{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 確率ロボティクス2017第4回\n", "\n", "上田隆一\n", "\n", "2017年10月11日@千葉工業大学\n", "\n", "## 今日やること\n", "\n", "モンテカルロ近似された$bel$にセンサ情報を反映\n", "\n", "* 考え方\n", " * センサの値とパーティクルの姿勢を比較\n", " * センサの値が得られそうな姿勢のパーティクルは真の姿勢の有力な候補\n", " * センサの値が得られそうな姿勢のパーティクルはそうでもない\n", " * 前回使わなかった重みを使用\n", " \n", "## ランドマークの準備\n", "\n", "現在主流はレーザレンジファインダーを使う方法ですが、シミュレーションが大変なので点ランドマークで。\n", "\n", "* 点ランドマーク\n", " * 環境中での絶対位置が分かっている目印\n", " * ロボットから観測すると、次のことが（曖昧さと共に）分かる\n", " * どっちの方角に見えるか\n", " * 距離はどれくらいか" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from copy import copy\n", "import math, random\n", "import matplotlib.pyplot as plt # for plotting data\n", "from matplotlib.patches import Ellipse # for drawing\n", "\n", " \n", "actual_landmarks = [np.array([-0.5,0.0]),np.array([0.5,0.0]),np.array([0.0,0.5])]\n", "\n", "def draw_landmarks(landmarks):\n", " xs = [ e[0] for e in landmarks]\n", " ys = [ e[1] for e in landmarks]\n", " plt.scatter(xs,ys,s=300,marker=\"*\",label=\"landmarks\",color=\"orange\")\n", " \n", "draw_landmarks(actual_landmarks)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ロボットの描画" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "actual_x = np.array([0.3,0.2,math.pi*20.0/180]) #ロボットの実際の姿勢\n", "\n", "def draw_robot(pose):\n", " plt.quiver([pose[0]],[pose[1]],[math.cos(pose[2])],[math.sin(pose[2])],color=\"red\",label=\"actual robot motion\")\n", " \n", "draw_robot(actual_x)\n", "draw_landmarks(actual_landmarks)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 観測モデルの作成\n", "\n", "まず、ロボットからランドマークがどの向き、距離に見えるか計算してみましょう。これは、ロボットが360度どこからでも誤差なくランドマークを観測できる時の観測モデルですが、後から制限します。" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def relative_landmark_pos(pose,landmark):\n", " x,y,theta = pose\n", " lx,ly = landmark\n", " distance = math.sqrt((x -lx)**2 + (y-ly)**2)\n", " direction = math.atan2(ly-y, lx-x) - theta\n", " \n", " return (distance, direction,lx,ly) # 実際の位置も一緒に返す" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(0.8246211251235323, -3.2456798408617948, -0.5, 0.0), (0.28284271247461906, -1.1344640137963142, 0.5, 0.0), (0.4242640687119285, 2.0071286397934789, 0.0, 0.5)]\n" ] } ], "source": [ "measurements = [ relative_landmark_pos(actual_x,e) for e in actual_landmarks]\n", "print(measurements)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "描画する関数も作成しましょう。" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def draw_observation(pose, measurement):\n", " x,y,theta = pose\n", " distance, direction,lx,ly = measurement\n", " lx = distance*math.cos(theta + direction) + x\n", " ly = distance*math.sin(theta + direction) + y\n", " plt.plot([pose[0], lx],[pose[1], ly],color=\"pink\")\n", " \n", "def draw_observations(pose, measurements):\n", " for m in measurements:\n", " draw_observation(pose, m)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_landmarks(actual_landmarks)\n", "draw_robot(actual_x)\n", "draw_observations(actual_x,measurements)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "観測モデルを作成します。\n", "\n", "* 見える範囲の制限\n", " * とりあえずロボットから左右90度にしましょう。\n", "* 雑音\n", " * 距離計測に真値の10%の標準偏差の雑音\n", " * 方向計測に標準偏差5degの雑音" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def observation(pose, landmark):\n", " actual_distance,actual_direction,lx,ly = relative_landmark_pos(pose,landmark)\n", " # 方向の制限（cosの値が正）\n", " if (math.cos(actual_direction) < 0.0):\n", " return None\n", " \n", " measured_distance = random.gauss(actual_distance,actual_distance*0.1) \n", " measured_direction = random.gauss(actual_direction,5.0/180.0*math.pi) \n", " \n", " return (measured_distance, measured_direction,lx,ly)\n", "\n", "def observations(pose,landmarks):\n", " return filter(lambda x: x != None, [ observation(pose,e) for e in landmarks])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "actual_x = np.array([0.3,0.2,math.pi*180.0/180]) #姿勢は変えること\n", "measurements = observations(actual_x, actual_landmarks)\n", "\n", "draw_landmarks(actual_landmarks)\n", "draw_robot(actual_x)\n", "draw_observations(actual_x, measurements)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ロボットを歩行させてみましょう" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "先週作ったコードに今の観測モデルを載せる。" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "### クラスや関数のコピペ ###\n", "\n", "class Particle:\n", " def __init__(self,w):\n", " self.pose = np.array([0.0,0.0,0.0])\n", " self.weight = w\n", " \n", " def __repr__(self):\n", " return \"pose: \" + str(self.pose) + \" weight: \" + str(self.weight)\n", " \n", "\n", "def f(x_old,u):\n", " pos_x, pos_y, pos_theta = x_old\n", " act_fw, act_rot = u\n", " \n", " act_fw = random.gauss(act_fw,act_fw/10)\n", " dir_error = random.gauss(0.0, math.pi / 180.0 * 3.0)\n", " act_rot = random.gauss(act_rot,act_rot/10)\n", " \n", " pos_x += act_fw * math.cos(pos_theta + dir_error)\n", " pos_y += act_fw * math.sin(pos_theta + dir_error)\n", " pos_theta += act_rot\n", " \n", " return np.array([pos_x,pos_y,pos_theta])\n", "\n", "### 描画関数は少し変更を ###\n", "def draw(pose,particles): \n", " fig = plt.figure(i,figsize=(8, 8))\n", " sp = fig.add_subplot(111, aspect='equal')\n", " sp.set_xlim(-1.0,1.0)\n", " sp.set_ylim(-0.5,1.5)\n", " \n", " xs = [e.pose[0] for e in particles]\n", " ys = [e.pose[1] for e in particles]\n", " vxs = [math.cos(e.pose[2])*e.weight for e in particles] #重みで長さを変えるようにしましょう\n", " vys = [math.sin(e.pose[2])*e.weight for e in particles] #重みで長さを変えるようにしましょう\n", " plt.quiver(xs,ys,vxs,vys,color=\"blue\",label=\"particles\")\n", " \n", " plt.quiver([pose[0]],[pose[1]],[math.cos(pose[2])],[math.sin(pose[2])],color=\"red\",label=\"actual robot motion\")" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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HmflsPbsMOKIFP1eSpHGtFSF+OPCrhvm1dVlfPgBc1zC/T0R0RsSyiHhLC/ojSdK40PTp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\nqKZCPCIOiogbImJ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U0qrq/RHgNuC4Rh+SUro8pdSZUuqcNm1aE5otSVLZmhHiC4GjImJWREwG5gC9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\n+xURxwGXAWenlFbXlTf8dzl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k9RcNDfBKqcl85ap8fXurLXIv800cEk0tGeKS1NfWbyg3ma/fkAdj2X7b3GQ+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\nEJckqaAMcUmSCsoQlySpoAx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vWtVw+dCjqnnqv7Zw4oTd0LsXTJsAwxL6bi2vgDfWeLX1o/Oxowawc2d9r2qr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\nqRMXERHJlDpxERGRTKkTFxERydRPfgu2LZnsLnwAAAAASUVORK5CYII=\n", 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CF86qgcW7WDloH+7/yXoSQOl09cIlPyjERaSgDRjQ9tKyd9U3wPJqGD6EKTPK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\n", 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pf72XZJ0wppuVRIYu7YmLSP/bVQ27a2DuDBjdixPbNT70KOMU4iLJKMRFpM/+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\n", 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XLiJ9p7+y01cAU1Oeb5vYtgJvUk/d/o90LxBCmA3MBqiqqurhGlIi/W/zZvj0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\npYnPZIeUc7+ZOO914Lh8fzbdvK6/J/6WJD+fOV3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "### 行動もコピペベースで。ランドマークの観測と描画を入れる ###\n", "\n", "actual_x = np.array([0.0,0.0,0.0]) #ロボットの実際の姿勢\n", "particles = [Particle(1.0/100) for i in range(100)]\n", "u = np.array([0.2,math.pi / 180.0 * 20]) #ロボットの移動\n", "\n", "import copy\n", "\n", "path = [actual_x]\n", "particle_path = [copy.deepcopy(particles)]\n", "measurementss = [observations(actual_x, actual_landmarks)]\n", "for i in range(10):\n", " actual_x = f(actual_x,u)\n", " path.append(actual_x)\n", " measurementss.append(observations(actual_x,actual_landmarks))\n", "\n", " for p in particles:\n", " p.pose = f(p.pose,u)\n", " particle_path.append(copy.deepcopy(particles))\n", "\n", "for i,p in enumerate(path):\n", " draw(path[i],particle_path[i])\n", " draw_landmarks(actual_landmarks)\n", " draw_observations(path[i],measurementss[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 観測をパーティクルに反映\n", "\n", "* 重みを使う\n", " * パーティクルの姿勢と観測されたランドマークの位置の矛盾の度合いで重みを変化\n", " * 矛盾が大きい: 重みを小さく\n", " * 矛盾が小さい: 重みを大きく\n", "* 計算の方法\n", " * 正規分布の確率密度関数を利用\n", " * $\\mathcal{N}(distance,distanceの10\\%)$を重みにかける\n", " * $\\mathcal{N}(direction, 5\\text{[deg]})$を重みにかける" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "### パーティクルの姿勢と観測結果を比較する関数 ###\n", "from scipy.stats import norm # ガウス分布（正規分布）のオブジェクトをインポート\n", "def likelihood(pose, measurement):\n", " x,y,theta = pose\n", " distance, direction,lx,ly = measurement\n", " \n", " # パーティクルの姿勢から観測されるはずのランドマークの距離と向き\n", " rel_distance, rel_direction, tmp_x,tmp_y = relative_landmark_pos(pose,(lx,ly))\n", "\n", " # 誤差をガウスで評価\n", " return norm.pdf(x = distance - rel_distance, loc = 0.0, scale = rel_distance / 10.0) \\\n", " * norm.pdf(x = direction - rel_direction, loc = 0.0, scale = 5.0/180.0 * math.pi)\n", " \n", "### パーティクル群の重みを変更する関数 ###\n", "def change_weights(particles, measurement):\n", " for p in particles:\n", " p.weight *= likelihood(p.pose, measurement)\n", " \n", " # 重みの合計を1に保つ\n", " ws = [ p.weight for p in particles ]\n", " s = sum(ws)\n", " for p in particles: p.weight = p.weight / s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "関数を適用してみましょう。" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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SVGfXXpuHQB01asn5K62UHyzy2GPLBviiRfCNb8Dpp8Nbby27zZV5gwP5NZ/l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\nMCJeqlnWb49ZRJwbEc9FO7d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HHOOjuRXWrl32POPnnis9/7yXt9nGx0evV0seJsdxGhtK+jZjeU5qXWGHmtkn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\n1wshzEuVv5e0Xgn7NTKzfDObZGbpoF5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iAAB0Ur7hZY8/Hh6fP99vg+Fl06eHId+nj3TyyX4/WhMfPVr6x3/0HeJefTU8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\n", 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9enl+8mRfaz1dHTqU/sPggQdg3Lj81Fcqn4K4iEiMtGjhm6SkevFFD8YtWnh+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\nREQkphTERUREYur/AX2zY3wSCoeuAAAAAElFTkSuQmCC\n", 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vPq9Z0wNwXG6uP42//XYi7eq0adJ//+sBeostfNsLL/jTb/Pmfo3r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\nHdtvkh6K3feXSpqBVdLPi4xtAABEVNSb0wEAqLI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uKYn50tPD7aWlMWw+blwMuy9fnvt8Rx8dgT5qVEzPmu3ttzOBnm8ft9sujmqX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\nJBQhDgBAQhHiAAAkVL1C3My6m9njZvZ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+U1r2XUm9pOoa6fgHpCHvkzY8K/3pDGnHekkuvffb0kFXlLq2QLdhZovcPZXP\nOuixDejpVt8WrnuPPkc6/fkQ4FJ4P/15afTZ4ZT6KvphAsoNIQ70ZA11UsNOacJM6djbQ0v0TJX9\npWPvCNMbdoT5AZQNemsAerJeldKkl9ufb8zHwwtAWeFIHACASBHiAABEihAHACBShDgAAJEixAEA\niBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACRIsQBAIgUIQ4AQKQIcQAAIkWI\nAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECkCHEAACJFiAMAEClCHACASBHiAABE\nihAHACBShDgAAJEixAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACRIsQB\nAIgUIQ4AQKQIcQAAIkWIAwAQKUIcAIBIEeIAAESqICFuZhPN7AUzW2lmU7NMv8zMlpvZEjObb2Zj\nMqbVm9ni5DW7EPUBAKAnqMx3BWZWIelnkj4kaY2khWY2292XZ8z2jKSUu28zs0sk/UDSucm07e5+\naL71AACgpynEkfiRkla6+yp33yVppqRJmTO4+2Puvi0ZXSBpZAE+FwCAHq0QIT5C0msZ42uSstZc\nLGlOxni1mdWa2QIzO6sA9QEAoEfI+3R6R5jZJyWlJB2fUTzG3dea2T6SHjWzpe7+UpZlp0iaIkmj\nR48uSn0BAChnhTgSXytpVMb4yKSsCTP7oKQrJZ3p7jvT5e6+NnlfJelxSYdl+xB3n+buKXdP1dTU\nFKDaAADErRAhvlDSeDMbZ2Z9JE2W1KSVuZkdJulmhQBfl1E+xMyqkuFhkiZIymwQBwAAWpH36XR3\nrzOzSyXNk1Qhabq7P2dmV0uqdffZkq6XNEDSvWYmSa+6+5mSDpR0s5k1KPyguK5Zq3YAANAKc/dS\n16HDUqmU19bWlroaAAB0mpktcvdUPuugxzYAACJFiAMAEClCHACASBHiAABEihAHACBShDgAAJEi\nxAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACRIsQBAIgUIQ4AQKQIcQAA\nIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECkCHEAACJFiAMAEClCHACASBHi\nAABEihAHACBShDgAAJEixAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACR\nIsQBAIiaCPBlAAAONklEQVQUIQ4AQKQIcXS9hnpp2bXhHUDh8R3rsQhxdL31/yst+ab05l9KXROg\ne+I71mMR4uh6r9wlyaSX7yp1TYDuie9Yj0WIo2t5g/TqvZI8vHtDqWsEdC98x3o0Qhxd662npYbd\nYbhhl/TWwtLWB+hu+I71aAUJcTObaGYvmNlKM5uaZXqVmd2dTH/KzMZmTLsiKX/BzD5ciPqgjLw8\nQ6rfHobrt0uvzChtfYDuhu9Yj1aZ7wrMrELSzyR9SNIaSQvNbLa7L8+Y7WJJG9x9PzObLOn7ks41\ns/dImizpIEl7S/qjmb3b3WliGZOdb0sLPi3VbWk57c0FUnp3er208hZp47KW81UOkI6eLlUN7dq6\nAjHiO4ZW5B3iko6UtNLdV0mSmc2UNElSZohPkvSdZPg+STeamSXlM919p6TVZrYyWd+TBagXiqX3\nQKmyn7T2/vbnrd8qvTG/ZfmY86XegwpfN6A74DuGVhTidPoISa9ljK9JyrLO4+51kjZJ2jPHZVHu\nevWWJtwlHXuXVNlfsorclrOKcHRw7Axpwp1Sr0L8pgS6Ib5jaEU0DdvMbIqZ1ZpZ7fr160tdHWQz\n9jzp1KXSoPdIFf3anreiX5jv1CXS2MnFqR8QO75jaKYQIb5W0qiM8ZFJWdZ5zKxS0h6S3spxWUmS\nu09z95S7p2pqagpQbXSJAeOkUxZJYz8RjgCyqewfpp+yKMwPIHd8x5ChECG+UNJ4MxtnZn0UGqrN\nbjbPbEkXJsNnS3rU3T0pn5y0Xh8nabykpwtQJ5RSr95S3+HhdpdsGnZLffcO8wHoOL5jSOQd4sk1\n7kslzZP0vKR73P05M7vazM5MZvuVpD2ThmuXSZqaLPucpHsUGsHNlfRFWqZ3E6vvaPofjGX8Z9Kw\nK0wH0Hl8x6DCtE6Xuz8k6aFmZd/KGN4h6ZxWlv2epO8Voh4oE5tXSDv+2The0Vca/XHp1Xsa72fd\n8br0zkpp4H6lqSMQM75jSETTsA0RefXecL9qr2qp3yjp5CelY34d3vuNCuX/31UkgA7jO4YEIY7C\nW31buCY3+hzp9OelIe8L5UPeF8ZHnx1O9626rbT1BGLFdwwJQhyF1VAnNeyUJsyUjr09tJLNVNlf\nOvaOML1hR5gfQO74jiGDhUbicUmlUl5bW1vqagAA0GlmtsjdU/msgyNxAAAiRYgDABApQhwAgEgR\n4gAARIoQBwAgUoQ4AACRIsQBAIgUIQ4AQKQIcQAAIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAA\nkSLEAQCIFCEOAECkCHEAACJFiAMAEClCHACASBHiAABEihAHACBShDgAAJEixAEAiBQhDgBApAhx\nAAAiRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACRIsQBAIgUIQ4AQKQIcQAAIkWIAwAQKUIcAIBI\nEeIAAESKEAcAIFKEOAAAkSLEAQCIFCEOAECkCHEAACJFiAMAEKm8QtzMhprZI2a2InkfkmWeQ83s\nSTN7zsyWmNm5GdN+bWarzWxx8jo0n/oAANCT5HskPlXSfHcfL2l+Mt7cNkkXuPtBkiZK+omZDc6Y\n/nV3PzR5Lc6zPgAA9Bj5hvgkSbclw7dJOqv5DO7+oruvSIb/IWmdpJo8PxcAgB4v3xDfy91fT4b/\nKWmvtmY2syMl9ZH0Ukbx95LT7D82s6o2lp1iZrVmVrt+/fo8qw0AQPzaDXEz+6OZLcvympQ5n7u7\nJG9jPcMl3SHpU+7ekBRfIekASf8qaaiky1tb3t2nuXvK3VM1NRzIAwBQ2d4M7v7B1qaZ2RtmNtzd\nX09Cel0r8w2S9AdJV7r7gox1p4/id5rZrZK+1qHaAwDQg+V7On22pAuT4Qsl3d98BjPrI+n3km53\n9/uaTRuevJvC9fRledYHAIAeI98Qv07Sh8xshaQPJuMys5SZ3ZLM83FJx0m6KMutZHea2VJJSyUN\nk3RtnvUBAKDHsHApOy6pVMpra2tLXQ0AADrNzBa5eyqfddBjGwAAkSLEAQCIFCEOAECkCHEAACJF\niAMAEClCHACASBHiAABEihAHACBShDgAAJEixAEAiBQhDgBApAhxAAAiRYgDABApQhwAgEgR4gAA\nRIoQBwAgUoQ4AACRIsQBAIgUIQ4AQKQIcQAAIkWIAwAQKUIcAIBIEeIAAESKEAcAIFKEOAAAkSLE\nAQCIFCEOAECkCHEAACJFiAMAEClCHACASBHiAABEihAHACBShDgAAJEixAEAiBQhDgBApAhxAAAi\nRYgDABApQhwAgEgR4gAARIoQBwAgUoQ4AACRIsQBAIgUIQ4AQKQIcQAAIkWIAwAQqbxC3MyGmtkj\nZrYieR/Synz1ZrY4ec3OKB9nZk+Z2Uozu9vM+uRTHwAAepJ8j8SnSprv7uMlzU/Gs9nu7ocmrzMz\nyr8v6cfuvp+kDZIuzrM+AAD0GPmG+CRJtyXDt0k6K9cFzcwknSTpvs4sDwBAT5dviO/l7q8nw/+U\ntFcr81WbWa2ZLTCzdFDvKWmju9cl42skjcizPgAA9BiV7c1gZn+U9K4sk67MHHF3NzNvZTVj3H2t\nme0j6VEzWyppU0cqamZTJE1JRnea2bKOLB+JYZLeLHUlukh33Ta2Kz7dddvYrvjsn+8K2g1xd/9g\na9PM7A0zG+7ur5vZcEnrWlnH2uR9lZk9LukwSb+VNNjMKpOj8ZGS1rZRj2mSpiWfW+vuqfbqHpvu\nul1S9902tis+3XXb2K74mFltvuvI93T6bEkXJsMXSrq/+QxmNsTMqpLhYZImSFru7i7pMUlnt7U8\nAADILt8Qv07Sh8xshaQPJuMys5SZ3ZLMc6CkWjN7ViG0r3P35cm0yyVdZmYrFa6R/yrP+gAA0GO0\nezq9Le7+lqR/y1JeK+kzyfBfJb23leVXSTqyEx89rRPLxKC7bpfUfbeN7YpPd902tis+eW+bhbPa\nAAAgNnS7CgBApMo2xM3sHDN7zswazKzVlolmNtHMXki6bp2aUV6WXbrm0lWtmZ2Y0U3tYjPbkb6/\n3sx+bWarM6YdWvytaKk7d8Gb4z471MyeTP5ml5jZuRnTymqftfadyZheleyDlck+GZsx7Yqk/AUz\n+3Ax692eHLbrMjNbnuyf+WY2JmNa1r/LcpHDtl1kZusztuEzGdMuTP52V5jZhc2XLaUctuvHGdv0\nopltzJhWtvvMzKab2Tpr5VZoC36abPcSMzs8Y1rH9pe7l+VLoUHc/pIel5RqZZ4KSS9J2kdSH0nP\nSnpPMu0eSZOT4V9IuqTU25TU5QeSpibDUyV9v535h0p6W1K/ZPzXks4u9XZ0drskbWmlvCz3V67b\nJundksYnw3tLel3S4HLbZ219ZzLm+YKkXyTDkyXdnQy/J5m/StK4ZD0Vpd6mDmzXiRnfo0vS29XW\n32U5vHLctosk3Zhl2aGSViXvQ5LhIaXeply3q9n8X5I0PZJ9dpykwyUta2X6qZLmSDJJR0t6qrP7\nq2yPxN39eXd/oZ3ZjpS00t1XufsuSTMlTTIr6y5dO9pV7dmS5rj7ti6tVf66cxe87W6bu7/o7iuS\n4X8o9JlQU7Qa5i7rd6bZPJn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XZCktlR5+2OcxT7fXXj4Jy9Spvnoa97kBgBBvlupq6bXXUq3t2bPrTh4iSZ06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\n2gEAQD0shJDrOjRbSUlJKC8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "actual_x = np.array([0.0,0.0,0.0]) #ロボットの実際の姿勢\n", "particles = [Particle(1.0/100) for i in range(100)]\n", "u = np.array([0.2,math.pi / 180.0 * 20]) #ロボットの移動\n", "\n", "path = [actual_x]\n", "particle_path = [copy.deepcopy(particles)]\n", "measurementss = [observations(actual_x, actual_landmarks)]\n", "for i in range(10):\n", " actual_x = f(actual_x,u)\n", " path.append(actual_x)\n", " ms = observations(actual_x,actual_landmarks)\n", " measurementss.append(ms)\n", "\n", " for p in particles:\n", " p.pose = f(p.pose,u)\n", " \n", " for m in ms:\n", " change_weights(particles, m)\n", " particle_path.append(copy.deepcopy(particles))\n", "\n", "for i,p in enumerate(path):\n", " draw(path[i],particle_path[i])\n", " draw_landmarks(actual_landmarks)\n", " draw_observations(path[i],measurementss[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## sensor update\n", "\n", "* 実装したのはsensor updateと言われる処理\n", "* ベイズの定理を利用\n", " * $P(A|B) = \\dfrac{P(B|A)P(A)}{P(A,B)} = \\dfrac{P(B|A)P(A)}{\\sum_{A'} P(B|A')P(A')} = \\eta^{-1}P(B|A)P(A) $\n", " * A: 推定したいもの（= 自己位置）\n", " * B: 情報（= ランドマークの観測結果）\n", "* 自己位置推定の式に当てはめる\n", " * $bel (\\boldsymbol{x} | \\boldsymbol{z} ) = \\dfrac{p(\\boldsymbol{z} |\\boldsymbol{x} )bel(\\boldsymbol{x}) }{\\int p(\\boldsymbol{z} |\\boldsymbol{x}' )bel(\\boldsymbol{x}') d \\boldsymbol{x}'} = \\eta^{-1} p(\\boldsymbol{z} |\\boldsymbol{x} )bel(\\boldsymbol{x}) $\n", " * $bel (\\boldsymbol{x})$: パーティクルの分布\n", " * $\\boldsymbol{z}$: 計測したランドマークまでの距離と向き\n", " * $p(\\boldsymbol{z} |\\boldsymbol{x} )$: 姿勢$\\boldsymbol{x}$で計測値$\\boldsymbol{z}$を得るという事象に対する密度\n", " * パーティクルの重みに対して `norm.pdf` を二回かけた時の計算に相当\n", " * $\\eta$: ベイズの定理の分母\n", " * 先ほどのプログラム中の重みの合計 `s` に相当\n", "\n", "## まとめ\n", "\n", "* 観測をパーティクルの分布に反映させた\n", "* 問題\n", " * 重みが特定のパーティクルに偏る\n", " * 数式上は問題がない\n", " * 近似精度が劣化\n", "* 次回: リサンプリング" ] }, { "cell_type": "code", "execution_count": null, 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