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jhitesma/piko-90.ipynb

Created April 8, 2017 16:47
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piko-90.ipynb
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"Autotune data: pts = 256, aux_data_len = 0, timestep = 2.00ms\n"
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}
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"source": [
"%matplotlib inline\n",
"\n",
"# Import all the numerical computing stuff we need...\n",
"\n",
"from dronin import autotune\n",
"import numpy as np\n",
"import pandas\n",
"import math\n",
"from scipy import fftpack, signal\n",
"from bokeh.plotting import figure, show\n",
"from bokeh.io import output_notebook\n",
"from bokeh.models import LinearAxis, Range1d, Span\n",
"\n",
"output_notebook() # Tell bokeh to send plots to notebook\n",
"\n",
"# And load up a datafile of autotune data. In this file, the average\n",
"# motor commands and gyro responses from all 90-120 wobbles during the\n",
"# autotune sequence are stored.\n",
"df, time_step = autotune.read_autotune_lump('/Users/jhitesma/piko-90.bin', filter_freq=55, filter_order=0)#, filter_order=6)\n"
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"# next let's plot what the roll gyro does vs. the flight controller's roll command\n",
"\n",
"p = figure(title=\"roll gyro vs actuators\")\n",
"p.line(df.time, df.gyroX)\n",
"p.extra_y_ranges = { 'actuation' : Range1d(min(df.desiredX), max(df.desiredX)) }\n",
"p.line(df.time, df.desiredX, y_range_name='actuation', color=\"red\")\n",
"p.add_layout(LinearAxis(y_range_name=\"actuation\"), 'right')\n",
"\n",
"show(p)\n",
"\n",
"# Looks really nasty, huh? This is the gyro data vs. the actuator data. They're clearly related\n",
"# but phase is off and shape is a fair bit different."
]
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" return new Date();\n",
" }\n",
" \n",
" var force = false;\n",
" \n",
" if (typeof (window._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
" window._bokeh_onload_callbacks = [];\n",
" window._bokeh_is_loading = undefined;\n",
" }\n",
" \n",
" \n",
" \n",
" if (typeof (window._bokeh_timeout) === \"undefined\" || force === true) {\n",
" window._bokeh_timeout = Date.now() + 0;\n",
" window._bokeh_failed_load = false;\n",
" }\n",
" \n",
" var NB_LOAD_WARNING = {'data': {'text/html':\n",
" \"<div style='background-color: #fdd'>\\n\"+\n",
" \"<p>\\n\"+\n",
" \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
" \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
" \"</p>\\n\"+\n",
" \"<ul>\\n\"+\n",
" \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
" \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
" \"</ul>\\n\"+\n",
" \"<code>\\n\"+\n",
" \"from bokeh.resources import INLINE\\n\"+\n",
" \"output_notebook(resources=INLINE)\\n\"+\n",
" \"</code>\\n\"+\n",
" \"</div>\"}};\n",
" \n",
" function display_loaded() {\n",
" if (window.Bokeh !== undefined) {\n",
" document.getElementById(\"96b1fbbc-1314-4fcf-94f7-146af9ff05a2\").textContent = \"BokehJS successfully loaded.\";\n",
" } else if (Date.now() < window._bokeh_timeout) {\n",
" setTimeout(display_loaded, 100)\n",
" }\n",
" }\n",
" \n",
" function run_callbacks() {\n",
" window._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
" delete window._bokeh_onload_callbacks\n",
" console.info(\"Bokeh: all callbacks have finished\");\n",
" }\n",
" \n",
" function load_libs(js_urls, callback) {\n",
" window._bokeh_onload_callbacks.push(callback);\n",
" if (window._bokeh_is_loading > 0) {\n",
" console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
" return null;\n",
" }\n",
" if (js_urls == null || js_urls.length === 0) {\n",
" run_callbacks();\n",
" return null;\n",
" }\n",
" console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
" window._bokeh_is_loading = js_urls.length;\n",
" for (var i = 0; i < js_urls.length; i++) {\n",
" var url = js_urls[i];\n",
" var s = document.createElement('script');\n",
" s.src = url;\n",
" s.async = false;\n",
" s.onreadystatechange = s.onload = function() {\n",
" window._bokeh_is_loading--;\n",
" if (window._bokeh_is_loading === 0) {\n",
" console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
" run_callbacks()\n",
" }\n",
" };\n",
" s.onerror = function() {\n",
" console.warn(\"failed to load library \" + url);\n",
" };\n",
" console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
" document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
" }\n",
" };var element = document.getElementById(\"96b1fbbc-1314-4fcf-94f7-146af9ff05a2\");\n",
" if (element == null) {\n",
" console.log(\"Bokeh: ERROR: autoload.js configured with elementid '96b1fbbc-1314-4fcf-94f7-146af9ff05a2' but no matching script tag was found. \")\n",
" return false;\n",
" }\n",
" \n",
" var js_urls = [];\n",
" \n",
" var inline_js = [\n",
" function(Bokeh) {\n",
" (function() {\n",
" var fn = function() {\n",
" var docs_json = 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"p = figure(title=\"roll gyrodiff vs actuators\")\n",
"p.line(df.time, df.derivgyroX)\n",
"p.extra_y_ranges = { 'actuation' : Range1d(min(df.desiredX), max(df.desiredX)) }\n",
"p.line(df.time, df.desiredX, y_range_name='actuation', color=\"red\")\n",
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"\n",
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"# If we differentiate the gyro, the shape is more clearly related, but boy is\n",
"# there a lot of noise."
]
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"p = figure(title=\"filtered roll gyrodiff vs actuators\")\n",
"p.line(df.time, df.derivfilteredX)\n",
"p.extra_y_ranges = { 'actuation' : Range1d(min(df.desiredX), max(df.desiredX)) }\n",
"p.line(df.time, df.desiredX, y_range_name='actuation', color=\"red\")\n",
"p.add_layout(LinearAxis(y_range_name=\"actuation\"), 'right')\n",
"\n",
"show(p)\n",
"\n",
"# Low pass filtering clearly helps. Now let's get down to business of finding how the input\n",
"# relates to the output."
]
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" \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
" \"</ul>\\n\"+\n",
" \"<code>\\n\"+\n",
" \"from bokeh.resources import INLINE\\n\"+\n",
" \"output_notebook(resources=INLINE)\\n\"+\n",
" \"</code>\\n\"+\n",
" \"</div>\"}};\n",
" \n",
" function display_loaded() {\n",
" if (window.Bokeh !== undefined) {\n",
" document.getElementById(\"2fef0a03-e222-4d03-aec6-25c44a65eca7\").textContent = \"BokehJS successfully loaded.\";\n",
" } else if (Date.now() < window._bokeh_timeout) {\n",
" setTimeout(display_loaded, 100)\n",
" }\n",
" }\n",
" \n",
" function run_callbacks() {\n",
" window._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
" delete window._bokeh_onload_callbacks\n",
" console.info(\"Bokeh: all callbacks have finished\");\n",
" }\n",
" \n",
" function load_libs(js_urls, callback) {\n",
" window._bokeh_onload_callbacks.push(callback);\n",
" if (window._bokeh_is_loading > 0) {\n",
" console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
" return null;\n",
" }\n",
" if (js_urls == null || js_urls.length === 0) {\n",
" run_callbacks();\n",
" return null;\n",
" }\n",
" console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
" window._bokeh_is_loading = js_urls.length;\n",
" for (var i = 0; i < js_urls.length; i++) {\n",
" var url = js_urls[i];\n",
" var s = document.createElement('script');\n",
" s.src = url;\n",
" s.async = false;\n",
" s.onreadystatechange = s.onload = function() {\n",
" window._bokeh_is_loading--;\n",
" if (window._bokeh_is_loading === 0) {\n",
" console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
" run_callbacks()\n",
" }\n",
" };\n",
" s.onerror = function() {\n",
" console.warn(\"failed to load library \" + url);\n",
" };\n",
" console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
" document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
" }\n",
" };var element = document.getElementById(\"2fef0a03-e222-4d03-aec6-25c44a65eca7\");\n",
" if (element == null) {\n",
" console.log(\"Bokeh: ERROR: autoload.js configured with elementid '2fef0a03-e222-4d03-aec6-25c44a65eca7' but no matching script tag was found. \")\n",
" return false;\n",
" }\n",
" \n",
" var js_urls = [];\n",
" \n",
" var inline_js = [\n",
" function(Bokeh) {\n",
" (function() {\n",
" var fn = function() {\n",
" var docs_json = 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" \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
" \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
" \"</ul>\\n\"+\n",
" \"<code>\\n\"+\n",
" \"from bokeh.resources import INLINE\\n\"+\n",
" \"output_notebook(resources=INLINE)\\n\"+\n",
" \"</code>\\n\"+\n",
" \"</div>\"}};\n",
" \n",
" function display_loaded() {\n",
" if (window.Bokeh !== undefined) {\n",
" document.getElementById(\"0be3cf6a-974b-404b-bcbf-c266dd93f17b\").textContent = \"BokehJS successfully loaded.\";\n",
" } else if (Date.now() < window._bokeh_timeout) {\n",
" setTimeout(display_loaded, 100)\n",
" }\n",
" }\n",
" \n",
" function run_callbacks() {\n",
" window._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
" delete window._bokeh_onload_callbacks\n",
" console.info(\"Bokeh: all callbacks have finished\");\n",
" }\n",
" \n",
" function load_libs(js_urls, callback) {\n",
" window._bokeh_onload_callbacks.push(callback);\n",
" if (window._bokeh_is_loading > 0) {\n",
" console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
" return null;\n",
" }\n",
" if (js_urls == null || js_urls.length === 0) {\n",
" run_callbacks();\n",
" return null;\n",
" }\n",
" console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
" window._bokeh_is_loading = js_urls.length;\n",
" for (var i = 0; i < js_urls.length; i++) {\n",
" var url = js_urls[i];\n",
" var s = document.createElement('script');\n",
" s.src = url;\n",
" s.async = false;\n",
" s.onreadystatechange = s.onload = function() {\n",
" window._bokeh_is_loading--;\n",
" if (window._bokeh_is_loading === 0) {\n",
" console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
" run_callbacks()\n",
" }\n",
" };\n",
" s.onerror = function() {\n",
" console.warn(\"failed to load library \" + url);\n",
" };\n",
" console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
" document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
" }\n",
" };var element = document.getElementById(\"0be3cf6a-974b-404b-bcbf-c266dd93f17b\");\n",
" if (element == null) {\n",
" console.log(\"Bokeh: ERROR: autoload.js configured with elementid '0be3cf6a-974b-404b-bcbf-c266dd93f17b' but no matching script tag was found. \")\n",
" return false;\n",
" }\n",
" \n",
" var js_urls = [];\n",
" \n",
" var inline_js = [\n",
" function(Bokeh) {\n",
" (function() {\n",
" var fn = function() {\n",
" var docs_json = 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" console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
" run_inline_js();\n",
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"</script>"
]
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" </div>\n",
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" window._bokeh_timeout = Date.now() + 0;\n",
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" }\n",
" \n",
" var NB_LOAD_WARNING = {'data': {'text/html':\n",
" \"<div style='background-color: #fdd'>\\n\"+\n",
" \"<p>\\n\"+\n",
" \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
" \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
" \"</p>\\n\"+\n",
" \"<ul>\\n\"+\n",
" \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
" \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
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" \"<code>\\n\"+\n",
" \"from bokeh.resources import INLINE\\n\"+\n",
" \"output_notebook(resources=INLINE)\\n\"+\n",
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"[ 34810092.59873442]\n",
"[ 2244194.6258314]\n",
"[ 20894386.92508978]\n"
]
}
],
"source": [
"def find_real_peak(series):\n",
" p = np.argmax(series)\n",
" \n",
" min_idx = p - 3\n",
" \n",
" if (min_idx < 0):\n",
" min_idx = 0\n",
" \n",
" max_idx = p + 3\n",
" \n",
" if (max_idx >= len(series)):\n",
" max_idx = len(series) - 1\n",
" \n",
" fit = np.polyfit(range(min_idx, max_idx+1), series[min_idx:max_idx+1], 2)\n",
" \n",
" peak = fit[1] / -fit[0] / 2\n",
"\n",
" return fit[1] / -fit[0] / 2\n",
"\n",
"\n",
"\n",
"# For now, we just want to figure the parameters that existing autotune\n",
"# uses, but in a more accurate and more robust way. In the future we'll\n",
"# do much fancier things.\n",
"\n",
"# So, for each of the three axes, let's perform fourier analysis in order to\n",
"# correlate the differentiated, filtered gyros vs. the actuator command.\n",
"# This will tell us the delay, or tau. From \n",
"\n",
"def compute_axis(desired_series, diff_gyro_series, filter_order=3,\n",
" percentile_cutoff=2, plot_tau=True, series_cutoff=2,\n",
" axis_name=\"\"):\n",
" desired_fft = fftpack.fft(desired_series)\n",
" diff_fft = fftpack.fft(diff_gyro_series)\n",
"\n",
" desired_fft_r = -desired_fft.conjugate()\n",
"\n",
" correl = fftpack.ifft(desired_fft_r * diff_fft) \n",
"\n",
" tau_offset = find_real_peak(np.abs(correl[0:len(correl)/series_cutoff]))\n",
" \n",
" if plot_tau:\n",
" p = figure(title=\"%s delay time vs. correlation\"%(axis_name), y_axis_type = \"log\")\n",
" p.line(np.linspace(0,len(correl) / 2 * time_step, len(correl) / 2), np.abs(correl[0:len(correl)/2]))\n",
" tauspan = Span(location=tau_offset * time_step, dimension='height', line_color='red', line_width=1)\n",
" #bogospan = Span(location=.0168, dimension='height', line_color='green', line_width=1)\n",
" #p.renderers.extend([bogospan])\n",
" p.renderers.extend([tauspan])\n",
" show(p)\n",
"\n",
" # half cycles per sample.e\n",
" filter_edge = filter_order / tau_offset / 3.14159 / 1.22\n",
"\n",
" # A nth order filter doesn't result in n* the delay with bessel\n",
" # design technique. 1.22 is a fudge factor for order 3. Not sure where\n",
" # 1.22 comes from :D\n",
" db, da = signal.iirfilter(filter_order, [filter_edge], btype='lowpass', ftype='bessel')\n",
"\n",
" #w, gd = signal.group_delay((db, da))\n",
" #p = figure()\n",
" #p.line(w, gd)\n",
" #show(p)\n",
" \n",
" desired_series = pandas.concat([desired_series, desired_series], ignore_index = True)\n",
" \n",
" delayedact = signal.lfilter(db, da, desired_series)\n",
" \n",
" delayedact = delayedact[len(delayedact)/2:]\n",
" \n",
" # Now compare the response magnitude of the filtered waveform vs. the\n",
" # differentiated gyro series, to compute beta and then the bias.\n",
" span_desired = np.percentile(delayedact, [percentile_cutoff, 100-percentile_cutoff])\n",
"\n",
" span_gyrodiff = np.percentile(diff_gyro_series, [percentile_cutoff, 100-percentile_cutoff])\n",
"\n",
" lin_gain = (span_gyrodiff[1]-span_gyrodiff[0]) / (span_desired[1]-span_desired[0])\n",
" \n",
" bias = delayedact.mean() * lin_gain - diff_gyro_series.mean()\n",
"\n",
" return (tau_offset, lin_gain, bias, delayedact * lin_gain - bias)\n",
" \n",
"def compute_axis_by_name(series_name, do_plots=True, series_cutoff=2):\n",
" desired = df['desired'+series_name]\n",
" deriv_filtered = df['derivfiltered'+series_name]\n",
" \n",
" tau_offset, lin_gain, bias, adjact = compute_axis(desired, deriv_filtered, plot_tau=do_plots,\n",
" series_cutoff=series_cutoff,\n",
" axis_name=series_name)\n",
" \n",
" df['adjdesired' + series_name] = pandas.Series(adjact)\n",
" \n",
" print \"Axis %s: tau=%.1f samples (%0.2f ms / %0.3f)\"%(series_name, tau_offset, tau_offset*time_step*1000, math.log(tau_offset*time_step))\n",
" print \"\\tgain=%0.1f (beta=%0.3f), bias=%0.1f\"%(lin_gain, math.log(lin_gain / time_step), bias)\n",
" \n",
" if (do_plots):\n",
" p = figure(title=\"%s shifted to line up\"%(series_name))\n",
" \n",
" p.line(df.time, deriv_filtered)\n",
" p.line(df.time, adjact, color=\"green\")\n",
"\n",
" show(p)\n",
" \n",
" p = figure(title=\"residual %s\"%(series_name))\n",
" \n",
" p.line(df.time, deriv_filtered - adjact)\n",
" show(p)\n",
"\n",
"compute_axis_by_name(\"X\", series_cutoff=5)\n",
"compute_axis_by_name(\"Y\", series_cutoff=5)\n",
"compute_axis_by_name(\"Z\", series_cutoff=5)\n",
"\n",
"print np.correlate(df.derivfilteredX, df.derivfilteredX)\n",
"print np.correlate(df.derivfilteredX, df.derivfilteredY)\n",
"print np.correlate(df.derivfilteredX, df.derivfilteredZ)\n",
"print np.correlate(df.derivfilteredY, df.derivfilteredY)\n",
"print np.correlate(df.derivfilteredY, df.derivfilteredZ)\n",
"print np.correlate(df.derivfilteredZ, df.derivfilteredZ)"
]
},
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