",
    "# add traces for each error\n",
    "fig.add_trace(\n",
    "    go.Scatter(y=normalized_residual, mode=\"lines\", name=f\"Experiment\")\n",
    ")\n",
    "fig.update_layout(\n",
    "    xaxis_title=\"Timesteps\",\n",
    "    yaxis_title=\"Normalized Ergodic Metric\",\n",
    "    title=\"Normalized Coverage Residual\",\n",
    ")\n",
    "fig.show()"
   ]
  },
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