1391 lines
38 KiB
Plaintext
1391 lines
38 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "da2f6efd",
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"metadata": {},
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"source": [
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"# Fun with Aruco\n",
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"\n",
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"We use Aruco markers to calculate the angular velocity of cheap-ish stage lighting"
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]
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},
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{
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"cell_type": "markdown",
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"id": "23bed7f2",
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"metadata": {},
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"source": [
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"## Imports"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "91e61bf0",
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"metadata": {},
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"outputs": [],
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"source": [
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"import math\n",
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"\n",
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"import numpy as np\n",
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"import scipy.signal\n",
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"import cv2, PIL\n",
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"from cv2 import aruco\n",
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"import matplotlib as mpl\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e1742fba",
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"metadata": {},
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"source": [
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"## Marker\n",
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"\n",
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"The marker that should be printed (ours was drawn by hand ¯\\\\\\_(ツ)\\_/¯)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "7337ad91",
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"metadata": {},
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"outputs": [],
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"source": [
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"aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)\n",
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"img = aruco.drawMarker(aruco_dict, 1, 700)\n",
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"\n",
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"fig, ax = plt.subplots()\n",
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"ax.imshow(img, cmap = mpl.cm.gray, interpolation = \"nearest\")\n",
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"ax.axis(\"off\")\n",
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"\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e5a9c142",
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"metadata": {},
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"source": [
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"## Input\n",
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"\n",
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"We read a captured video file and find the rotation of the marker."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "b574834e",
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"metadata": {},
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"outputs": [],
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"source": [
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"def read_rotation_data(video_filename, roi_topleft, roi_bottomright):\n",
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" cap = cv2.VideoCapture(video_filename)\n",
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" fps = cap.get(cv2.CAP_PROP_FPS)\n",
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"\n",
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" phi = []\n",
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" t = []\n",
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"\n",
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" frames_ok = 0\n",
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" frames_err = 0\n",
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" \n",
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" report = int(fps + 0.5)\n",
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" \n",
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" while cap.isOpened():\n",
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" # get frame data\n",
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" frame_id = cap.get(1)\n",
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" ret, frame = cap.read()\n",
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" if not ret:\n",
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" break\n",
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" \n",
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" # get region of interest\n",
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" (a, b) = roi_topleft\n",
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" (c, d) = roi_bottomright\n",
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" roi = frame[b:d, a:c]\n",
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"\n",
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" # find aruco marker\n",
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" corners, ids, rejectedImgPoints = aruco.detectMarkers(roi, aruco_dict)\n",
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"\n",
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" # calculate direction\n",
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" try:\n",
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" [[[a, b, c, d]]] = corners\n",
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" p1 = (a + b) / 2\n",
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" p2 = (d + c) / 2\n",
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"\n",
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" [x1, y1] = map(int, p1)\n",
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" [x2, y2] = map(int, p2)\n",
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"\n",
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" [dx, dy] = p2 - p1\n",
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" dy *= -1 # coordinates start in top left of image\n",
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" # so y axis is flipped\n",
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"\n",
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" phi.append(math.atan2(dy, dx))\n",
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" frames_ok += 1\n",
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" except ValueError as e:\n",
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" phi.append(None)\n",
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" frames_err += 1\n",
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" \n",
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" # time\n",
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" t.append(frame_id / fps)\n",
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" \n",
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" if frame_id % report == 0:\n",
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" print(f\"\\r{frames_ok} frames ok, {frames_err} frames err\", end=\"\")\n",
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" \n",
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" print()\n",
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" del cap\n",
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" return t, phi"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e431d5af",
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"metadata": {},
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"source": [
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"The input contains several periods of the head moving back and forth.\n",
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"We overlay them on top of each other, such that we can average them later"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "b5d07cc1",
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"metadata": {},
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"outputs": [],
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"source": [
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"def overlay(global_t, global_phi, offset, period, flip_even=True):\n",
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" \n",
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" merged_t = []\n",
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" phi = []\n",
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" \n",
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" for (t, v) in zip(global_t, global_phi):\n",
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" (n, relative_t) = divmod(t + offset, period)\n",
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" \n",
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" # filter undetected markers\n",
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" if not v:\n",
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" continue\n",
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" \n",
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" # flip even periods\n",
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" if flip_even and n % 2 == 0:\n",
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" v *= -1\n",
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" \n",
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" phi.append(v)\n",
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" merged_t.append(relative_t)\n",
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" \n",
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" return merged_t, phi"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7c461964",
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"metadata": {},
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"source": [
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"Since our data is in the form `(timestamp, value)`, we need to group several data points into buckets before we can calculate the average."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c1c2def4",
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"metadata": {},
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"outputs": [],
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"source": [
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"def get_buckets(t, phi, bucket_size):\n",
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" t_max = max(t)\n",
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" num_buckets = int(t_max // bucket_size + 1.5)\n",
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" \n",
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" buckets = [[] for _ in range(num_buckets)]\n",
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"\n",
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" for (now, v) in zip(t, phi):\n",
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" buckets[int(now // bucket_size)].append(v)\n",
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" \n",
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" return buckets"
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]
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},
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{
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"cell_type": "markdown",
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"id": "91576c76",
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"metadata": {},
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"source": [
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"# Tilt 180 Degrees"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "62131fc1",
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"metadata": {},
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"outputs": [],
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"source": [
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"cap = cv2.VideoCapture(\"tilt_180.mp4\")\n",
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"fps = cap.get(cv2.CAP_PROP_FPS)\n",
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"\n",
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"phi = []\n",
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"t = []\n",
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"\n",
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"frames_ok = 0\n",
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"frames_err = 0\n",
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"\n",
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"report = int(fps + 0.5)\n",
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"\n",
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"while cap.isOpened():\n",
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" # get frame data\n",
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" frame_id = cap.get(1)\n",
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" ret, frame = cap.read()\n",
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" break\n",
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"\n",
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"del cap\n",
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"\n",
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"fig = plt.figure(figsize=(15, 7))\n",
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"ax = fig.add_subplot(1, 2, 1)\n",
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"ax.imshow(frame)\n",
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"\n",
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"roi_topleft = (1400, 600)\n",
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"roi_bottomright = (2300, 1500)\n",
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"\n",
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"(a, b) = roi_topleft\n",
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"(c, d) = roi_bottomright\n",
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"roi = frame[b:d, a:c]\n",
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"\n",
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"ax = fig.add_subplot(1, 2, 2)\n",
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"ax.imshow(roi)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8b9e1d0d",
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"metadata": {},
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"outputs": [],
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"source": [
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"global_t, global_phi = read_rotation_data(\"tilt_180.mp4\", (1400, 600), (2300, 1500))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "a9b830fc",
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"metadata": {},
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"outputs": [],
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"source": [
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"fig = plt.figure(figsize=(15, 7))\n",
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"ax = fig.add_subplot()\n",
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"ax.plot(global_t, global_phi)\n",
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"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
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"ax.set_xlabel(\"Time [s]\")\n",
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"ax.set_ylabel(\"Angle [rad]\")\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "91ac96c4",
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"metadata": {},
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"outputs": [],
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"source": [
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"# raw\n",
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"\n",
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"period = 5\n",
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"t, phi = overlay(global_t, global_phi, 3.07, 2 * period, flip_even = False)\n",
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"\n",
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"# fix discontinuity and shift so 0 is vertical center\n",
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"for (i, x) in enumerate(t):\n",
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" if phi[i] < -1:\n",
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" phi[i] += math.tau\n",
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" phi[i] -= math.tau / 2\n",
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" \n",
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"# overlay again to merge both motions\n",
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"\n",
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"t, phi = overlay(t, phi, 0, period)\n",
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"\n",
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"phi_0 = phi[np.argmin(t)]\n",
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"\n",
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"for i in range(len(phi)):\n",
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" phi[i] -= phi_0\n",
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"\n",
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"# average\n",
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"\n",
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"bucket_size = dt = 0.025\n",
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"buckets = get_buckets(t, phi, bucket_size)\n",
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"bucket_offset = bucket_size / 2\n",
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"\n",
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"t_tilt = np.linspace(0 + bucket_offset, period + bucket_offset, len(buckets))\n",
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"pos_tilt = [sum(bucket) / len(bucket) for bucket in buckets]\n",
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"\n",
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"# velocity\n",
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"\n",
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"vel_tilt = np.diff(pos_tilt, prepend=0) / dt\n",
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"\n",
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"# acceleration\n",
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"\n",
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"n = 7 # the larger n is, the smoother curve will be\n",
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"b = [1.0 / n] * n\n",
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"a = 1\n",
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"vel_tilt_filtered = scipy.signal.lfilter(b,a,vel_tilt)\n",
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"\n",
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"acc_tilt = np.diff(vel_tilt_filtered, prepend=0) / dt"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "3df2b5ce",
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"metadata": {},
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"outputs": [],
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"source": [
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"fig = plt.figure(figsize=(15,15))\n",
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"\n",
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"# raw\n",
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" \n",
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"ax = fig.add_subplot(3,1,1)\n",
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"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
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"ax.set_ylabel(\"Angle [rad]\")\n",
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"ax.scatter(t, phi, color=\"lightgray\")\n",
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"\n",
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"# average\n",
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"\n",
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"ax.plot(t_tilt, pos_tilt)\n",
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"\n",
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"# velocity\n",
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"\n",
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"ax = fig.add_subplot(3,1,2)\n",
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"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
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"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
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"ax.plot(t_tilt, vel_tilt)\n",
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"ax.plot(t_tilt, vel_tilt_filtered, color=\"gray\")\n",
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"\n",
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"acc_start_time = 0.65\n",
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"acc_stop_time = 0.9\n",
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"dec_start_time = 1.5\n",
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"dec_stop_time = 1.85\n",
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"\n",
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"for x in [acc_start_time, acc_stop_time, dec_start_time, dec_stop_time]:\n",
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" ax.axvline(x, color='gray', linestyle='dotted')\n",
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"\n",
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"# acceleration\n",
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"\n",
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"ax = fig.add_subplot(3,1,3)\n",
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"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
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"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
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"ax.set_xlabel(\"Time [s]\")\n",
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"ax.plot(t_tilt, acc_tilt)\n",
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"\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "89e17f29",
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"metadata": {},
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"outputs": [],
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"source": [
|
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"# approximated constant acceleration\n",
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"\n",
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"acc_tilt_approx = np.zeros(len(acc_tilt))\n",
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"\n",
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"t_0 = acc_stop_time - acc_start_time\n",
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"t_1 = dec_start_time - acc_stop_time\n",
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"t_2 = dec_stop_time - dec_start_time\n",
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"h = pos_tilt[-1] # 0.5 * math.tau\n",
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"\n",
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"acc_start = np.searchsorted(t_tilt, acc_start_time)\n",
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"acc_stop = np.searchsorted(t_tilt, acc_stop_time)\n",
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"\n",
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"acc_value = h / ((t_0 / 2 + t_1 + t_2 / 2) * t_0)\n",
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"\n",
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"print(f\"acceleration: {acc_value: .2f} ({acc_value / math.pi: .2f} pi)\")\n",
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"\n",
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"dec_start = np.searchsorted(t_tilt, dec_start_time)\n",
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"dec_stop = np.searchsorted(t_tilt, dec_stop_time)\n",
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"\n",
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"dec_value = -1 * acc_value * (acc_stop - acc_start) / (dec_stop - dec_start)\n",
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"\n",
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"print(f\"deceleration: {dec_value: .2f} ({dec_value / math.pi: .2f} pi)\")\n",
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"\n",
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"acc_tilt_approx[acc_start:acc_stop].fill(acc_value)\n",
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"acc_tilt_approx[dec_start:dec_stop].fill(dec_value)\n",
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"\n",
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"# approximated velocity\n",
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"\n",
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"vel_tilt_approx = np.cumsum(acc_tilt_approx) * dt\n",
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"\n",
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"# approximated position\n",
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"\n",
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"pos_tilt_approx = np.cumsum(vel_tilt_approx) * dt"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "b0bc02f4",
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"metadata": {},
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"outputs": [],
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"source": [
|
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"fig = plt.figure(figsize=(15,15))\n",
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"\n",
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"# raw\n",
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" \n",
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"ax = fig.add_subplot(3,1,1)\n",
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"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
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"ax.set_ylabel(\"Angle [rad]\")\n",
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"ax.scatter(t, phi, color=\"lightgray\")\n",
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"\n",
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"# average\n",
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"\n",
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"ax.plot(t_tilt, pos_tilt)\n",
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"\n",
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"ax.plot(t_tilt, pos_tilt_approx)\n",
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"\n",
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"# velocity\n",
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"\n",
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"ax = fig.add_subplot(3,1,2)\n",
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"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
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"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
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"ax.plot(t_tilt, vel_tilt)\n",
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"ax.plot(t_tilt, vel_tilt_filtered, color=\"gray\", linestyle=\"dotted\")\n",
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"\n",
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"for x in [acc_start_time, acc_stop_time, dec_start_time, dec_stop_time]:\n",
|
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" ax.axvline(x, color='gray', linestyle='dotted')\n",
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" \n",
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"ax.plot(t_tilt, vel_tilt_approx)\n",
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"\n",
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"# acceleration\n",
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"\n",
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"ax = fig.add_subplot(3,1,3)\n",
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"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
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"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
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"ax.set_xlabel(\"Time [s]\")\n",
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"ax.plot(t_tilt, acc_tilt, color=\"lightgray\")\n",
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"\n",
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"for x in [acc_start_time, acc_stop_time, dec_start_time, dec_stop_time]:\n",
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" ax.axvline(x, color='gray', linestyle='dotted')\n",
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" \n",
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|
"ax.plot(t_tilt, acc_tilt_approx, color=\"C1\")\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "163e4dca",
|
|
"metadata": {},
|
|
"source": [
|
|
"# 360 Degrees"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "e7c5bd8b",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"global_t, global_phi = read_rotation_data(\"rotate_360.mp4\", (600, 1500), (1500, 2400))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "4be22807",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15, 7))\n",
|
|
"ax = fig.add_subplot()\n",
|
|
"ax.plot(global_t, global_phi)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "7d6f3694",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# raw\n",
|
|
"\n",
|
|
"period = 5\n",
|
|
"t, phi = overlay(global_t, global_phi, 2.5, period)\n",
|
|
"\n",
|
|
"# fix discontinuity\n",
|
|
"for (i, x) in enumerate(t):\n",
|
|
" if phi[i] < 3 * x - 5:\n",
|
|
" phi[i] += math.tau\n",
|
|
"\n",
|
|
"# average\n",
|
|
"\n",
|
|
"bucket_size = dt = 0.025\n",
|
|
"buckets = get_buckets(t, phi, bucket_size)\n",
|
|
"bucket_offset = bucket_size / 2\n",
|
|
"\n",
|
|
"t_360 = np.linspace(0 + bucket_offset, period + bucket_offset, len(buckets))\n",
|
|
"pos_360 = [sum(bucket) / len(bucket) for bucket in buckets]\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"vel_360 = np.diff(pos_360, prepend=0) / dt\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"n = 7 # the larger n is, the smoother curve will be\n",
|
|
"b = [1.0 / n] * n\n",
|
|
"a = 1\n",
|
|
"vel_360_filtered = scipy.signal.lfilter(b,a,vel_360)\n",
|
|
"\n",
|
|
"acc_360 = np.diff(vel_360_filtered, prepend=0) / dt"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "f659cc9a",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15,15))\n",
|
|
"\n",
|
|
"# raw\n",
|
|
" \n",
|
|
"ax = fig.add_subplot(3,1,1)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"ax.scatter(t, phi, color=\"lightgray\")\n",
|
|
"\n",
|
|
"# average\n",
|
|
"\n",
|
|
"ax.plot(t_360, pos_360)\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,2)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
|
|
"ax.plot(t_360, vel_360)\n",
|
|
"ax.plot(t_360, vel_360_filtered, color=\"gray\")\n",
|
|
"\n",
|
|
"for x in [0.65, 1.45, 2.3, 3.25]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,3)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.plot(t_360, acc_360)\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "6e7da8e8",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Approximation\n",
|
|
"\n",
|
|
"From the velocity graph, it looks like the acceleration is fairly constant:\n",
|
|
"There are distinct phases where the head is accelerating and decelerating, and the velocity is constant everywhere else.\n",
|
|
"\n",
|
|
"Sadly, the noise in the acceleration graph is too strong to confirm this behavior.\n",
|
|
"Therefore, we take the start and stop times which we can see in the velocity graph, and calculate what constant acceleration would be necessary to produce these curves:\n",
|
|
"\n",
|
|
"<img src=\"formula.png\">"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "106d2335",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# approximated constant acceleration\n",
|
|
"\n",
|
|
"acc_360_approx = np.zeros(len(acc_360))\n",
|
|
"\n",
|
|
"acc_start_time = 0.65\n",
|
|
"acc_stop_time = 1.45\n",
|
|
"dec_start_time = 2.3\n",
|
|
"dec_stop_time = 3.25\n",
|
|
"\n",
|
|
"t_0 = acc_stop_time - acc_start_time\n",
|
|
"t_1 = dec_start_time - acc_stop_time\n",
|
|
"t_2 = dec_stop_time - dec_start_time\n",
|
|
"h = math.tau\n",
|
|
"\n",
|
|
"acc_start = np.searchsorted(t_360, 0.65)\n",
|
|
"acc_stop = np.searchsorted(t_360, 1.45)\n",
|
|
"\n",
|
|
"acc_value = h / ((t_0 / 2 + t_1 + t_2 / 2) * t_0)\n",
|
|
"\n",
|
|
"print(f\"acceleration: {acc_value: .2f} ({acc_value / math.pi: .2f} pi)\")\n",
|
|
"\n",
|
|
"dec_start = np.searchsorted(t_360, 2.3)\n",
|
|
"dec_stop = np.searchsorted(t_360, 3.25)\n",
|
|
"\n",
|
|
"dec_value = -1 * acc_value * (acc_stop - acc_start) / (dec_stop - dec_start)\n",
|
|
"\n",
|
|
"print(f\"deceleration: {dec_value: .2f} ({dec_value / math.pi: .2f} pi)\")\n",
|
|
"\n",
|
|
"acc_360_approx[acc_start:acc_stop].fill(acc_value)\n",
|
|
"acc_360_approx[dec_start:dec_stop].fill(dec_value)\n",
|
|
"\n",
|
|
"# approximated velocity\n",
|
|
"\n",
|
|
"vel_360_approx = np.cumsum(acc_360_approx) * dt\n",
|
|
"\n",
|
|
"# approximated position\n",
|
|
"\n",
|
|
"pos_360_approx = np.cumsum(vel_360_approx) * dt"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "48716f50",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15,15))\n",
|
|
"\n",
|
|
"# raw\n",
|
|
" \n",
|
|
"ax = fig.add_subplot(3,1,1)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"ax.scatter(t, phi, color=\"lightgray\")\n",
|
|
"\n",
|
|
"# average\n",
|
|
"\n",
|
|
"ax.plot(t_360, pos_360)\n",
|
|
"\n",
|
|
"ax.plot(t_360, pos_360_approx)\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,2)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
|
|
"ax.plot(t_360, vel_360)\n",
|
|
"ax.plot(t_360, vel_360_filtered, color=\"gray\", linestyle=\"dotted\")\n",
|
|
"\n",
|
|
"for x in [0.65, 1.45, 2.3, 3.25]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
" \n",
|
|
"ax.plot(t_360, vel_360_approx)\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,3)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.plot(t_360, acc_360, color=\"lightgray\")\n",
|
|
"\n",
|
|
"for x in [0.65, 1.45, 2.3, 3.25]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
" \n",
|
|
"ax.plot(t_360, acc_360_approx, color=\"C1\")\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9b0adcee",
|
|
"metadata": {},
|
|
"source": [
|
|
"# 540 Degrees"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "8b75f733",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"global_t, global_phi = read_rotation_data(\"rotate_540.mp4\", (600, 1500), (1500, 2400))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "bef17bf1",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15, 7))\n",
|
|
"ax = fig.add_subplot()\n",
|
|
"ax.plot(global_t[:750], global_phi[:750])\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "08df7358",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# raw\n",
|
|
"\n",
|
|
"period = 5\n",
|
|
"\n",
|
|
"# overlay, keeping forward and back motion separate\n",
|
|
"t, phi = overlay(global_t, global_phi, 0.05, 2 * period, flip_even = False)\n",
|
|
"\n",
|
|
"# fix discontinuity and shift so 0 is vertical center\n",
|
|
"for (i, x) in enumerate(t):\n",
|
|
" if phi[i] >= max(-3 * x + 5, 3 * x - 23):\n",
|
|
" phi[i] -= math.tau\n",
|
|
" phi[i] += 1.5 * math.pi\n",
|
|
" \n",
|
|
"# overlay again to merge both motions\n",
|
|
"\n",
|
|
"t, phi = overlay(t, phi, 0, period)\n",
|
|
"\n",
|
|
"phi_0 = phi[np.argmin(t)]\n",
|
|
"\n",
|
|
"for i in range(len(phi)):\n",
|
|
" phi[i] -= phi_0\n",
|
|
" \n",
|
|
"# average\n",
|
|
"\n",
|
|
"bucket_size = dt = 0.025\n",
|
|
"buckets = get_buckets(t, phi, bucket_size)\n",
|
|
"bucket_offset = bucket_size / 2\n",
|
|
"\n",
|
|
"t_540 = np.linspace(0 + bucket_offset, period + bucket_offset, len(buckets))\n",
|
|
"pos_540 = [sum(bucket) / len(bucket) for bucket in buckets]\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"vel_540 = np.diff(pos_540, prepend=0) / dt\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"n = 7 # the larger n is, the smoother curve will be\n",
|
|
"b = [1.0 / n] * n\n",
|
|
"a = 1\n",
|
|
"vel_540_filtered = scipy.signal.lfilter(b,a,vel_540)\n",
|
|
"\n",
|
|
"acc_540 = np.diff(vel_540_filtered, prepend=0) / dt"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "4b226630",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15,15))\n",
|
|
"\n",
|
|
"# raw\n",
|
|
" \n",
|
|
"ax = fig.add_subplot(3,1,1)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"ax.scatter(t, phi, color=\"lightgray\")\n",
|
|
"\n",
|
|
"# average\n",
|
|
"\n",
|
|
"ax.plot(t_540, pos_540)\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,2)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
|
|
"ax.plot(t_540, vel_540)\n",
|
|
"ax.plot(t_540, vel_540_filtered, color=\"gray\")\n",
|
|
"\n",
|
|
"for x in [0.65, 1.45, 3.2, 4.15]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,3)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.plot(t_540, acc_540)\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "252158d8",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Approximation"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "245fc545",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# approximated constant acceleration\n",
|
|
"\n",
|
|
"acc_540_approx = np.zeros(len(acc_540))\n",
|
|
"\n",
|
|
"acc_start_time = 0.65\n",
|
|
"acc_stop_time = 1.45\n",
|
|
"dec_start_time = 3.2\n",
|
|
"dec_stop_time = 4.15\n",
|
|
"\n",
|
|
"t_0 = acc_stop_time - acc_start_time\n",
|
|
"t_1 = dec_start_time - acc_stop_time\n",
|
|
"t_2 = dec_stop_time - dec_start_time\n",
|
|
"h = 1.5 * math.tau\n",
|
|
"\n",
|
|
"acc_start = np.searchsorted(t_540, acc_start_time)\n",
|
|
"acc_stop = np.searchsorted(t_540, acc_stop_time)\n",
|
|
"\n",
|
|
"acc_value = h / ((t_0 / 2 + t_1 + t_2 / 2) * t_0)\n",
|
|
"\n",
|
|
"print(f\"acceleration: {acc_value: .2f} ({acc_value / math.pi: .2f} pi)\")\n",
|
|
"\n",
|
|
"dec_start = np.searchsorted(t_540, dec_start_time)\n",
|
|
"dec_stop = np.searchsorted(t_540, dec_stop_time)\n",
|
|
"\n",
|
|
"dec_value = -1 * acc_value * (acc_stop - acc_start) / (dec_stop - dec_start)\n",
|
|
"\n",
|
|
"print(f\"deceleration: {dec_value: .2f} ({dec_value / math.pi: .2f} pi)\")\n",
|
|
"\n",
|
|
"acc_540_approx[acc_start:acc_stop].fill(acc_value)\n",
|
|
"acc_540_approx[dec_start:dec_stop].fill(dec_value)\n",
|
|
"\n",
|
|
"# approximated velocity\n",
|
|
"\n",
|
|
"vel_540_approx = np.cumsum(acc_540_approx) * dt\n",
|
|
"\n",
|
|
"# approximated position\n",
|
|
"\n",
|
|
"pos_540_approx = np.cumsum(vel_540_approx) * dt"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "d2baff7c",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15,15))\n",
|
|
"\n",
|
|
"# raw\n",
|
|
" \n",
|
|
"ax = fig.add_subplot(3,1,1)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"ax.scatter(t, phi, color=\"lightgray\")\n",
|
|
"\n",
|
|
"# average\n",
|
|
"\n",
|
|
"ax.plot(t_540, pos_540)\n",
|
|
"\n",
|
|
"ax.plot(t_540, pos_540_approx)\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,2)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
|
|
"ax.plot(t_540, vel_540)\n",
|
|
"ax.plot(t_540, vel_540_filtered, color=\"gray\", linestyle=\"dotted\")\n",
|
|
"\n",
|
|
"for x in [acc_start_time, acc_stop_time, dec_start_time, dec_stop_time]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
" \n",
|
|
"ax.plot(t_540, vel_540_approx)\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,3)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.plot(t_540, acc_540, color=\"lightgray\")\n",
|
|
"\n",
|
|
"for x in [acc_start_time, acc_stop_time, dec_start_time, dec_stop_time]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
" \n",
|
|
"ax.plot(t_540, acc_540_approx, color=\"C1\")\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "6dba7e18",
|
|
"metadata": {},
|
|
"source": [
|
|
"# 180 degrees"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "1aa14192",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"global_t, global_phi = read_rotation_data(\"rotate_180.mp4\", (600, 1500), (1500, 2400))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "126c1611",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15, 7))\n",
|
|
"ax = fig.add_subplot()\n",
|
|
"ax.plot(global_t[:750], global_phi[:750])\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "8634be80",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# raw\n",
|
|
"\n",
|
|
"period = 5\n",
|
|
"t, phi = overlay(global_t, global_phi, 6.6, 2 * period, flip_even = False)\n",
|
|
"\n",
|
|
"# fix discontinuity and shift so 0 is vertical center\n",
|
|
"for (i, x) in enumerate(t):\n",
|
|
" if phi[i] < -1:\n",
|
|
" phi[i] += math.tau\n",
|
|
" phi[i] -= math.pi / 2\n",
|
|
" \n",
|
|
"# overlay again to merge both motions\n",
|
|
"\n",
|
|
"t, phi = overlay(t, phi, 0, period)\n",
|
|
"\n",
|
|
"phi_0 = phi[np.argmin(t)]\n",
|
|
"\n",
|
|
"for i in range(len(phi)):\n",
|
|
" phi[i] -= phi_0\n",
|
|
"\n",
|
|
"# average\n",
|
|
"\n",
|
|
"bucket_size = dt = 0.025\n",
|
|
"buckets = get_buckets(t, phi, bucket_size)\n",
|
|
"bucket_offset = bucket_size / 2\n",
|
|
"\n",
|
|
"t_180 = np.linspace(0 + bucket_offset, period + bucket_offset, len(buckets))\n",
|
|
"pos_180 = [sum(bucket) / len(bucket) for bucket in buckets]\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"vel_180 = np.diff(pos_180, prepend=0) / dt\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"n = 7 # the larger n is, the smoother curve will be\n",
|
|
"b = [1.0 / n] * n\n",
|
|
"a = 1\n",
|
|
"vel_180_filtered = scipy.signal.lfilter(b,a,vel_180)\n",
|
|
"\n",
|
|
"acc_180 = np.diff(vel_180_filtered, prepend=0) / dt"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "0e85ff00",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15,15))\n",
|
|
"\n",
|
|
"# raw\n",
|
|
" \n",
|
|
"ax = fig.add_subplot(3,1,1)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"ax.scatter(t, phi, color=\"lightgray\")\n",
|
|
"\n",
|
|
"# average\n",
|
|
"\n",
|
|
"ax.plot(t_180, pos_180)\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,2)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
|
|
"ax.plot(t_180, vel_180)\n",
|
|
"ax.plot(t_180, vel_180_filtered, color=\"gray\")\n",
|
|
"\n",
|
|
"acc_start_time = 0.65\n",
|
|
"acc_stop_time = 1.45\n",
|
|
"dec_start_time = 1.45\n",
|
|
"dec_stop_time = 2.4\n",
|
|
"\n",
|
|
"for x in [acc_start_time, acc_stop_time, dec_start_time, dec_stop_time]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,3)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.plot(t_180, acc_180)\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e9c0a9ef",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Approximation"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "d1a7564e",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# approximated constant acceleration\n",
|
|
"\n",
|
|
"acc_180_approx = np.zeros(len(acc_540))\n",
|
|
"\n",
|
|
"t_0 = acc_stop_time - acc_start_time\n",
|
|
"t_1 = dec_start_time - acc_stop_time\n",
|
|
"t_2 = dec_stop_time - dec_start_time\n",
|
|
"h = 0.5 * math.tau\n",
|
|
"\n",
|
|
"acc_start = np.searchsorted(t_180, acc_start_time)\n",
|
|
"acc_stop = np.searchsorted(t_180, acc_stop_time)\n",
|
|
"\n",
|
|
"acc_value = h / ((t_0 / 2 + t_1 + t_2 / 2) * t_0)\n",
|
|
"\n",
|
|
"print(f\"acceleration: {acc_value: .2f} ({acc_value / math.pi: .2f} pi)\")\n",
|
|
"\n",
|
|
"dec_start = np.searchsorted(t_180, dec_start_time)\n",
|
|
"dec_stop = np.searchsorted(t_180, dec_stop_time)\n",
|
|
"\n",
|
|
"dec_value = -1 * acc_value * (acc_stop - acc_start) / (dec_stop - dec_start)\n",
|
|
"\n",
|
|
"print(f\"deceleration: {dec_value: .2f} ({dec_value / math.pi: .2f} pi)\")\n",
|
|
"\n",
|
|
"acc_180_approx[acc_start:acc_stop].fill(acc_value)\n",
|
|
"acc_180_approx[dec_start:dec_stop].fill(dec_value)\n",
|
|
"\n",
|
|
"# approximated velocity\n",
|
|
"\n",
|
|
"vel_180_approx = np.cumsum(acc_180_approx) * dt\n",
|
|
"\n",
|
|
"# approximated position\n",
|
|
"\n",
|
|
"pos_180_approx = np.cumsum(vel_180_approx) * dt"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "89c99381",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15,15))\n",
|
|
"\n",
|
|
"# raw\n",
|
|
" \n",
|
|
"ax = fig.add_subplot(3,1,1)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"ax.scatter(t, phi, color=\"lightgray\")\n",
|
|
"\n",
|
|
"# average\n",
|
|
"\n",
|
|
"ax.plot(t_180, pos_180)\n",
|
|
"\n",
|
|
"ax.plot(t_180, pos_180_approx)\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,2)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
|
|
"ax.plot(t_180, vel_180)\n",
|
|
"ax.plot(t_180, vel_180_filtered, color=\"gray\", linestyle=\"dotted\")\n",
|
|
"\n",
|
|
"for x in [acc_start_time, acc_stop_time, dec_start_time, dec_stop_time]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
" \n",
|
|
"ax.plot(t_180, vel_180_approx)\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,3)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"ax.plot(t_180, acc_180, color=\"lightgray\")\n",
|
|
"\n",
|
|
"for x in [acc_start_time, acc_stop_time, dec_start_time, dec_stop_time]:\n",
|
|
" ax.axvline(x, color='gray', linestyle='dotted')\n",
|
|
" \n",
|
|
"ax.plot(t_180, acc_180_approx, color=\"C1\")\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "82c5bfa6",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Comparison"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "04772b01",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"fig = plt.figure(figsize=(15,15))\n",
|
|
"\n",
|
|
"# position\n",
|
|
" \n",
|
|
"ax = fig.add_subplot(3,1,1)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angle [rad]\")\n",
|
|
"\n",
|
|
"ax.plot(t_180, pos_180, color=\"lightgray\", linewidth=7)\n",
|
|
"ax.plot(t_180, pos_180_approx)\n",
|
|
"\n",
|
|
"ax.plot(t_360, pos_360, color=\"lightgray\", linewidth=7)\n",
|
|
"ax.plot(t_360, pos_360_approx)\n",
|
|
"\n",
|
|
"ax.plot(t_540, pos_540, color=\"lightgray\", linewidth=7)\n",
|
|
"ax.plot(t_540, pos_540)\n",
|
|
"\n",
|
|
"# velocity\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,2)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Angular Velocity [rad / s]\")\n",
|
|
"\n",
|
|
"ax.plot(t_180, vel_180, color=\"lightgray\")\n",
|
|
"ax.plot(t_180, vel_180_approx)\n",
|
|
"\n",
|
|
"ax.plot(t_360, vel_360, color=\"lightgray\")\n",
|
|
"ax.plot(t_360, vel_360_approx)\n",
|
|
"\n",
|
|
"ax.plot(t_540, vel_540, color=\"lightgray\")\n",
|
|
"ax.plot(t_540, vel_540_approx)\n",
|
|
"\n",
|
|
"# acceleration\n",
|
|
"\n",
|
|
"ax = fig.add_subplot(3,1,3)\n",
|
|
"ax.yaxis.set_major_locator(mpl.ticker.MultipleLocator(base=math.tau/2))\n",
|
|
"ax.set_ylabel(\"Acceleration [rad / $s^2$]\")\n",
|
|
"ax.set_xlabel(\"Time [s]\")\n",
|
|
"\n",
|
|
"ax.plot(t_180, acc_180_approx)\n",
|
|
"ax.plot(t_360, acc_360_approx)\n",
|
|
"ax.plot(t_540, acc_540_approx)\n",
|
|
"\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "374c818e",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Model"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "f2790606",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"v_max = 3.61 # rad / s\n",
|
|
"\n",
|
|
"a_acc = 4.51 # rad / s^2\n",
|
|
"a_dec = 3.83 # rad / s^2\n",
|
|
"\n",
|
|
"def time_taken(delta_phi, v_0):\n",
|
|
"\n",
|
|
" time_acc = (v_max - v_0) / a_acc\n",
|
|
" print(f\"{time_acc=}\")\n",
|
|
"\n",
|
|
" traveled_while_acc = (v_max ** 2 - v_0 ** 2) / (2 * a_acc)\n",
|
|
" print(f\"{traveled_while_acc=}\")\n",
|
|
"\n",
|
|
" time_dec = v_max / a_dec\n",
|
|
" print(f\"{time_dec=}\")\n",
|
|
"\n",
|
|
" traveled_while_dec = (v_max ** 2) / (2 * a_dec)\n",
|
|
" print(f\"{traveled_while_dec=}\")\n",
|
|
"\n",
|
|
" traveled_while_cruising = delta_phi - (traveled_while_acc + traveled_while_dec)\n",
|
|
" print(f\"{traveled_while_cruising=}\")\n",
|
|
"\n",
|
|
" time_cruise = traveled_while_cruising / v_max\n",
|
|
" print(f\"{time_cruise=}\")\n",
|
|
"\n",
|
|
" time_total = time_acc + time_cruise + time_dec\n",
|
|
" print(f\"{time_total=}\")\n",
|
|
" "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "84b206bf",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Comparison 180 degrees"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "b5e37028",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# model\n",
|
|
"print(\"Model:\")\n",
|
|
"time_taken(math.pi, 0)\n",
|
|
"\n",
|
|
"# actual\n",
|
|
"acc_start_time = 0.65\n",
|
|
"acc_stop_time = 1.45\n",
|
|
"dec_start_time = 1.45\n",
|
|
"dec_stop_time = 2.4\n",
|
|
"print(\"\\nActual:\")\n",
|
|
"print(f\"time acc: {acc_stop_time - acc_start_time}\")\n",
|
|
"print(f\"time dec: {dec_stop_time - dec_start_time}\")\n",
|
|
"print(f\"time cruising: {dec_start_time - acc_stop_time}\")\n",
|
|
"print(f\"time total: {dec_stop_time - acc_start_time}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "4b71b1c6",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Comparison 360 degrees"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "a286ed66",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# model\n",
|
|
"print(\"Model:\")\n",
|
|
"time_taken(math.tau, 0)\n",
|
|
"\n",
|
|
"# actual\n",
|
|
"acc_start_time = 0.65\n",
|
|
"acc_stop_time = 1.45\n",
|
|
"dec_start_time = 2.3\n",
|
|
"dec_stop_time = 3.25\n",
|
|
"print(\"\\nActual:\")\n",
|
|
"print(f\"time acc: {acc_stop_time - acc_start_time}\")\n",
|
|
"print(f\"time dec: {dec_stop_time - dec_start_time}\")\n",
|
|
"print(f\"time cruising: {dec_start_time - acc_stop_time}\")\n",
|
|
"print(f\"time total: {dec_stop_time - acc_start_time}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "4e808bfe",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Comparison 540 degrees"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "6b10a04f",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"\n",
|
|
"# model\n",
|
|
"print(\"Model:\")\n",
|
|
"time_taken(3 * math.pi, 0)\n",
|
|
"\n",
|
|
"# actual\n",
|
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"acc_start_time = 0.65\n",
|
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"acc_stop_time = 1.45\n",
|
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"dec_start_time = 3.2\n",
|
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"dec_stop_time = 4.15\n",
|
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"print(\"\\nActual:\")\n",
|
|
"print(f\"time acc: {acc_stop_time - acc_start_time}\")\n",
|
|
"print(f\"time dec: {dec_stop_time - dec_start_time}\")\n",
|
|
"print(f\"time cruising: {dec_start_time - acc_stop_time}\")\n",
|
|
"print(f\"time total: {dec_stop_time - acc_start_time}\")"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"interpreter": {
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|
"hash": "fce917ee5987da4ee7f9f72fa808934308e0fb8739a0828f8cbf1cedb5699222"
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},
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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