robot acceleration calculator.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from itertools import cycle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Robot Parameters\n",
    "\n",
    "robot_weight = 11 #kg\n",
    "bare_motor_torque = 4.2/40 * 4 * .93 #Nm * 4 motors\n",
    "bare_motor_speed = 150*40 #RPM\n",
    "wheel_coefficient_of_friction = 0.8 # coefficient of static friction\n",
    "wheel_efficiency = 1 # Mecanum wheels = 0.7, Tank wheels = 1\n",
    "gearbox_efficiency = 0.97 # Efficiency of the gearbox  (if known)\n",
    "wheel_diameter = 0.102 # meters  (4 in. = 0.102 m)\n",
    "rotational_inertia = 0.0015\n",
    "\n",
    "# Delta t\n",
    "dt = 0.001\n",
    "\n",
    "#Distances\n",
    "travel_distances = np.array([.75, 1.5]) # Target Distance (m)\n",
    "\n",
    "# Desired Distances\n",
    "\n",
    "reduction_min = 5\n",
    "reduction_max = 30\n",
    "reduction_delta = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# my variables (don't touch)\n",
    "circumference = wheel_diameter * math.pi #meters\n",
    "maxGroundForce = 9.8 * robot_weight * wheel_coefficient_of_friction\n",
    "wheelRadius = wheel_diameter / 2\n",
    "\n",
    "motorTorqueSlope = bare_motor_torque / bare_motor_speed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ts = 4.2 / 40 # Stall Torque (bare motor) (Nm)\n",
    "Is = 8.5      # Stall current (A)\n",
    "If = 0.2      # No Load Current (A)\n",
    "nf = 150 * 40 # Free Speed (RPM)\n",
    "Vn = 12       # Nominal Voltage (V)\n",
    "rb = 0.1      # Internal Battery Resistance (Ohms)\n",
    "Ie = 1        # External Current Draw (A)\n",
    "\n",
    "c3 = (Ts*Vn - Ts*Ie*rb)/(Vn) - (Ts*rb*Is*(Vn-Ie*rb))/(Vn*(Vn + rb*Is))\n",
    "c4 = (Ts**2 * rb)/(nf*Vn + nf*Is*rb) - (Ts)/(nf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# my functions\n",
    "def acceleration (curSpeed, gearReduction):\n",
    "    #print (\"curSpeed \" + str(curSpeed))\n",
    "    motorRpm = curSpeed / circumference * 60 * gearReduction\n",
    "    #print(\"motorRpm \" + str(motorRpm))\n",
    "    motorTorque = (bare_motor_torque - motorTorqueSlope * motorRpm) * gearReduction * gearbox_efficiency\n",
    "    #motorTorque = bare_motor_torque * gearReduction * gearbox_efficiency\n",
    "    #print(\"motorTorque \" + str(motorTorque))\n",
    "\n",
    "    acceleration = motorTorque / (wheelRadius*robot_weight/wheel_efficiency + rotational_inertia / wheelRadius)\n",
    "    \n",
    "    groundForce = robot_weight * acceleration\n",
    "    if groundForce > maxGroundForce:\n",
    "        acceleration = maxGroundForce / robot_weight * wheel_efficiency\n",
    "    \n",
    "    #print(\"accleration \" + str(acceleration))\n",
    "    return acceleration\n",
    "\n",
    "def calcTimeForReduction(targetDist, gearReduction):\n",
    "    distTravled = 0\n",
    "    speed = 0\n",
    "    time = 0\n",
    "    \n",
    "    while distTravled < targetDist:\n",
    "        speed += dt * acceleration(speed, gearReduction)\n",
    "        distTravled += speed * dt\n",
    "        time += dt\n",
    "        #print(\"distTravled \" + str(distTravled))\n",
    "        #print(\"time \" + str(time))\n",
    "    \n",
    "    return time\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Fill my array\n",
    "\n",
    "ratioTests = np.arange(reduction_min, reduction_max, reduction_delta, dtype = np.float64)\n",
    "data = np.zeros((travel_distances.size, ratioTests.size))\n",
    "\n",
    "minimums = np.zeros((2, travel_distances.size))\n",
    "\n",
    "i2 = 0\n",
    "j2 = 0\n",
    "tempMin = 0\n",
    "tempRatio = 0\n",
    "\n",
    "for curDist in travel_distances:\n",
    "    j2 = 0\n",
    "    tempMin = 0;\n",
    "    for curRatio in ratioTests:\n",
    "        # Find new time\n",
    "        tempTime = calcTimeForReduction(curDist, curRatio)\n",
    "        data[i2, j2] = tempTime\n",
    "        \n",
    "        # Check for min\n",
    "        if tempTime < tempMin or tempMin == 0:\n",
    "            tempMin = tempTime\n",
    "            tempRatio = curRatio\n",
    "        \n",
    "        j2 += 1\n",
    "    \n",
    "    minimums[0, i2] = tempRatio\n",
    "    minimums[1, i2] = tempMin\n",
    "    i2 += 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faf201c9e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = cycle([\"aqua\", \"black\", \"blue\", \"fuchsia\", \"gray\", \"green\", \"lime\", \"maroon\", \"navy\", \"olive\", \"purple\", \"red\", \"silver\", \"teal\", \"yellow\"])\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "for i in range (0, travel_distances.size):\n",
    "    ax.plot(ratioTests, data[i], label=str(travel_distances[i]) + \" m, Min: \" + str(round(minimums[0, i], 3)), color=next(colors))\n",
    "    \n",
    "ax.plot(minimums[0], minimums[1], \"ko\")\n",
    "    \n",
    "    \n",
    "ax.set_xlabel(\"Gear Reduction\", fontsize=15)\n",
    "ax.set_ylabel(\"Time\", fontsize=18)\n",
    "\n",
    "ax.legend(loc=\"best\")\n",
    "\n",
    "ax.margins(0.1)\n",
    "fig.tight_layout()\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11.3  , 10.4  ,  9.1  ],\n",
       "       [ 0.933,  1.13 ,  1.481]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimums   # 6 motor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11.3  , 10.4  ,  9.1  ],\n",
       "       [ 0.933,  1.13 ,  1.481]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimums    # 4 motor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\begin{cases} \\frac{T^{2} c_{1}}{2} & \\text{for}\\: c_{2}^{3} = 0 \\\\\\frac{c_{1}}{c_{2}^{2}} + \\frac{e^{T c_{2}}}{c_{2}^{3}} \\left(T c_{1} c_{2}^{2} - c_{1} c_{2}\\right) & \\text{otherwise} \\end{cases}$$"
      ],
      "text/plain": [
       "⎧             2                             \n",
       "⎪            T ⋅c₁                     3    \n",
       "⎪            ─────               for c₂  = 0\n",
       "⎪              2                            \n",
       "⎪                                           \n",
       "⎨      ⎛       2        ⎞  T⋅c₂             \n",
       "⎪ c₁   ⎝T⋅c₁⋅c₂  - c₁⋅c₂⎠⋅ℯ                 \n",
       "⎪─── + ────────────────────────   otherwise \n",
       "⎪  2               3                        \n",
       "⎪c₂              c₂                         \n",
       "⎩                                           "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_printing(True)\n",
    "t = Symbol('t')\n",
    "T = Symbol('T')\n",
    "c1 = Symbol('c_1')\n",
    "c2 = Symbol('c_2')\n",
    "integrate(c1*t*exp(c2*t),(t,0,T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ (c_1/c_2**2 + (T*c_1*c_2**2 - c_1*c_2)*exp(T*c_2)/c_2**3 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-LambertW(1)]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(T + exp(T), T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1 - LambertW(-E))/c_2]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_1 = Symbol(\"c_1\")\n",
    "c_2 = Symbol(\"c_2\")\n",
    "t = Symbol(\"t\")\n",
    "solve(-(c_1*(c_2*t - 1) - c_1*exp(t*c_2)) / (c_2**2), t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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