{ "metadata": { "name": "", "signature": "sha256:2e3972d976c717ad848830ea8bdd67a2de2015c9556e9d85e21df2688cc41ee3" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook is inspired by watching the videos for Underactuated Robotics MIT lectures and edx course. The videos of the example robots in the course were very cool (look for cart pole swingup and acrobot videos on youtube). Unfortunately I had already committed myself to a couple of different MOOCs while Underactuated Robotics was running, so couldn't dedicate enough time to keep up, but I want to dig into the material at a more leisurely pace, as it's still available online.\n", "\n", "I wanted to investigate some of the ideas in the course, and brush up on the areas I'm weak on. Time permitting, I'm planning to code up some of the concepts in the course.\n", "\n", "I discovered iPython notebooks via the Practical Numerical Methods with Python MOOC, and it's a great idea to create a digital copy of my notes and the algorithms via code." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Undamped Pendulum Dynamics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dynamics of an simple undamped is given in the following equation\n", "\n", "The angular acceleration $\\frac{d^2{\\phi}}{dt^2}={\\alpha}(t)=-\\frac{g}{l} {sin{\\phi(t)}}$\n", "\n", "The angular velocity is ${\\omega}(t)$.\n", "Euler integration gives:\n", "\n", "$$\\begin{eqnarray}\n", "{\\omega}(t + {\\Delta}t) = {\\omega}(t) + {\\Delta}t.{\\alpha}(t) \\\\\n", "{\\phi}(t + {\\Delta}t) = {\\phi}(t) + {\\Delta}t.{\\omega}(t)\n", "\\end{eqnarray}$$" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Coding" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is simple to code up. First, import the required libraries." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy \n", "import math\n", "from matplotlib import pyplot\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The method simulate_pendulum initialises the result arrays, and the for loop performs an Euler integration over the time period." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# constants\n", "g = 9.81\n", "l = 1.0\n", "\n", "def simulate_pendulum(phi_init, omega_init, numSteps, deltaT):\n", " t = numpy.zeros(numSteps)\n", "\n", " phi = numpy.zeros(numSteps)\n", " phi[0] = phi_init\n", "\n", " omega = numpy.zeros(numSteps)\n", " omega[0] = omega_init\n", "\n", " for n in range(1,numSteps):\n", " t[n] = deltaT * n # store the time for plotting.\n", "\n", " alpha_t = -(g/l) * math.sin(phi[n-1])\n", " omega_t = omega[n-1] + (delta_t * alpha_t)\n", " phi_t = phi[n-1] + (delta_t * omega_t)\n", " omega[n] = omega_t\n", " phi[n] = phi_t\n", "\n", " return (t, phi, omega)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The method can be ran for a set of initial conditions, and the results stored in a tuple of time against angle and angular velocity." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# initial conditions\n", "phi_0 = math.pi / 6. # initial angle\n", "omega_0 = 0. # pendulum initially at rest\n", "\n", "N = 1000 # time steps to run the simulation for\n", "delta_t = 0.01 # simulation step size\n", "\n", "(t, phi, omega) = simulate_pendulum(phi_0, omega_0, N, delta_t)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the results shows the expected periodic motion." ] }, { "cell_type": "code", "collapsed": false, "input": [ "pyplot.figure(figsize=(10,4))\n", "pyplot.xlabel('t', fontsize=14)\n", "pyplot.ylabel(r'$\\phi$', fontsize=14)\n", "pyplot.hold(True)\n", "pyplot.plot(t, phi)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 22, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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1JIUZMgRWroSjR11H4kYSesVBSVwSGsagJC7KeY1K4gpQzA+czMMmrisaT1TM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\niDEVZPRomDvXdRTZ8fFN6oN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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Phase Portrait" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A phase portrait of the undamped pendulum can be generated.\n", "\n", "The state vector of the pendulum is: \n", "\n", "$$ \\mathbf{x} = \\begin{bmatrix} {\\phi} \\\\\n", "{\\dot{\\phi}} \\\\\n", "\\end{bmatrix}$$\n", "\n", "and the phase portrait is a plot of the trajectories at each point in the state space, i.e.\n", "\n", "$$ \\dot{\\mathbf{x}} = \\begin{bmatrix} \\dot{{\\phi}} \\\\\n", "\\ddot{{\\phi}} \\\\\n", "\\end{bmatrix} \n", "= \\begin{bmatrix} {\\omega} \\\\\n", "-\\frac{g}{l} {sin{\\phi(t)}} \\\\\n", "\\end{bmatrix}$$\n", "\n", "The phase portrait can be plotted with the following code:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# this gives the trajectories - the derivative of the state-space matrix\n", "def dX_dt(X):\n", " #phi = X[0]\n", " #omega = X[1] = phi_dot\n", " #omega_dot = -(g/l)*math.sin(phi)\n", " #return phi_dot, omega_dot\n", " return numpy.array([ X[1], -(g/l)*numpy.sin(X[0]) ]);\n", "\n", "x = numpy.linspace(-math.pi*1.25, math.pi*1.25, 21)\n", "y = numpy.linspace(-8, 8, 20)\n", "\n", "(X,Y) = numpy.meshgrid(x, y)\n", "(DX, DY) = dX_dt([X, Y])\n", "\n", "pyplot.figure(figsize=(10,5))\n", "pyplot.xlabel(r'$\\phi$', fontsize=14)\n", "pyplot.ylabel(r'$\\omega$', fontsize=14)\n", "pyplot.quiver(X, Y, DX, DY)\n", "\n", "# simulate a second trajectory with a larger initial angle\n", "(t2, phi_large, omega_large) = simulate_pendulum(math.pi * 0.99, 0, N, delta_t)\n", "\n", "coords = zip(omega, phi)\n", "pyplot.hold(True)\n", "pyplot.plot(phi, omega, color='b', label='$\\phi_0=\\pi/6$')\n", "pyplot.plot(phi_large, omega_large, color='g', label='$\\phi_0=0.99\\pi$')\n", "pyplot.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 23, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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KFSsESRisTiSbU+kPpVKJ4cOHw8DAQJAdHbUPnIuLS67+PikpKYL18dmzZ2Fg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"text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This shows the stable fixed point when ${\\phi}$ is zero and $\\dot{\\phi}$ is zero, and the unstable fixed points where $\\dot{\\phi}$ is zero and ${\\phi}$ is at $\\pm{\\pi}$ radians (where the pendulum is balanced in the top position)." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Animation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The pendulum can be plotted over time using the JSAnimation library, using the trajectory that has already been calculated.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from JSAnimation import IPython_display\n", "from matplotlib import animation\n", "\n", "fig = pyplot.figure(figsize=(8,5))\n", "ax = pyplot.axes(xlim=(0,2), ylim=(-0.2,2))\n", "line, = pyplot.plot([],[])\n", "time_text = pyplot.text(0.02, 1.90, '')\n", "\n", "def animate(i):\n", " phi_step = phi[i]\n", " line.set_data([1,1-math.sin(phi_step)],[1,1-math.cos(phi_step)])\n", " time_text.set_text('time = %.1f' % t[i])\n", " \n", "\n", "animation.FuncAnimation(fig, animate,\n", " frames=200, interval=20)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", "
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\n", "\n", "\n", "\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 24, "text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Pendulum with Damping" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equation for a pendulum with viscous damping introduces a torque proportional,to the angular velocity:\n", "\n", "$\\ddot{\\phi}=-\\frac{g}{l} {sin{\\phi(t)}} - b\\dot{\\phi}(t)$\n", "\n", "And the code is modified to include this damping term." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def simulate_pendulum_damped(phi_init, omega_init, numSteps, deltaT, damping):\n", " t = numpy.zeros(numSteps)\n", "\n", " phi = numpy.zeros(numSteps)\n", " phi[0] = phi_init\n", "\n", " omega = numpy.zeros(numSteps)\n", " omega[0] = omega_init\n", "\n", " for n in range(1,numSteps):\n", " t[n] = deltaT * n # store the time for plotting.\n", "\n", " alpha_t = (-(g/l) * math.sin(phi[n-1])) - (damping * omega[n-1])\n", " omega_t = omega[n-1] + (delta_t * alpha_t)\n", " phi_t = phi[n-1] + (delta_t * omega_t)\n", " omega[n] = omega_t\n", " phi[n] = phi_t\n", "\n", " return (t, phi, omega)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, the values can be generated and the plots generated. A damping factor of b = 0.5 results in:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "damping = 0.5\n", "(t_damped, phi_damped, omega_damped) = simulate_pendulum_damped(phi_0, omega_0, N, delta_t, damping)\n", "\n", "pyplot.figure(figsize=(10,4))\n", "pyplot.xlabel('t', fontsize=14)\n", "pyplot.ylabel(r'$\\phi$', fontsize=14)\n", "pyplot.hold(True)\n", "pyplot.plot(t_damped, phi_damped)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 26, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "# this gives the trajectories - the derivative of the state-space matrix\n", "def dX_dt_damped(X, damping):\n", " #phi = X[0]\n", " #omega = X[1] = phi_dot\n", " #omega_dot = -(g/l)*math.sin(phi)\n", " #return phi_dot, omega_dot\n", " return numpy.array([ X[1], (-(g/l)*numpy.sin(X[0]))-(damping * X[1]) ]);\n", "\n", "x = numpy.linspace(-1.25, 1.25, 21)\n", "y = numpy.linspace(-2, 2, 20)\n", "\n", "(X,Y) = numpy.meshgrid(x, y)\n", "(DX, DY) = dX_dt_damped([X, Y], 0.5)\n", "\n", "pyplot.figure(figsize=(10,5))\n", "pyplot.xlabel(r'$\\phi$', fontsize=14)\n", "pyplot.ylabel(r'$\\omega$', fontsize=14)\n", "pyplot.quiver(X, Y, DX, DY)\n", "\n", "coords = zip(omega_damped, phi_damped)\n", "pyplot.hold(True)\n", "pyplot.plot(phi_damped, omega_damped, label='b=0.5')\n", "pyplot.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 27, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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dw927dzFt2jTx3+Gibdu2SExMZG2tIuDv74979+7h3r177NoyPMgGro4gJKL2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ATo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\no9F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"text": [ "" ] } ], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The phase portrait shows that the effect of the damping is to modify the y, or in this case $\\dot{\\phi}$, component of the trajectory vectors, so that the trajectory is directed towards the centre of the plot." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "https://www.edx.org/course/underactuated-robotics-mitx-6-832x \n", "http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-832-underactuated-robotics-spring-2009/readings/MIT6_832s09_read_ch02.pdf \n", "http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about \n", "\n", "www.lajpe.org/may09/05_Giacomo_Torzo.pdf \n", "http://en.wikipedia.org/wiki/State-space_representation \n", "http://kestrel.nmt.edu/~raymond/software/python_notes/paper004.html \n", "http://nbviewer.ipython.org/github/pv/SciPy-Cookbook/blob/master/ipython/LoktaVolterraTutorial.ipynb \n", "http://jakevdp.github.io/blog/2012/08/18/matplotlib-animation-tutorial/" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Contact" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "http://taumuon-jabuka.blogspot.co.uk/ \n", "https://github.com/taumuon \n" ] } ], "metadata": {} } ] }