Robot localization example added.

Still needs work; code is messy, and Q is not computed. But I am getting correct results. Also need to expand explanations and scenarios. Need to remove now redundant explanations in EKF chapter, since they exist in the UKF chapter.
2015-06-08 07:23:52 -07:00
1 parent f8057cd917
commit 88d200b9a8
@@ -16,7 +16,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
@@ -250,7 +250,7 @@
       "<IPython.core.display.HTML object>"
      ]
     },
-     "execution_count": 1,
+     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -303,7 +303,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
@@ -312,7 +312,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x751ac88>"
+       "<matplotlib.figure.Figure at 0x6b5f2b0>"
      ]
     },
     "metadata": {},
@@ -352,7 +352,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
@@ -361,7 +361,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x751a710>"
+       "<matplotlib.figure.Figure at 0x6b4ccf8>"
      ]
     },
     "metadata": {},
@@ -427,7 +427,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
@@ -436,7 +436,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x445e0b8>"
+       "<matplotlib.figure.Figure at 0x6b4cb00>"
      ]
     },
     "metadata": {},
@@ -642,7 +642,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
@@ -667,7 +667,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
@@ -690,7 +690,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
@@ -765,16 +765,16 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x87649b0>"
+       "<matplotlib.figure.Figure at 0x7c636a0>"
      ]
     },
     "metadata": {},
@@ -782,9 +782,9 @@
    },
    {
     "data": {
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truncated
+      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x87eb828>"
+       "<matplotlib.figure.Figure at 0x72e16d8>"
      ]
     },
     "metadata": {},
@@ -792,9 +792,9 @@
    },
    {
     "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwMAAAEtCAYAAABUG7xMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x86e8e80>"
+       "<matplotlib.figure.Figure at 0x6bf02b0>"
      ]
     },
     "metadata": {},
@@ -889,7 +889,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": true
@@ -897,7 +897,7 @@
   "outputs": [
    {
     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nUqOHbKQnT/0tv+59MpOT+AmTXbj1s0kQCQAAAABJRU5ErkJggg==\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{x_{pos}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}}\\end{matrix}\\right]$$"
      ],
@@ -909,7 +909,7 @@
       "⎣╲╱  x_alt  + x_pos       ╲╱  x_alt  + x_pos  ⎦"
      ]
     },
-     "execution_count": 9,
+     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -974,7 +974,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
@@ -1001,7 +1001,7 @@
       "⎣          2                                                          ⎦"
      ]
     },
-     "execution_count": 10,
+     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -1036,7 +1036,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": true
@@ -1046,7 +1046,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x87c4a90>"
+       "<matplotlib.figure.Figure at 0x72e1cc0>"
      ]
     },
     "metadata": {},
@@ -1171,7 +1171,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": false
@@ -1198,7 +1198,7 @@
       "⎣0  0                  1                 ⎦"
      ]
     },
-     "execution_count": 12,
+     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -1238,7 +1238,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
@@ -1288,7 +1288,7 @@
       "                                                  ⎦"
      ]
     },
-     "execution_count": 13,
+     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -1348,7 +1348,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
@@ -1371,7 +1371,7 @@
       "⎣  (px - x)  + (py - y)        (px - x)  + (py - y)        ⎦"
      ]
     },
-     "execution_count": 14,
+     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -1394,7 +1394,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
@@ -1428,7 +1428,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
@@ -1479,7 +1479,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
@@ -1556,7 +1556,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
@@ -1582,7 +1582,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "scrolled": true
@@ -1613,7 +1613,7 @@
    "            plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=6,\n",
    "                                    facecolor='b', alpha=0.08)\n",
    "\n",
-    "            x, y= sim_pos[0, 0], sim_pos[1, 0]\n",
+    "            x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "            for lmark in landmarks:\n",
    "                d = np.sqrt((lmark[0] - x)**2 + (lmark[1] - y)**2)  \n",
    "                a = atan2(lmark[1] - y, lmark[0] - x) - sim_pos[2, 0]\n",
@@ -1632,7 +1632,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": true
@@ -1640,9 +1640,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0xa5e3f28>"
+       "<matplotlib.figure.Figure at 0x9c1b400>"
      ]
     },
     "metadata": {},
@@ -1652,7 +1652,41 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "[ 0.0199192   0.02067011  0.00153754]\n"
+      "[ 0.02427096  0.04335114  0.00222081]\n"
+     ]
+    }
+   ],
+   "source": [
+    "landmarks = array([[5, 10], [10, 5], [15, 15], [20, 5]])\n",
+    "landmarks = array([[5, 10], [10, 5], [15, 15]])\n",
+    "\n",
+    "ekf = run_localization(landmarks, sigma_vel=0.1, sigma_steer=np.radians(1),\n",
+    "                      sigma_range=0.3, sigma_bearing=0.1)\n",
+    "print(ekf.P.diagonal())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x9e2d400>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[ 0.01981129  0.02080953  0.001537  ]\n"
     ]
    }
   ],
@@ -1668,7 +1702,7 @@
   "cell_type": "markdown",
   "metadata": {},
   "source": [
-    "I have plotted the landmarks as solid squares. The path of the robot is drawn with a dashed line, which is admittedly hard to see. The covariance after the predict step is drawn in a very light shade of blue, and the covariance after all of the landmark measurements are incorporated are shown in green. To make them visible at this scale I have set the ellipse boundary at 10$\\sigma$.\n",
+    "I have plotted the landmarks as solid squares. The path of the robot is drawn with a dashed line, which is admittedly hard to see. The covariance after the predict step is drawn in a very light shade of blue, and the covariance after all of the landmark measurements are incorporated are shown in green. To make them visible at this scale I have set the ellipse boundary at 6$\\sigma$.\n",
    "\n",
    "From this we can see that there is a lot of uncertainty added by our motion model, and that most of the error in in the direction of motion. We can see that from the shape of the blue ellipses. After a few steps we can see that the filter incorporates the landmark measurements. \n",
    "\n",
@@ -1818,7 +1852,7 @@
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
-   "version": "3.4.1"
+   "version": "3.4.3"
  }
 },
 "nbformat": 4,
@@ -58,77 +58,36 @@ def move(x, u, dt, wheelbase):



-
-
-def state_unscented_transform(Sigmas, Wm, Wc, noise_cov):
-    """ Computes unscented transform of a set of sigma points and weights.
-    returns the mean and covariance in a tuple.
-    """
-
-    kmax, n = Sigmas.shape
-
+def state_mean(sigmas, Wm):
    x = np.zeros(3)
    sum_sin, sum_cos = 0., 0.

-    for i in range(len(Sigmas)):
-        s = Sigmas[i]
+    for i in range(len(sigmas)):
+        s = sigmas[i]
        x[0] += s[0] * Wm[i]
        x[1] += s[1] * Wm[i]
        sum_sin += sin(s[2])*Wm[i]
        sum_cos += cos(s[2])*Wm[i]

    x[2] = atan2(sum_sin, sum_cos)
+    return x


-    # new covariance is the sum of the outer product of the residuals
-    # times the weights
-    P = np. zeros((n, n))
-    for k in range(kmax):
-        y = residual_x(Sigmas[k],  x)
-        P += Wc[k] * np.outer(y, y)
-
-    if noise_cov is not None:
-        P += noise_cov
-
-    return (x, P)
-
-
-
-def z_unscented_transform(Sigmas, Wm, Wc, noise_cov):
-    """ Computes unscented transform of a set of sigma points and weights.
-    returns the mean and covariance in a tuple.
-    """
-
-    kmax, n = Sigmas.shape
-
+def z_mean(sigmas, Wm):
    x = np.zeros(2)
    sum_sin, sum_cos = 0., 0.

-    for i in range(len(Sigmas)):
-        s = Sigmas[i]
+    for i in range(len(sigmas)):
+        s = sigmas[i]
        x[0] += s[0] * Wm[i]
        sum_sin += sin(s[1])*Wm[i]
        sum_cos += cos(s[1])*Wm[i]

    x[1] = atan2(sum_sin, sum_cos)
+    return x


-    # new covariance is the sum of the outer product of the residuals
-    # times the weights
-    P = np.zeros((n, n))
-    for k in range(kmax):
-        y = residual_h(Sigmas[k], x)
-
-        P += Wc[k] * np.outer(y, y)
-
-
-    if noise_cov is not None:
-        P += noise_cov
-
-    return (x, P)
-
-
-sigma_r = 1.
+sigma_r = .3
 sigma_h =  .1#np.radians(1)
 sigma_steer =  np.radians(.01)
 dt = 1.0
@@ -136,7 +95,8 @@ wheelbase = 0.5

 m = array([[5, 10],
           [10, 5],
-           [15, 15]])
+           [15, 15],
+           [20, 5]])


 def fx(x, dt, u):
@@ -155,7 +115,9 @@ def Hx(x, landmark):
    return Hx

 points = MerweScaledSigmaPoints(n=3, alpha=1.e-3, beta=2, kappa=0)
-ukf= UKF(dim_x=3, dim_z=2, fx=fx, hx=Hx, dt=dt, points=points)
+ukf= UKF(dim_x=3, dim_z=2, fx=fx, hx=Hx, dt=dt, points=points,
+         x_mean_fn=state_mean, z_mean_fn=z_mean,
+         residual_x=residual_x, residual_z=residual_h)
 ukf.x = array([2, 6, .3])
 ukf.P = np.diag([.1, .1, .2])
 ukf.R = np.diag([sigma_r**2, sigma_h**2])
@@ -169,12 +131,12 @@ xp = ukf.x.copy()
 plt.figure()
 plt.scatter(m[:, 0], m[:, 1])

-for i in range(250):
+for i in range(200):
    xp = move(xp, u, dt/10., wheelbase) # simulate robot
    plt.plot(xp[0], xp[1], ',', color='g')

    if i % 10 == 0:
-        ukf.predict(fx_args=u, UT=state_unscented_transform)
+        ukf.predict(fx_args=u)

        plot_covariance_ellipse((ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=3,
                                facecolor='b', alpha=0.08)
@@ -184,8 +146,7 @@ for i in range(250):
            a = atan2(lmark[1] - xp[1], lmark[0] - xp[0]) - xp[2] + randn()*sigma_h
            z = np.array([d, a])

-            ukf.update(z, hx_args=(lmark,), UT=z_unscented_transform,
-                       residual_x=residual_x, residual_h=residual_h)
+            ukf.update(z, hx_args=(lmark,))

        plot_covariance_ellipse((ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=3,
                                facecolor='g', alpha=0.4)
@@ -195,4 +156,5 @@ for i in range(250):

 plt.axis('equal')
 plt.title("UKF Robot localization")
-plt.show()
+plt.show()
+print(ukf.P.diagonal())