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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Plotting from NPendulum Environment"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In Explauto, an *environment* implements the physical properties of the interaction between the robot body and the environment in which it evolves. Explauto come with several sensorimotor systems available from the [environment package](http://flowersteam.github.io/explauto/explauto.environment.html). To learn how to set an environment, look at the notebook [Setting Environments](https://github.com/flowersteam/explauto/blob/master/notebook/setting_environments.ipynb)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from explauto.environment import environments\n",
      "print 'Available environments: {}'.format(environments.keys())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Available environments: ['npendulum', 'pendulum', 'simple_arm']\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will use the npendulum environment for this tutorial. It consists in the simulation of a multiple pendulum with $n+1$ nodes, aiming to model a string. The first node is the one which undergoes the input force.\n",
      "\n",
      "This environment comes with a predefined configuration, named *default*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "env_cls, env_configs, _ = environments['npendulum']\n",
      "print 'Available configurations for the simple arm environment: {}'.format(env_configs.keys())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Available configurations for the simple arm environment: ['default']\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the case of the npendulum environment, a configuration must defines the following values:\n",
      "* nb_joints (number $n$ of the joints)\n",
      "* m_mins and m_maxs (bounds of the motor space)\n",
      "* s_mins ans s_maxs (bounds of the sensory space)\n",
      "* length_ratio (length ratio from one segment to the following one)\n",
      "* noise (gaussian noise added in the sensor space)\n",
      "\n",
      "For more advanced settings, please look at the [npendulum environment documentation](http://flowersteam.github.io/explauto/explauto.environment.html#explauto.environment.npendulum.npendulum.NPendulumEnvironment).\n",
      "\n",
      "Then we create the Environment instance."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "config = env_configs['default']\n",
      "\n",
      "print 'Default configuration for the npendulum:'\n",
      "for config_key, value in config.items():\n",
      "    print '\\t{}: {}'.format(config_key, value)\n",
      "\n",
      "environment = env_cls(**config)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Default configuration for the npendulum:\n",
        "\ts_mins: [-450.   -1.]\n",
        "\tm_mins: [-0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1]\n",
        "\tnoise: 0.02\n",
        "\ts_maxs: [ 450.    1.]\n",
        "\tm_maxs: [ 0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1]\n",
        "\tn: 5\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Each environment has an [update](http://flowersteam.github.io/explauto/explauto.environment.html#explauto.environment.environment.Environment.update) method, we take as argument a motor command vector $m$. It computes $m\\_bounds$, the command $m$ bounded according to the configuration used (m_mins, m_maxs values), then computes the corresponding sensory effect vector $s$ and returns the position and velocity of the last effector.\n",
      "\n",
      "$m$ is a list of ten elements that are the amplitude of each step function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi\n",
      "m = [0.01,0.06,-0.05,0.01,0.,0.,0.,0.,-0.1,0.01]\n",
      "print environment.update(m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  1.00000000e-02   6.00000000e-02  -5.00000000e-02   1.00000000e-02\n",
        "   0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
        "  -1.00000000e-01   1.00000000e-02   8.15708828e+01  -6.32193953e-01]\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then, we add the noise :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s = environment.compute_sensori_effect(m)\n",
      "print s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The simple arm environment also comes with few methods to visualize the arm shape for a given motor configuration."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first one plot the position of the end effector at the end of the movement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "\n",
      "ax = axes()\n",
      "environment.plot_s(ax, s)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['pi']\n",
        "`%matplotlib` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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       "text": [
        "<matplotlib.figure.Figure at 0x7fb4f7169990>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second one computes and plots the position of the end effector from $m$. In this example, we generate goals and plot them."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "\n",
      "motor_configurations = environment.random_motors(n=5)\n",
      "ax = axes()\n",
      "for m in motor_configurations:\n",
      "    environment.plot_and_compute(ax, m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEPCAYAAABGP2P1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLTsAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb4f715d050>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The third one plots the whole npendulum. The squared point is the end effector."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "\n",
      "motor_configurations = environment.random_motors(n=1)\n",
      "ax = axes()\n",
      "for m in motor_configurations:\n",
      "    environment.plot_npendulum(ax, m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gdeI0NCSS4iIRmDHDVhdNnWq9BUku3Y9ARALpww/tbOQRI+DRR3U2cjK5niMQEYmpb19b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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb4f46da110>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The last one generates .png files that contains the whole pendulum image, in order to create a video. The computation may take few minutes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "m = [0.01,0.06,-0.05,0.01,0.,0.,0.,0.,-0.1,0.01]\n",
      "environment.animate_pendulum(m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb4f5fc7b50>"
       ]
      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}