02-01_interval_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "from ipynb.fs.defs.utilities import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interval analysis for the determination of the workspace of an electromagnetic navigation system\n",
    "\n",
    "\n",
    "The interval analysis method for the determination of the workspace of 2d electromagnetic navigation system is adapted from the approch proposed in [Gouttefarde 2011](https://ieeexplore.ieee.org/document/5657268) for parallel cable-driven robot.\n",
    "\n",
    "The method essentially consists in using interval arithmetic to check boxes of space instead of individual poses.\n",
    "\n",
    "This is valid for linear magnetic model with dipole terms only (see .yaml file in the models folder of this repository).\n",
    "\n",
    "**N.B.** This notebook requires the library [PyInterval](https://pyinterval.readthedocs.io/en/latest/index.html) and the [python binding](https://benensta.github.io/pyIbex/) of [ibex](http://www.ibex-lib.org/).\n",
    "\n",
    "The method is applied here to a 2d example previously treated with a discretization approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Application to a 2D example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load systems calibration\n",
    "cal_path_mns = 'models/mns_2coils_90deg.yaml'\n",
    "model_mns = ForwardModelMPEM()\n",
    "model_mns.setCalibrationFile(cal_path_mns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Build initial box\n",
    "pmin = -0.1\n",
    "pmax = 0.1\n",
    "xi = interval[pmin, pmax] \n",
    "yi = interval[pmin, pmax]\n",
    "z = 0.\n",
    "InitBox = Create2DBox(xi,yi)\n",
    "\n",
    "#Define inputs interval and task set\n",
    "Imin = -1\n",
    "Imax = 1\n",
    "bmin = -0.02\n",
    "bmax = 0.02\n",
    "\n",
    "#Load system model\n",
    "yaml_file = open(cal_path_mns)\n",
    "parsed_yaml_file = yaml.load(yaml_file, Loader=yaml.FullLoader)\n",
    "\n",
    "#Define precision of bissection and run the determination algoritgm\n",
    "eps = 0.005\n",
    "L, Lin, Lout, Lneg, iteration = Ws2DDetermination(InitBox, bmin, bmax, Imin, Imax, eps, parsed_yaml_file,z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "    // Updates the figure title.\n",
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       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
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       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
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       "\n",
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       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
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       "            return;\n",
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       "            fig.imageObj.src = evt.data;\n",
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       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"799.3333333333334\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Workspace determination by interval analysis')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coil_length = 0.05\n",
    "coil_width = 0.03\n",
    "\n",
    "fig = plt.figure(figsize=(8, 4))\n",
    "\n",
    "ax = fig.gca()\n",
    "\n",
    "#Plot rectangle in\n",
    "for i in range(len(Lin)):\n",
    "    Box = Lin[i]\n",
    "    xo = Box[0][0][0][0]\n",
    "    yo = Box[1][0][0][0]\n",
    "    dx = Box[0][0][0][1] - xo\n",
    "    dy = Box[1][0][0][1] - yo\n",
    "    rect = patches.Rectangle((xo,yo),dx,dy,linewidth=1,edgecolor='black',facecolor='green',alpha=0.5)\n",
    "    ax.add_patch(rect)\n",
    "    \n",
    "#Plot rectangle undetermined\n",
    "for i in range(len(Lneg)):\n",
    "    Box = Lneg[i]\n",
    "    xo = Box[0][0][0][0]\n",
    "    yo = Box[1][0][0][0]\n",
    "    dx = Box[0][0][0][1] - xo\n",
    "    dy = Box[1][0][0][1] - yo\n",
    "    rect = patches.Rectangle((xo,yo),dx,dy,linewidth=1,edgecolor='black',facecolor='gray',alpha=0.2)\n",
    "    ax.add_patch(rect)\n",
    "    \n",
    "#Plot rectangle out\n",
    "for i in range(len(Lout)):\n",
    "    Box = Lout[i]\n",
    "    xo = Box[0][0][0][0]\n",
    "    yo = Box[1][0][0][0]\n",
    "    dx = Box[0][0][0][1] - xo\n",
    "    dy = Box[1][0][0][1] - yo\n",
    "    rect = patches.Rectangle((xo,yo),dx,dy,linewidth=1,edgecolor='black',facecolor='red',alpha=0.2)\n",
    "    ax.add_patch(rect)\n",
    "\n",
    "#Plot coils\n",
    "coll = Coils2DPatch(coil_length,coil_width,cal_path_mns)\n",
    "ax.add_collection(coll)\n",
    " \n",
    "#Plot figure\n",
    "plt.show()\n",
    "ax.axis('equal')\n",
    "ax.set_title('Workspace determination by interval analysis')\n"
   ]
  }
 ],
 "metadata": {
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