{ "cells": [ { "cell_type": "markdown", "id": "39b9c69a-618e-4bc2-b0be-e25112faeb82", "metadata": {}, "source": [ "# condynsate.Simulator" ] }, { "cell_type": "markdown", "id": "181aafc5-8a6c-4d07-bebe-abf5c85a42ab", "metadata": {}, "source": [ "## Setting up the Simulation Environment" ] }, { "cell_type": "markdown", "id": "1d5b66ed-1358-4c4e-a3c4-175901739f5b", "metadata": {}, "source": [ "Import necessary `condynsate` modules" ] }, { "cell_type": "code", "execution_count": 1, "id": "50eb09ae-dfc2-4a77-8574-d0fed168b673", "metadata": {}, "outputs": [], "source": [ "from condynsate import Simulator as conSim\n", "from condynsate import __assets__ as assets" ] }, { "cell_type": "markdown", "id": "6d80475e-9ddd-4bac-98be-05fc8b73f361", "metadata": {}, "source": [ "Create a instance of `condynsate.simulator` that does not use the keyboard or the animator but does use the visualizer." ] }, { "cell_type": "code", "execution_count": 2, "id": "565a9027-172b-4544-bace-237b965bb6a2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "You can open the visualizer by visiting the following URL:\n", "http://127.0.0.1:7002/static/\n" ] } ], "source": [ "simulator = conSim(keyboard = False,\n", " visualization = True,\n", " animation = False)" ] }, { "cell_type": "markdown", "id": "56ed8fc8-eb28-47a9-9864-ee36e0ff07eb", "metadata": {}, "source": [ "Load the pendulum into the simulator. Set `fixed = true` so that the base link of the pendulum is fixed in space. Set `update_vis = true` so that its position updates are reflected in the visualizer. Additionally, set the base pitch to 180 degrees and the yaw to 90 degrees so the pendulum is oriented downward and swings in the YZ visual plane, respectively." ] }, { "cell_type": "code", "execution_count": 3, "id": "5e61389d-70c0-44d7-8729-18ce724f5e2a", "metadata": {}, "outputs": [], "source": [ "pendulum = simulator.load_urdf(urdf_path = assets['pendulum'],\n", " fixed = True,\n", " update_vis = True,\n", " yaw = 1.571, # All angle arguments are in radians\n", " pitch = 3.142) # All angle arguments are in radians" ] }, { "cell_type": "markdown", "id": "396cc406-c0fb-4bd9-8ee7-c2335a3da46f", "metadata": {}, "source": [ "Set the `\"chassis_to_arm\"` joint friction to some small value. The `\"chassis_to_arm\"` joint is the rotational joint about which the pendulum swings" ] }, { "cell_type": "code", "execution_count": 4, "id": "0f374fde-afae-40f2-be1a-06dd206b4baf", "metadata": {}, "outputs": [], "source": [ "simulator.set_joint_damping(urdf_obj = pendulum,\n", " joint_name = 'chassis_to_arm',\n", " damping = 0.05)" ] }, { "cell_type": "markdown", "id": "7a096161-a4db-428d-b7b8-691a1aa52523", "metadata": {}, "source": [ "Set the initial angle of the pendulum. We denote that this is an initial condition with the `initial_cond = True` flag and we make the change instantaneously by using the `physics = False` flag." ] }, { "cell_type": "code", "execution_count": 5, "id": "d1d531ab-b22d-44a6-bb6b-4f3d0907c966", "metadata": {}, "outputs": [], "source": [ "initial_angle = 0.1745\n", "simulator.set_joint_position(urdf_obj = pendulum,\n", " joint_name = 'chassis_to_arm',\n", " position = initial_angle, # For a rotational joint, this value is in radians\n", " initial_cond = True,\n", " physics = False)" ] }, { "cell_type": "markdown", "id": "665ab804-aa3a-40ac-8e05-9e345d7afaaa", "metadata": {}, "source": [ "## Setting up Data Collection" ] }, { "cell_type": "markdown", "id": "8b2107c6-ffaa-4d2b-ae2c-05a48566c980", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "1823d785-1cb1-4374-95cb-e531ec75ee92", "metadata": {}, "source": [ "For fun, we will compare the dynamics of our nonlinear simulation to the small-angle linear approximation of pendulum dynamics. To do so, we define the small-angle pendulum dynamics approximations." ] }, { "cell_type": "code", "execution_count": 6, "id": "896119bf-6f9e-4d96-a951-3a2038d0c6ee", "metadata": {}, "outputs": [], "source": [ "# Use a numerical integrator and the linear approximation of pendulum dynamics to get an estimated trajectory\n", "import numpy as np\n", "linear_angle = lambda t : initial_angle * np.cos(np.sqrt(9.81/1.0) * np.array(t))\n", "linear_angle_vel = lambda t : -np.sqrt(9.81/1.0) * initial_angle * np.sin(np.sqrt(9.81/1.0) * np.array(t))" ] }, { "cell_type": "markdown", "id": "d12343a0-9d61-42bf-9bc8-e59b8a6c6ffa", "metadata": {}, "source": [ "Create an empty dictionary to collect simulation data" ] }, { "cell_type": "code", "execution_count": 7, "id": "d6da1071-adba-4f9c-8b45-9bf4cb22a33c", "metadata": {}, "outputs": [], "source": [ "data = {'angle' : [],\n", " 'angle_vel' : [],\n", " 'time' : [],}" ] }, { "cell_type": "markdown", "id": "ee3b06b2-475d-457f-9f1e-e395ff061108", "metadata": {}, "source": [ "## Running the Simulation" ] }, { "cell_type": "markdown", "id": "1a171854-1b54-4a13-8762-ace0d7e78bda", "metadata": {}, "source": [ "Run the simulation in a loop. Begin by resetting the simulation using `condynsate.Simulator.reset`, then create a loop. The loop terminates when the flag `condynsate.Simulator.is_done` flips to True. In each time step of the simulation loop we do three things:\n", "1. Take a simulation time step.\n", "2. Extract and store the state of the `\"chassis_to_arm\"` joint. if a successful simulation step is taken. (Successful simulation steps are indicated by `condynsate.Simulator.step` having a `ret_code` greater than `0`.\n", "3. Reset the data dictionary if the simulation was reset during `condynsate.Simulator.step`. A simulation reset is indicated by `condynsate.Simulator.step` having a `ret_code` equal to `0`.\n", "\n", "By setting the `real_time = True` flag and `max_time = 5.0` in `condynsate.Simulator.step`, we tell the simulation to attempt to run in real time for 5 seconds. " ] }, { "cell_type": "code", "execution_count": 8, "id": "a5d68da8-7cf0-4792-93e0-1bdd90f8ade7", "metadata": {}, "outputs": [], "source": [ "# Reset before running a simulation loop\n", "simulator.reset()\n", "\n", "# Get the initial joint state at time t = 0.\n", "state = simulator.get_joint_state(urdf_obj = pendulum,\n", " joint_name = 'chassis_to_arm')\n", "data['time'].append(simulator.time)\n", "data['angle'].append(state['position'])\n", "data['angle_vel'].append(state['velocity'])\n", "\n", "# Create the main simulation loop\n", "while(not simulator.is_done): \n", " # Take a single physics step of condynsate.Simulator.dt seconds. This will\n", " # automatically update the physics and the visualizer, and attempts\n", " # to run in real time.\n", " ret_code = simulator.step(real_time = True,\n", " max_time = 5.0)\n", "\n", " # Add the simulation data at the current time if a simulation step is taken\n", " if ret_code > 0:\n", " state = simulator.get_joint_state(urdf_obj = pendulum,\n", " joint_name = 'chassis_to_arm')\n", " data['time'].append(simulator.time)\n", " data['angle'].append(state['position'])\n", " data['angle_vel'].append(state['velocity'])\n", " \n", " # Handle resetting the data collection if the simulation is reset.\n", " if ret_code == 0:\n", " data = {'angle' : [],\n", " 'angle_vel' : [],\n", " 'time' : [],}" ] }, { "cell_type": "markdown", "id": "87cb7090-cbb7-4e4e-9e8c-624323e00a8b", "metadata": {}, "source": [ "## Post-Processing" ] }, { "cell_type": "markdown", "id": "7ccf618c-4151-4f8a-8193-a07dbb6d9a31", "metadata": {}, "source": [ "Here we format and plot the data we collected during the simulation using the `matplotlib` package." ] }, { "cell_type": "code", "execution_count": 9, "id": "591882f7-c349-443f-a734-bb573bde41ac", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot simulation data\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "# Create the plot\n", "fig, axes = plt.subplots(ncols=1, nrows=2, sharex=True, figsize=(10,5))\n", "\n", "# Plot the angles\n", "axes[0].plot(data['time'], data['angle'], c='r', lw=2, label='Simulated')\n", "axes[0].plot(data['time'], linear_angle(data['time']), c='b', lw=2, ls=\"--\", label='Small-Angle')\n", "axes[0].set_ylabel(\"Angle [rad]\")\n", "axes[0].legend(bbox_to_anchor=(1.21, 1.05), frameon=False)\n", "\n", "# Plot the angluar velocities\n", "axes[1].plot(data['time'], data['angle_vel'], c='r', lw=2, label='Simulated')\n", "axes[1].plot(data['time'], linear_angle_vel(data['time']), c='b', lw=2, ls=\"--\", label='Small-Angle')\n", "axes[1].set_xlabel(\"Time [s]\")\n", "axes[1].set_ylabel(\"Angular Vel [rad/s]\")\n", "fig.suptitle(\"Small Angle Approximation vs. Simulation\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "24286591-cae5-47ec-a3c8-fbbdd1872f26", "metadata": {}, "source": [ "As expected, because the initial angle was small (~10 degrees) the period of the nonlinear simulation and linear approximation are close; however, due to the joint damping the amplitude of the simulation decreases with time. This behavior is not captured by the small-angle approximation. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.7" } }, "nbformat": 4, "nbformat_minor": 5 }