ep1.ipynb

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  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# Lista 02\n",
    "\n",
    "## Autores\n",
    "Lucas Hattori Costa: 10335847\n",
    " \n",
    "Bruno Scaglione: 10335812"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0350bd65-be68-4a47-8a5f-568d03fe60b8",
   "metadata": {},
   "source": [
    "## Libraries and data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "153a83d4-9a42-49d6-9091-40b57ec2b6f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import numpy.linalg as LA\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data = np.genfromtxt('./data/valores.csv', delimiter=',')\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88db41c5-ded6-4a2e-ba30-041c934b4a2b",
   "metadata": {},
   "source": [
    "## Global parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cecbaf56-4c68-4c5b-9df7-dbd61dbf53f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "l = 0.3\n",
    "h = 0.5\n",
    "dt = 0.25\n",
    "t_end = 250\n",
    "n_steps = int(t_end/dt)\n",
    "init_sigma = np.zeros((5, 5))\n",
    "init_sigma[3,3] = 10\n",
    "init_sigma[4,4] = 10\n",
    "init_state = np.zeros((5,))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c95f854-27f7-4ffc-886b-6eff1a135976",
   "metadata": {},
   "source": [
    "## Auxiliary Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4d6f90b6-63a2-4126-827f-201c45e13527",
   "metadata": {},
   "outputs": [],
   "source": [
    "def jacobian(X: np.array, u: np.array, which: str) -> np.array:\n",
    "    '''\n",
    "    Calculados analiticamente.\n",
    "    '''    \n",
    "    if which=='A':\n",
    "        ddx = (-u[0]*np.sin(X[2])*dt)\n",
    "        ddy = (u[0]*np.cos(X[2])*dt)\n",
    "        J = [\n",
    "            [1, 0, ddx, 0, 0],\n",
    "            [0, 1, ddy, 0, 0],\n",
    "            [0, 0, 1, 0, 0],\n",
    "            [0, 0, 0, 1, 0],\n",
    "            [0, 0, 0, 0, 1]\n",
    "        ]\n",
    "    elif which=='C':\n",
    "        sin = np.sin(X[2])\n",
    "        cos = np.cos(X[2])\n",
    "        J = [\n",
    "            [X[0]/np.sqrt(X[0]**2 + X[1]**2 + h**2), X[1]/np.sqrt(X[0]**2 + X[1]**2 + h**2), 0, 0, 0],\n",
    "            [0,      0,     -X[3]*sin + X[4]*cos, cos, sin],\n",
    "            [0,      0,     -X[3]*cos - X[4]*sin, -sin, cos]\n",
    "        ]\n",
    "        \n",
    "    return np.array(J, dtype='float')\n",
    "\n",
    "def F(X_prev: np.array, u_prev: np.array) -> np.array:\n",
    "    '''\n",
    "    Calculada analiticamente.\n",
    "    '''\n",
    "    return np.array([\n",
    "        X_prev[0] + u_prev[0] * np.cos(X_prev[2]) * dt,\n",
    "        X_prev[1] + u_prev[0] * np.sin(X_prev[2]) * dt,\n",
    "        X_prev[2] + u_prev[0] * dt * np.tan(u_prev[1])/ l,\n",
    "        X_prev[3],\n",
    "        X_prev[4]\n",
    "    ])\n",
    "\n",
    "def Q(x_prev):\n",
    "    sf, se = 0.25, 0.25\n",
    "    srho = ((h**2 + x_prev[0]**2 + x_prev[1]**2) / (20**2))\n",
    "    return np.array([\n",
    "        [srho, 0, 0],\n",
    "        [0, sf, 0],\n",
    "        [0, 0, se]\n",
    "    ])\n",
    "\n",
    "def R(x_prev, u):\n",
    "    '''\n",
    "    DE ESTADO\n",
    "    '''\n",
    "    cos = np.cos(x_prev[2])\n",
    "    sin = np.sin(x_prev[2])\n",
    "    M =  np.array([\n",
    "        [cos, -sin, 0, 0, 0],\n",
    "        [sin,  cos, 0, 0, 0],\n",
    "        [0, 0, 1, 0, 0],\n",
    "        [0, 0, 0, 1, 0],\n",
    "        [0, 0, 0, 0, 1]\n",
    "    ])\n",
    "    \n",
    "    sl = (dt * u[0] / 6)**2\n",
    "    sr = (dt * u[0] / 12)**2\n",
    "    stheta = (dt * u[0] / (8*l))**2\n",
    "    \n",
    "    # Matriz R no referencial local\n",
    "    Rl = np.array([\n",
    "        [sl, 0, 0, 0, 0],\n",
    "        [0, sr, 0, 0, 0],\n",
    "        [0, 0, stheta, 0, 0],\n",
    "        [0, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 0]\n",
    "    ])\n",
    "    \n",
    "    return M @ Rl @ M.T\n",
    "\n",
    "def G(x_prev):\n",
    "    sin = np.sin(x_prev[2])\n",
    "    cos = np.cos(x_prev[2])\n",
    "    return np.array([\n",
    "        np.sqrt(x_prev[0]**2 + x_prev[1]**2 + h**2),\n",
    "        ( x_prev[3] * cos + x_prev[4] * sin),\n",
    "        (-x_prev[3] * sin + x_prev[4] * cos)\n",
    "    ])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72b67a80-12cc-4c37-9878-3bfc6647d08f",
   "metadata": {},
   "source": [
    "## EKF\n",
    "\n",
    "Implementação do Filtro de Kalman extendido"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d35144a6-905f-4bb2-a502-cb7eac0d8abc",
   "metadata": {},
   "outputs": [],
   "source": [
    "class EKF:\n",
    "    def __init__(self, f, g, x_est, Sigma_est, Q, R, data):\n",
    "        '''EKF(f, h, x0, u0)\n",
    "\n",
    "        x' = f(x, u)    state transition function\n",
    "        z' = g(x)       observation function\n",
    "        x0              initial state estimate\n",
    "        Sigma0          initial cov matrix estimate\n",
    "        Q               stochastic matrix for observation\n",
    "        R               stochastic matrix for state'''\n",
    "        self.f, self.g = f, g\n",
    "        self.x = np.array(x_est)\n",
    "        self.I = np.eye(len(x_est))\n",
    "        self.Sigma = Sigma_est\n",
    "        self.Q, self.R = Q, R\n",
    "        self.u = data[:,:2]\n",
    "        self.z = data[:,2:]\n",
    "        self.X = np.array([self.x])\n",
    "        self.first = True\n",
    "    \n",
    "    def predict(self, t: int):\n",
    "        A = jacobian(X=self.x, u=self.u[t], which='A')\n",
    "        self.Sigma = (A @ self.Sigma @ A.T) + self.R(self.x, self.u[t])\n",
    "        self.x = self.f(self.x, self.u[t])\n",
    "        self.X = np.append(self.X,[self.x], axis=0)\n",
    "\n",
    "    def update(self, t: int):\n",
    "        x, Sigma, Q, I, g, z = self.x, self.Sigma, self.Q, self.I, self.g, self.z\n",
    "        C = jacobian(X=x, u=z[t], which='C')\n",
    "        y = z[t] - g(x)\n",
    "        y = np.array([y]).T\n",
    "        S = (C @ Sigma @ C.T) + Q(x)\n",
    "        K = Sigma @ C.T @ LA.inv(S)\n",
    "        innovation = K @ y\n",
    "        \n",
    "        self.x = np.array([x+innovation[i][0] for (i,x) in np.ndenumerate(self.x)])\n",
    "        self.Sigma = (I - K @ C) @ Sigma            "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7062b23-697c-4bf0-8a3e-f65d1d1148ff",
   "metadata": {},
   "source": [
    "## Questão 04\n",
    "\n",
    "Como nessa etapa não são consideradas as medições, o filtro de Kalman se reduz à parte de predição."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "aacea9e6-8ea3-49d6-a18a-8545eb8bd774",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "ekf_q4 = EKF(F, G, init_state, init_sigma, Q, R, data)\n",
    "for t in range(n_steps):\n",
    "    ekf_q4.predict(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0b815de1-c024-4d2d-b414-24aeada81856",
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>$\\theta$</th>\n",
       "      <th>f_x</th>\n",
       "      <th>f_y</th>\n",
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       "      <th>0</th>\n",
       "      <td>16014.490169</td>\n",
       "      <td>16888.802363</td>\n",
       "      <td>-273.775722</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
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       "      <td>18573.995386</td>\n",
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       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>0.000000</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000000</td>\n",
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       "      <td>0.000000</td>\n",
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       "              x             y    $\\theta$   f_x   f_y\n",
       "0  16014.490169  16888.802363 -273.775722   0.0   0.0\n",
       "1  16888.802363  18573.995386 -293.912740   0.0   0.0\n",
       "2   -273.775722   -293.912740    6.510417   0.0   0.0\n",
       "3      0.000000      0.000000    0.000000  10.0   0.0\n",
       "4      0.000000      0.000000    0.000000   0.0  10.0"
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     "execution_count": 6,
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   "source": [
    "pd.DataFrame(ekf_q4.Sigma, columns=['x','y',r'$\\theta$',r'f_x',r'f_y'])"
   ]
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ekf_q4.X[:,0], ekf_q4.X[:,1])\n",
    "plt.ylabel('Coordenada em y')\n",
    "plt.xlabel('Coordenada em x')\n",
    "plt.title(r'Coordenadas (x,y) percorridas pelo robô - $t_f=250s$', fontsize=13)\n",
    "plt.savefig('./images/caminhoQ4.png', dpi=600)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ada0a156-e3e2-40b8-b4ba-321302276339",
   "metadata": {},
   "source": [
    "## Questão 06"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "34b177a4-1f2d-4bdd-9d39-8d5d37b2d4b8",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "ekf_q6 = EKF(F, G, init_state, init_sigma, Q, R, data)\n",
    "for t in range(int(1375/dt)):\n",
    "    ekf_q6.predict(t)\n",
    "    ekf_q6.update(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d94af1b3-d1f7-414c-adcc-26fb3759711f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>$\\theta$</th>\n",
       "      <th>f_x</th>\n",
       "      <th>f_y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.010847</td>\n",
       "      <td>0.002988</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>-0.000008</td>\n",
       "      <td>-0.000004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.002988</td>\n",
       "      <td>0.000831</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>-0.000002</td>\n",
       "      <td>-0.000001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000005</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>0.000267</td>\n",
       "      <td>-0.000250</td>\n",
       "      <td>-0.000124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.000008</td>\n",
       "      <td>-0.000002</td>\n",
       "      <td>-0.000250</td>\n",
       "      <td>0.000500</td>\n",
       "      <td>0.000224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.000004</td>\n",
       "      <td>-0.000001</td>\n",
       "      <td>-0.000124</td>\n",
       "      <td>0.000224</td>\n",
       "      <td>0.000156</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y  $\\theta$       f_x       f_y\n",
       "0  0.010847  0.002988  0.000005 -0.000008 -0.000004\n",
       "1  0.002988  0.000831  0.000001 -0.000002 -0.000001\n",
       "2  0.000005  0.000001  0.000267 -0.000250 -0.000124\n",
       "3 -0.000008 -0.000002 -0.000250  0.000500  0.000224\n",
       "4 -0.000004 -0.000001 -0.000124  0.000224  0.000156"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(ekf_q6.Sigma, columns=['x','y',r'$\\theta$',r'f_x',r'f_y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9c94fa52-0c9c-4728-9fb8-afa4e6967157",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ekf_q6.X[:,0], ekf_q6.X[:,1])\n",
    "plt.ylabel('Coordenada em y')\n",
    "plt.xlabel('Coordenada em x')\n",
    "plt.title(r'Coordenadas (x,y) percorridas pelo robô - $t_f=1375s$', fontsize=13)\n",
    "plt.savefig('./images/caminhoQ6.png',dpi=600)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}