S72_drone_actions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "i-gXNsu92PZA",
   "metadata": {},
   "source": [
    "# Multi-rotor Aircraft"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "130JPhHidKS4",
   "metadata": {
    "colab_type": "text",
    "tags": [
     "no-tex"
    ]
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/gtbook/robotics/blob/main/S72_drone_actions.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "Zp7gzudsDCy5",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install -q -U gtbook\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0r7YjGMlyqc9",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "from dataclasses import dataclass\n",
    "\n",
    "import gtsam\n",
    "from gtbook.drone import axes\n",
    "\n",
    "import plotly.express as px\n",
    "try:\n",
    "    import google.colab\n",
    "except:\n",
    "    import plotly.io as pio\n",
    "    pio.renderers.default = \"png\"\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", category=FutureWarning)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "N9xAZ4LIohhW",
   "metadata": {},
   "source": [
    "```{index} action; quadrotor flight\n",
    "```\n",
    "\n",
    "> Using four rotors to fly in 3D."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ca29243",
   "metadata": {
    "tags": [
     "no-pdf"
    ]
   },
   "source": [
    "<img src=\"Figures7/S72-Autonomous_camera_drone-06.jpg\" alt=\"Splash image with steampunk drone in various poses\" width=\"40%\" align=center style=\"vertical-align:middle;margin:10px 0px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "PC3xUjHFtmcH",
   "metadata": {},
   "source": [
    "```{index} navigation frame, body frame, FLU convention\n",
    "```\n",
    "The dynamics and kinematics of quadrotors and in general *multi*-rotor aircraft are those of simple rigid 3D bodies. Many different coordinate frame conventions are used in the literature. We introduce one good choice below, and convert equations from the literature to this convention where needed.\n",
    "\n",
    "The equations for control and navigation we develop below are most useful when expressed in a local **navigation frame** $N$. For MAV applications this frame is almost always assumed to be non-rotating and aligned with gravity, but can otherwise be defined arbitrarily.\n",
    "For example, the **East-North-Up (ENU)** convention defines the $x, y$ and $z$ axes along\n",
    "the east, north, and upward directions, respectively.\n",
    "The origin of the navigation frame is often chosen as the take-off point.\n",
    "Another choice is the UTM (Universal Transverse Mercator) coordinate system, which defines 60 locally flat coordinate frames on earth.\n",
    "\n",
    "We also define a **body frame** $B$ as having its origin at the center of mass of the vehicle. We fix the X-axis as pointing to the front of the vehicle (not always the direction of travel), the Y-axis as pointing to the left, and the Z-axis pointing up, the so-called **FLU convention**. In aerospace applications the so-called FRD convention with the Z-axis *down* is also popular, but it really is just matter of choice, and we find FLU to be more intuitive.\n",
    "\n",
    "We then define:\n",
    "\n",
    "- the vehicle's *position* $r^{n}\\doteq[x,y,z]^{T}$,\n",
    "\n",
    "- its linear velocity $v^n=\\dot{r^{n}}\\doteq[u,v,w]^{T}$,\n",
    "\n",
    "- the attitude $R^n_b\\doteq[\\hat{x}^n_b,\\hat{y}^n_b,\\hat{z}^n_b]\\in SO(3)$, a $3\\times 3$ rotation matrix with the columns of the body frame $B$ expressed in the navigation frame $N$,\n",
    "\n",
    "- the body angular velocity $\\omega^b\\doteq[p,q,r]^{T}$.\n",
    "\n",
    "Above the superscript $n$ and $b$ denote quantities expressed in the *navigation* and *body* frame, respectively. Together, these quantities allow us to talk about the *kinematics* of the drone: where it is and how it moves over time."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "QeuEe0QdANcN",
   "metadata": {},
   "source": [
    "## Drone Dynamics\n",
    "\n",
    "Kinematics alone is not enough, however: because an MAV has *mass*, we need to talk about how forces will bring about change in the velocity. One of us (Dellaert) has worked at the drone startup [Skydio](https://www.skydio.com/) and hence we will use one of its products as a prototypical example.\n",
    "\n",
    "<figure id=\"fig:Skydio\">\n",
    "<img src=\"https://github.com/gtbook/robotics/blob/main/Figures7/Skydio2axes.png?raw=1\" style=\"width:18cm\" alt=\"\">\n",
    "<figcaption>Skydio 2 drone with *Front-Left-Up* coordinate frame, and rotors labeled with coordinates. </figcaption>\n",
    "</figure>\n",
    "\n",
    "In particular, let us take the [Skydio 2+](https://www.skydio.com/skydio-2-plus) as a relevant example. Its mass, with battery, is about $800g$, but let's just say $1kg$ to make the calculations easier. Its dimensions are $229mm \\times 274mm$, but let us assume the motors are at $(+/- 0.10m, +/- 0.10m)$, which is not too far off. The figure above shows the setup."
   ]
  },
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   "cell_type": "markdown",
   "id": "E7sbuuKCOu1e",
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    "### Hover\n",
    "We denote by $f_i \\in \\mathbb{R}$ the amount of thrust provided by the $i^{th}$ rotor.\n",
    "This thrust is applied in the direction of the $z$-axis of the body frame.\n",
    "To hover, assuming we approximate the local gravity constant as $g=10m/s^2$, the four rotors *together* must provide a thrust of 10N upwards to compensate for gravity, i.e., 2.5N per motor. \n",
    "Of course, we need to be able to accelerate upwards, so let's assume each motor can provide up to double that, i.e., 0 to 5N. \n",
    "If the drone is level (i.e., the body $z$-axis is aligned with the direction of gravity), here are some sample accelerations we can deliver:\n",
    "\n",
    "- $f_i=0N$ for $i\\in{1..4}$: downwards acceleration at $-10\\frac{m}{s^2}$.\n",
    "- $f_i=2.5N$ for $i\\in{1..4}$: stable hover.\n",
    "- $f_i=5N$ for $i\\in{1..4}$: upwards acceleration at $10\\frac{m}{s^2}$.\n",
    "\n",
    "In general, the total force $F^b \\in \\mathbb{R}^3$ delivered by the rotors is aligned with the body Z-axis and is equal to\n",
    "\\begin{equation}\n",
    "F^b\n",
    "=\n",
    "\\begin{bmatrix}0 \\\\ 0 \\\\ F^b_z\\end{bmatrix}\n",
    "= \\sum_{i=1}^4 \\begin{bmatrix}0 \\\\ 0 \\\\ 1\\end{bmatrix} f_i.\n",
    "\\end{equation}\n",
    "As long as the drone is level, and hence the body $z$-axis is aligned with gravity, we can only accelerate up or down. The net acceleration in that case is obtained simply by subtracting the acceleration due to gravity. But, of course, only being to move up or down is not very useful, and is unlikely to happen anyway because of noise, wind, and other effects. Hence, below we look at how 3D orientation plays a role."
   ]
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   "id": "ifjhikLwfpUp",
   "metadata": {},
   "source": [
    "### Forward Flight\n",
    "\n",
    "The thrust delivered by the rotors is always aligned with the body frame's $z$-axis, and hence by rotating the quadrotor appropriately we can achieve any thrust direction in the navigation frame that we desire.\n",
    "For example, when the quadrotor *tilts* forward, some of the thrust delivered by the rotors \n",
    "will be directed toward generating horizontal acceleration. \n",
    "To get a handle on this, we need to calculate the thrust in the *navigation* frame $Nn$. This is accomplished by multiplying the 3D force $F^b$ in the body frame with the rotation matrix $R^n_b$:\n",
    "\\begin{equation}\n",
    "F^n = R^n_b \\begin{bmatrix}0 \\\\ 0 \\\\ F^b_z\\end{bmatrix} = \\hat{z}^n_b F^b_z.\n",
    "\\end{equation}\n",
    "Above $\\hat{z}^n_b$ is the third column of $R^n_b$, i.e., this is simply the $z$-axis of the body frame expressed in the navigation frame."
   ]
  },
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   "cell_type": "markdown",
   "id": "2BBQeea2Mo6f",
   "metadata": {},
   "source": [
    "As an example, let us assume that the Forward/$x$-axis of the FLU body frame is currently oriented along the \n",
    "North/$y$-axis of the ENU navigation frame, i.e., we are flying north. Then, if we tilt the body's Up/$z$-axis forward by an angle of $\\theta$ with respect to vertical, the body $z$-axis will have a $\\sin \\theta$ contribution towards the north (ENU $y$-axis), and a $\\cos \\theta$ up (ENU $z$-axis):\n",
    "\\begin{equation}\n",
    "\\hat{z}^n_b = \\begin{bmatrix}0 \\\\ \\sin \\theta \\\\ \\cos \\theta\\end{bmatrix}.\n",
    "\\end{equation}\n",
    "The thrust *vector* $F^n$ in the navigation frame is then obtained by multiplying with the total force $F^b_z$:\n",
    "\\begin{equation}\n",
    "F^n = \\begin{bmatrix}0 \\\\ \\sin \\theta \\\\ \\cos \\theta\\end{bmatrix} F^b_z.\n",
    "\\end{equation}\n",
    "The fact that $\\cos \\theta<1$ is potentially problematic: if we want to maintain level flight (not fall out of the sky!) we need to compensate for gravity by maintaining the constraint\n",
    "\\begin{equation}\n",
    "F^b_z \\cos \\theta  = 10.\n",
    "\\end{equation}\n",
    "That in turn means that the forward trust (along the navigation Y-axis) will be\n",
    "\\begin{equation}\n",
    "F^n_y = F^b_z  \\sin \\theta = \\frac{10}{\\cos \\theta} \\sin \\theta  = 10 \\tan \\theta  \n",
    "\\end{equation}\n",
    "This point bears repeating: if we tilt the drone to fly in a particular direction, the upward component of the thrust vector decreases, so we will have to *increase* total thrust, or we will lose altitude."
   ]
  },
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   "cell_type": "markdown",
   "id": "QoEpA3n5Xi7c",
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   "source": [
    "### Maximum Tilt and Thrust\n",
    "\n",
    "We can expand on this example to calculate what our maximum tilt angle would be, given bounded thrust. We are constrained by the maximum thrust $F^b_z$ we can deliver, which we assumed to be 20N above. Imposing this constraint in turn yields a constraint on $\\cos \\theta$:\n",
    "\\begin{equation}\n",
    "F^b_z = \\frac{10N}{\\cos \\theta} \\leq 20N \\rightarrow \\cos \\theta \\geq 0.5\n",
    "\\end{equation}\n",
    "From that we can deduce that the maximum tilt angle $\\theta$ is 60 degrees:\n",
    "\\begin{equation}\n",
    "-60^\\circ \\leq \\theta \\leq 60^\\circ\n",
    "\\end{equation}\n",
    "At that maximum tilt angle, we have\n",
    "\\begin{equation}\n",
    "F^n_y = 10 \\tan \\theta_{\\max} \\approx 17\n",
    "\\end{equation}\n",
    "So, we are limited to $17N$ of forward thrust, and this when tilting very aggressively at 60 degrees. If we tilt more, we can improve thrust even more (up to 20N) but the drone will quickly lose altitude. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "PtQ32QMlUg5t",
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   "source": [
    "```{index} drag, drag coefficient\n",
    "```\n",
    "### Drag and Maximum Velocity\n",
    "\n",
    "When drones fly through the air, they encounter air resistance, also known as **drag**, which\n",
    "can be understood as a force that acts opposite to the motion of the drone.\n",
    "Because of drag, constant forward thrust does *not* mean that the drone will continue accelerating.\n",
    "From the spec-sheet of the Skydio 2 drone we can see that the top speed in autonomous mode is 36Mph,\n",
    "which is about $16m/s$, while the theoretical top speed is probably more like $20m/s$. \n",
    "For air vehicles, the **drag coefficient**, which we denote by $k_d$,\n",
    "relates the vehicle speed to this resistive force.\n",
    "From physics we know that drag increases *quadratically* with velocity. \n",
    "Indeed, the drag force $k_d v_{top}^2$ at the top speed will exactly balance the maximum forward thrust of 17N:\n",
    "\\begin{equation}\n",
    "k_d v_{top}^2 = 17\n",
    "\\end{equation}\n",
    "If we assume the top speed of $20m/s$ is correct, we can estimate the drag coefficient $k_d$:\n",
    "\\begin{equation}\n",
    "k_d 20^2= 17 \\rightarrow k_d = 0.0425\n",
    "\\end{equation}\n",
    "Given the drag coefficient $k_d$, we can calculate a simple mapping from tilt angle $\\theta$ to the terminal forward velocity. For a given tilt angle $\\theta$ we first calculate the forward thrust $F^n_y$ in the navigation frame:\n",
    "\\begin{equation}\n",
    "F^n_y = \\tan \\theta \\cdot 10N\n",
    "\\end{equation}\n",
    "after which the velocity can be obtained by equating that to the drag force $k_d v^2$:\n",
    "\\begin{equation}\n",
    "\\tan \\theta \\cdot 10N = k_d v^2 \\rightarrow v = \\sqrt{\\frac{\\tan \\theta \\cdot 10}{k_d}}\n",
    "\\end{equation}\n",
    "Plugging in the estimated value of $k_d$ we obtain\n",
    "\\begin{equation}\n",
    "v \\approx 15 \\sqrt{\\tan \\theta}\n",
    "\\end{equation}\n",
    "With a smidgen of code we can build a lookup table `vmap` ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "AuOUnBraWHih",
   "metadata": {},
   "outputs": [],
   "source": [
    "vmap = {}\n",
    "for theta_deg in [0,1,5,10,15,20,30,40,50, 60]:\n",
    "  theta_rad = math.radians(theta_deg)\n",
    "  vmap[theta_deg] = 15. * math.sqrt(math.tan(theta_rad))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "UXgnZw7E4Gjd",
   "metadata": {},
   "source": [
    "...and plot it below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bNcT6HRr4NMY",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Velocity vs. Pitch Angle.\n",
    "#| label: fig:v_vs_theta\n",
    "px.line(x=list(vmap.keys()), y= list(vmap.values()), title=\"Velocity vs. Pitch Angle\",\n",
    "        labels={\"x\":\"Pitch Angle (deg)\", \"y\":\"Velocity (m/s)\"})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "EkAmikToNAY-",
   "metadata": {},
   "source": [
    "```{index} kinematics, statics, dynamics, linear velocity\n",
    "```\n",
    "## Drone Kinematics\n",
    "\n",
    "The subject of **kinematics** deals exclusively with positions and velocities, not the forces and accelerations involved to obtain those velocities. Kinematics should be contrasted with **statics** or steady-state force reasoning as we did above, and **dynamics** which describes the changing forces and accelerations over time.\n",
    "\n",
    "### Positional Kinematics\n",
    "\n",
    "For position, the vehicle's kinematics are straightforward. The time derivative $\\dot{r}^{n}$ of position $r^n$ in the navigation frame $N$ is equal to the **linear velocity** $v^n$, also in the navigation frame:\n",
    "\\begin{equation}\n",
    "\\dot{r}^{n}\t= v^n.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "875L18iKCOcx",
   "metadata": {},
   "source": [
    "```{index} angular velocity, roll, pitch, yaw\n",
    "```\n",
    "### Angular Velocity\n",
    "\n",
    "Just as we have a linear velocity $v^n$, a three-vector, we also have a 3-dimensional **angular velocity** $\\omega$,\n",
    "which is typically given *in the body frame* as $\\omega^b$.\n",
    "In this case, the components of $\\omega^b$ correspond to angular velocities around the respective body axes. \n",
    "This angular velocity vector has a very intuitive interpretation as an angle-axis interpretation: the vector can be viewed as a rotation axis in 3D, centered at the body coordinate frame, and its norm $\\|\\omega^b\\|$ is the instantaneous angular speed around that axis. \n",
    "\n",
    "For example, the drone steadily pitching downward by 10 degrees/second corresponds to a positive rotation around the body $y$-axis and the corresponding angular velocity is given by\n",
    "\\begin{equation}\n",
    "\\omega^b = \\begin{bmatrix}0 \\\\ 1 \\\\ 0\\end{bmatrix} 10 .\n",
    "\\end{equation}\n",
    "We use the *right hand rule*,\n",
    "which defines the a positive direction of angular velocity around a given axis is defined as counter-clockwise. \n",
    "Remember that in our FLU convention the $y$-axis points leftward from the center of the drone, and hence looking from the left a counter-clockwise movement corresponds to pitching *down*.\n",
    "\n",
    "In an FLU body frame, each of the axes is associated with a particular rotational motion:\n",
    "\n",
    "- **roll** is around the Forward/$x$-axis. Positive roll is to the right.\n",
    "- **pitch** is around the Left/$y$-axis. Positive pitch is downward.\n",
    "- **yaw** is around the Up/$z$-axis. Positive yaw is towards the left.\n",
    "\n",
    "Note that the statements associated with positive roll, pitch or yaw above are valid only when starting from upright hover. For example, when flying upside down, obviously yaw and pitch would behave oppositely.\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "When flying upside down but in the same direction, positive roll is still to the right. Think about it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ZX2fASwtBnMN",
   "metadata": {},
   "source": [
    "### Rotational Kinematics\n",
    "\n",
    "We can use rotation matrices to generalize the example above to arbitrary angular velocities. \n",
    "In Section 7.1 we have seen that $\\omega^b$ denotes the angular velocity of the body frame\n",
    "expressed in the coordinates relative to the body frame.\n",
    "Therefore, using the results from Section 7.1, we have\n",
    "\\begin{equation}\n",
    "\\dot{R}^n_b\t= \\hat{\\omega}^n R^n_b\n",
    "\\end{equation}\n",
    "and\n",
    "\\begin{equation}\n",
    "\\hat{\\omega}^b = \\left( R^n_b \\right)^T \\hat{\\omega}^n\n",
    "\\end{equation}\n",
    "The quantity $\\hat{\\omega}^b$ is a $3\\times 3$ skew-symmetric matrix, related to the angular velocity $\\omega^b$ as follows:\n",
    "\\begin{equation}\n",
    "\\hat{\\omega}^b\\doteq\\begin{bmatrix}\n",
    "0 & -\\omega^b_{z} & \\omega^b_{y}\\\\\n",
    "\\omega^b_{z} &  0& -\\omega^b_{x}\\\\\n",
    "-\\omega^b_{y} & \\omega^b_{x} &0\n",
    "\\end{bmatrix}.\n",
    "\\end{equation}\n",
    "As a reminder, as discussed in Section 7.1, $\\hat{\\omega}^b\\in \\mathfrak{so}(3)$, the Lie algebra associated with the 3D rotation group $SO(3)$. \n",
    "\n",
    "Regardless of whether we express the angular velocity with respect to\n",
    "the navigation or body frame,\n",
    "the time derivative $\\dot{R}^n_b$ of the $3\\times 3$ attitude (rotation matrix) $R^n_b$ is not very intuitive.\n",
    "In the next section we show how to integrate it over time to simulate or calculate the trajectory of the drone over time.\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "r_rmSxuOAVOg",
   "metadata": {},
   "source": [
    "## Simulation aka Forward Integrating\n",
    "\n",
    "Assuming we know the drone's velocity, we can calculate its position over time. More formally, if time histories $v^n(t)$ and $\\omega^b(t)$ for the linear and angular velocities are available, the vehicle's position $r^{n}(t)$ and attitude $R^n_b(t)$ can be integrated forward using the following two equations:\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "r^n_{k+1} &= r^n_{k} + d^k_{k+1}(v^n(t), \\Delta t)\\\\\n",
    "R^n_{b,k+1} &= R^n_{b,k} R^k_{k+1}(\\omega^b(t), \\Delta t)\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "where $\\Delta t$ is the sample time and the index $k$ refers to discretized times $t_k$, spaced $\\Delta t$ apart. Above we have conveniently used two magic functions $d^k_{k+1}(\\cdot)$ and $R^k_{k+1}(\\cdot)$, defined below:\n",
    "\n",
    "- $d^k_{k+1}(v^n(t), \\Delta t)$ computes the relative displacement obtained by exactly integrating the time-varying velocity $v^n(t)$ over the interval $(t_k,t_{k+1}]$, and\n",
    "- $R^k_{k+1}(\\omega^b(t), \\Delta t)$ computes the relative rotation obtained by exactly integrating the time-varying angular velocity $\\omega^b(t)$ over that same interval.\n",
    "\n",
    "Exactly integrating a time-varying quantity is not easy, however, so these abstract function definitions only get us so far. Below we see how to implement this *in practice*."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cQz0ZhyQRIzg",
   "metadata": {},
   "source": [
    "```{index} forward Euler method, backward Euler method, trapezoidal method\n",
    "```\n",
    "### Integrating Position\n",
    "\n",
    "The above is exact, but when implementing this in code we need to use a numerical integration scheme. For position, the simplest integration scheme is the **forward Euler method**\n",
    "\\begin{equation}\n",
    "d^k_{k+1}(v^n(t), \\Delta t) \\approx v^n(t_k) \\Delta t\n",
    "\\end{equation}\n",
    "which approximates velocity $v^n(t)$ over the interval $(t_k,t_{k+1}]$ as constant with value $v^n(t_k)$. Of course, this is just an approximation, and its quality depends both on the time step $\\Delta t$ (smaller is better) and on the nature of the trajectory (smoother is better). \n",
    "\n",
    "The forward Euler method is not the only possible integration scheme. There is also the **backward Euler method**, which uses $v^n(t_{k+1})$, and the **trapezoidal method**, which uses the average $0.5v^n(t_k)+0.5v^n(t_{k+1})$. More sophisticated integration schemes are possible, allowing for larger sample times $\\Delta t$, but they require more function evaluations of the velocity."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "l3jrD19O2At7",
   "metadata": {},
   "source": [
    "### Integrating Attitude\n",
    "\n",
    "For the attitude part, it turns out that the equivalent forward Euler method can be implemented *in closed form* using **Rodrigues' rotation formula**, which states that the rotation matrix\n",
    "corresponding to a rotation by angle $\\theta$ about a unit vector $K$ is given\n",
    "by\n",
    "\\begin{equation}\n",
    "R =  I + \\sin\\theta \\hat{K} + (1-\\cos\\theta) \\hat{K}^2\n",
    "\\end{equation}\n",
    "To apply this to our problem of integrating angular velocity at time $k$\n",
    "we define $K$ to be the unit vector $\\omega^b_k /\\|\\omega^b_k\\|$, and $\\theta=\\|\\omega^b_k\\| \\Delta t$ as the amount of rotation over the $\\Delta t$ interval.\n",
    "This is equivalent to approximating the total rotation during the interval $\\Delta t$\n",
    "by the constant angle $\\theta$,\n",
    "and leads to the following approximation for the corresponding rotation matrix:\n",
    "\\begin{equation}\n",
    "R^k_{k+1}(\\omega^b(t), \\Delta t) \\approx I + \\sin\\theta \\hat{K} + (1-\\cos\\theta) \\hat{K}^2\n",
    "\\end{equation}\n",
    "Again, note that this only an approximation because it is after all an Euler step: it is only exact if the time-varying angular velocity $\\omega^b(t)$ is actually constant over the interval.\n",
    "\n",
    "The last term in Rodrigues' formula is typically small for small sample times $\\Delta t$ because (a) $(1-\\cos\\theta)$ is small for small $\\theta$, and (b) the matrix $\\hat{K}^2$ contains squares of numbers smaller than 1. Hence, an often-used first-order approximation for Euler's method in rotation spaces is\n",
    "\\begin{equation}\n",
    "R^k_{k+1}(\\omega^b(t), \\Delta t) \\approx I + \\sin\\theta \\hat{K} \\approx I + \\hat{\\omega}^b_k \\Delta t =\n",
    "\\begin{bmatrix}\n",
    "1 & -\\omega^b_{z}\\Delta t  & \\omega^b_{y}\\Delta t \\\\\n",
    "\\omega^b_{z}\\Delta t  & 1 & -\\omega^b_{x}\\Delta t \\\\\n",
    "-\\omega^b_{y}\\Delta t  & \\omega^b_{x}\\Delta t  & 1\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "where we also used the small angle approximation $\\sin \\theta \\approx \\theta$.\n",
    "Note that strictly speaking this approximation (unlike Rodrigues' formula) departs the rotation manifold and we need to re-normalize to ensure that the attitude $R^n_b$ remains a proper orthonormal rotation matrix, i.e., $R^n_b\\in SO(3)$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eKtmM-5JKnT6",
   "metadata": {},
   "source": [
    "So, finally, we have a simple to implement approximation of the attitude integration step:\n",
    "\\begin{equation}\n",
    "R^n_{b,k+1} = R^n_{b,k} R^k_{k+1}(\\omega^b(t), \\Delta t) \n",
    "\\approx R^n_{b,k} \n",
    "\\begin{bmatrix}\n",
    "1 & -\\omega^b_{z}\\Delta t  & \\omega^b_{y}\\Delta t \\\\\n",
    "\\omega^b_{z}\\Delta t  & 1 & -\\omega^b_{x}\\Delta t \\\\\n",
    "-\\omega^b_{y}\\Delta t  & \\omega^b_{x}\\Delta t  & 1\n",
    "\\end{bmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cChcLU0MzNls",
   "metadata": {},
   "source": [
    "## An Example in Code\n",
    "\n",
    "Given the above, simulating the kinematics of a drone in code is not that hard. We can capture the math in a simple class. We use a python `dataclass` which is easy to initialize, and perform Euler integration in the `integrate` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "IfyiFo-hdp84",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class DroneKinematics:\n",
    "    rn: gtsam.Point3\n",
    "    vn: gtsam.Point3\n",
    "    nRb: gtsam.Rot3\n",
    "    wb: gtsam.Point3\n",
    "\n",
    "    def pose(self):\n",
    "        \"\"\"Return the current pose of the drone.\"\"\"\n",
    "        return gtsam.Pose3(self.nRb, self.rn)\n",
    "        \n",
    "    def integrate(self, dt):\n",
    "        \"\"\"Integrate the drone position/attitude forward in time by dt seconds.\"\"\"\n",
    "        self.rn += self.vn * dt  # integrate position\n",
    "        # calculate incremental rotation matrix using the exponential map\n",
    "        dR = gtsam.Rot3.Expmap(self.wb * dt)\n",
    "        self.nRb = self.nRb * dR  # integrate attitude"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aIFM8M6QxwDB",
   "metadata": {},
   "source": [
    "Above, the `Rot3.Expmap`, for \"exponential map\", implements Rodrigues' formula exactly. \n",
    "The approach is based on the exponential form of Rodrigues' formula:\n",
    "\\begin{equation}\n",
    "\\exp ( \\theta \\hat{K}) \\doteq I + \\sin\\theta \\hat{K} + (1-\\cos\\theta) \\hat{K}^2\n",
    "\\end{equation}\n",
    "which relies on the *exponential map* from $\\mathfrak{so}(3)$\n",
    "to $SO(3)$, a concept that generalizes to other Lie groups.\n",
    "\n",
    "Note that the `*` operator is overloaded in gtsam to properly compose 3D rotations.\n",
    "\n",
    "We demonstrate the above by forward integrating a quadrotor's position and orientation starting from a \"forward flight\" configuration at the origin, i.e., pitched forward by 10 degrees. We first specify the attitude using `Rot3.Pitch`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "gEZvcJAVastM",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.98  0.    0.17]\n",
      " [ 0.    1.    0.  ]\n",
      " [-0.17  0.    0.98]]\n"
     ]
    }
   ],
   "source": [
    "nRb0 = gtsam.Rot3.Pitch(math.radians(10))\n",
    "print(np.round(nRb0.matrix(),2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "kNWHS_n3YG8Q",
   "metadata": {},
   "source": [
    "Note that the forward $x$-axis (first column) is pointed slightly down, the $y$-axis is level, and the $z$-axis is pointed up but slightly forward. This time we are flying in the direction of the navigation $x$-axis, i.e., *eastward* in the ENU convention. We have calculated before that the velocity at this angle is $6~m/s$.\n",
    "\n",
    "Let us also assume that the 4 rotors conspire to create an angular velocity $\\omega^b$ around the vertical body axis of 10 degrees/second:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "VcPpvnKFE01o",
   "metadata": {},
   "outputs": [],
   "source": [
    "vb = gtsam.Point3(6,0,0)                # body velocity\n",
    "wb = gtsam.Point3(0,0,math.radians(10)) # angular velocity, 10 degrees per second around the Z-axis (up)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2q0FT3o8oWNc",
   "metadata": {},
   "source": [
    "We expect that a positive angular velocity around the $z$-axis, i.e., positive yaw, will correspond to a counter-clockwise spinning of the drone when looking from the top. Let us confirm this by implementing the kinematics in code.\n",
    "\n",
    "We can integrate the linear and angular velocities `vb` and `wb` above, *taking care to convert the body velocity to the navigation frame at each time step*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "qWb2YchmiwWz",
   "metadata": {},
   "outputs": [
    {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Drone kinematics simulation.\n",
    "#| label: fig:drone_kinematics\n",
    "vn0 = nRb0.rotate(vb)  # velocity in navigation frame\n",
    "drone = DroneKinematics(gtsam.Point3(0, 0, 0), vn0, nRb0, wb)\n",
    "\n",
    "fig = px.scatter_3d(x=[0], y=[0], z=[0])\n",
    "scale, labels = 5, [\"F\", \"L\", \"U\"]\n",
    "fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "for k in range(10):\n",
    "    drone.vn = drone.nRb.rotate(vb)  # velocity in navigation frame\n",
    "    drone.integrate(dt=1)\n",
    "    fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "fig.update_layout(showlegend=False, scene_aspectmode='data').show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "qjGSG4VPoWpL",
   "metadata": {},
   "source": [
    "Above we used the `gtbook.drone.axes` method, which hides more magic to create the axes.You can see that the drone takes off in the positive $x$-direction, which is East in the ENU convention, and then gradually turns towards the north, which is indeed a counter-clockwise rotation around vertical!\n",
    "\n",
    "### Exercises\n",
    "\n",
    "- Change the direction of the turn to the other side.\n",
    "- Change the code to use different values for $\\Delta t$ and observe the results.\n",
    "- Change the initial forward orientation to be the *northern* direction."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "LpI2H3rbwy5B",
   "metadata": {},
   "source": [
    "```{index} torque, mass, inertia matrix\n",
    "```\n",
    "## Full Rigid-Body Dynamics\n",
    "\n",
    "> Not hard to write down, but harder to understand.\n",
    "\n",
    "Ultimately we need to move a quadrotor by provide forces through the four rotors.\n",
    "Above we have discussed the forces that are applied by the rotors.\n",
    "We now extend this idea to include **torque**, which is the rotational version of force.\n",
    "The combination of forces and torques yield corresponding linear and angular accelerations.\n",
    "\n",
    "Let us start with Newton's second law, with the acceleration $a$ written suggestively as $\\dot{v}^n$, and immediately thinking in terms of force and velocity *vectors* in the navigation frame:\n",
    "\\begin{equation}\n",
    "F^n = m \\dot{v}^n\n",
    "\\end{equation}\n",
    "The **mass** $m$ can be seen as a scalar that *resists* motion: the higher the mass, the higher the force needed to produce an acceleration in any direction. Note that we could consider $m$ to be a diagonal matrix with the mass on the diagonal: acceleration is resisted the same way in all three axes, in whatever coordinate frame we choose.\n",
    "\n",
    "The same is (approximately) true for rotational motion.\n",
    "If we write the torques on the quadrotor with respect to the body frame,\n",
    "if the angular velocity is given by $\\omega^b$,\n",
    "the corresponding body torque is approximately given by\n",
    "\\begin{equation}\n",
    "\\tau^b \\approx I \\dot{\\omega}^b\n",
    "\\end{equation}\n",
    "This is only an approximation, because it ignores gyroscopic forces, but it is reasonable for small angular velocities $\\omega^b$.\n",
    "\n",
    "Here the **inertia matrix** $I$ is resisting *angular* motion.\n",
    "Expressed in an FLU body coordinate frame, the inertia matrix $I$ is typically approximated by a diagonal matrix with \"small-small-big\" diagonal elements, as the motor masses are further away from the $z$-axis than from the $x$- and \n",
    "$y$-axes, and hence resist acceleration around the $z$-axis more.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eHHXRpndVbA2",
   "metadata": {},
   "source": [
    "Let us calculate the moments of inertia assuming that each motor is 150 grams, and neglecting the body's mass for now. All four motors contribute to the moment of inertia $I_{xx}$ around the X-axis. Each motor, at a distance of $r = 0.1$ meters from the $x$-axis, contributes $m \\times r^2$ to the moment of inertia, which gives:\n",
    "\\begin{equation}\n",
    "I_{xx} = 4 \\times 0.15 \\times 0.1^2 = 0.006 \\, \\text{kg} \\cdot \\text{m}^2\n",
    "\\end{equation}\n",
    "Because of symmetry, $I_{yy}$ has the same value. For the moment of inertia $I_{zz}$ about the z-axis what counts is the distance of each motor from the z-axis, which is $\\sqrt{0.1^2 + 0.1^2}$ for each motor. Hence\n",
    "\\begin{equation}\n",
    "I_{zz} = 4 \\times 0.15 \\times (0.1^2 + 0.1^2) = 0.012 \\, \\text{kg} \\cdot \\text{m}^2\n",
    "\\end{equation}\n",
    "As you can see, because the motors are farther away from the $z$-axis than from the $x$- or $y$-axes, it takes twice the torque around the $z$-axis to get the same angular acceleration."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Uo9_hb0vbpq4",
   "metadata": {},
   "source": [
    "### Gyroscopic effects\n",
    "\n",
    "> From the approximate to the exact.\n",
    "\n",
    "If a quadrotor undergoes large angular velocities, we cannot ignore gyroscopic effects.\n",
    "In this case, the (exact) rotational dynamics equation is given by:\n",
    "\\begin{equation}\n",
    "\\tau^b = I \\dot{\\omega}^b + \\omega^b \\times I \\omega^b,\n",
    "\\end{equation}\n",
    "where $\\times$ is the vector cross-product. The second term is a set of quadratic components in the angular velocity $\\omega^b$ and that is why for small angular velocities they can be ignored. In fact, in many cases the orientation of a quadrotor is *actively controlled* to stay constant during hovering or in fast forward flight, and it is only in complicated maneuvers that large angular velocities occur."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "NBsvCS6-GTsj",
   "metadata": {},
   "source": [
    "### Generating Force and Torque\n",
    "\n",
    "What is still missing is how to translate from forces at the rotors to a force and torque on the *body*. In the body coordinate frame, the force equation is easy and we have seen it before:\n",
    "\\begin{equation}\n",
    "F^b_z = f \\doteq \\sum_i f_i.\n",
    "\\end{equation}\n",
    "Above the forces $f_i$ at the rotors are all oriented along the body $z$-coordinate axis (up!) and hence when we sum them we get a single force component $F^b_z$ along the body $z$-axis.\n",
    "\n",
    "We also need to include the effect of gravity, which acts along the negative $z$-axis of the navigation frame. \n",
    "If we denote by $F_\\mathrm{{tot}}$ the total force, which includes both the effects of the rotor thrusts and of gravity,\n",
    "we have have: \n",
    "\\begin{equation}\n",
    "F_\\mathrm{tot}^n = R^n_b F^b + m g^n\n",
    "\\end{equation}\n",
    "where $F^b \\doteq [0,0,f]^T$ is the 3D thrust vector in the body frame, and $g^n \\doteq [0,0,-g]^T$ is the gravity vector, expressed in the navigation frame."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8YefiLOKZ6A",
   "metadata": {},
   "source": [
    "The torque $\\tau^b$ in the body frame is a bit more involved, and is a function of the force vector $f$. The exact formula depends on the geometry of the rotors. For example, for a 4-motor “X” configuration with motor 1 forward left and numbered clockwise, we obtain\n",
    "\\begin{equation}\n",
    "\\tau^b = \\begin{bmatrix}\n",
    "l(f_{1}-f_{2}-f_{3}+f_{4})\\\\\n",
    "l(f_{1}+f_{2}-f_{3}-f_{4})\\\\\n",
    "\\kappa (f_{1}-f_{2}+f_{3}-f_{4})\\\\\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "where $l$ is the distance from the rotors to the center of mass, and $\\kappa$ is a torque constant.\n",
    "From this equation you can see that a quadrotor is like a differential drive robot but with *two* differential axes. Controlling it is easy in principle: *tilt, then move*. A part of $F^b_z$ will be used to keep the quadrotor flying, the other part will be used to overcome drag and attain a constant velocity in the chosen direction.\n",
    "\n",
    "The final piece of the puzzle is how exactly the rotors generate the individual forces $f_i$. We will not discuss that in detail here, but suffice to say that the forces $f_i$ are well understood functions of the rotor speed. Each motor also generates a small torque $\\kappa f_i$ around it's rotor axis,  proportional to the force with proportionality constant $\\kappa$. The rotation direction for each rotor determines which sign to use to calculate the $z$-component of the body torque $\\tau^b$.\n",
    "\n",
    "#### Exercises\n",
    "\n",
    "- Try to deeply understand the torque matrix above.\n",
    "- Try to create the torque matrix for a 4-motor \"+\" configuration."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sg_jrPvzyOxk",
   "metadata": {},
   "source": [
    "### Putting it all together\n",
    "\n",
    "> Kinematics and dynamics make motion.\n",
    "\n",
    "Kinematics governs how states are moved by velocities, and dynamics governs how accelerations are changed by forces and moments. Putting things together, the full equations of motion for the drone then read:\n",
    "\\begin{equation}\n",
    "\\begin{align}\n",
    "\\dot r^n &= v^n \\\\\n",
    "\\dot{R}^n_b\t&=  \\hat{\\omega}^n R^n_b \\\\\n",
    "m \\dot v ^n &= R^n_b F^b + m g^n \\\\\n",
    "I \\dot{\\omega}^b &= \\tau^b + \\omega^b \\times I \\omega^b\n",
    "\\end{align}\n",
    "\\end{equation}\n",
    "where $r^n$, $v^n$, $R^n_b$, and $\\omega^n$ are kinematic state, $F^b$ and $\\tau^b$ are dynamic inputs, and $m$ and $I$ are system parameters.\n",
    "\n",
    "With this, we can create the final version of a drone simulator, which we will use fully in Section 7.5. Note we model drag but neglect gyroscopic effects below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "JISeeYa-49IM",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class Drone(DroneKinematics):\n",
    "    g: float = 9.81\n",
    "    mass: float = 1.0\n",
    "    k_d: float = 0.0425                        # drag coefficient\n",
    "    gn: np.ndarray = gtsam.Point3(0, 0, -g)    # gravity vector in navigation frame.\n",
    "    I_xy: float = 4 * 0.15 * mass * 0.1**2     # All 4 motors contribute to I_xy\n",
    "    I_z: float = 4 * 0.15 * mass * 2 * 0.1**2  # I_z leverages longer arm\n",
    "    I = np.diag([I_xy, I_xy, I_z])             # Inertia matrix\n",
    "\n",
    "    # define integrate method that updates dynamics and then calls super's integrate method:\n",
    "    def integrate(self, f: float, tau:gtsam.Point3, dt=1.0):\n",
    "        \"\"\"Integrate equations of motion given dynamic inputs f and tau.\"\"\"\n",
    "        # Calculate net force in navigation frame, including gravity and drag:\n",
    "        Fb = gtsam.Point3(0, 0, f)\n",
    "        drag_force = -self.k_d * self.vn * np.linalg.norm(self.vn)\n",
    "        net_force = self.nRb.rotate(Fb) + self.gn + drag_force\n",
    "        \n",
    "        # Integrate velocity in navigation frame:\n",
    "        self.vn += net_force * dt / self.mass\n",
    "\n",
    "        # rotational drag, assume 10x smaller linearly proportional to angular velocity:\n",
    "        net_tau = tau - 0.1 * self.k_d * self.wb\n",
    "\n",
    "        # Integrate angular velocity in body frame:\n",
    "        self.wb[0] += net_tau[0] * dt / self.I_xy\n",
    "        self.wb[1] += net_tau[1] * dt / self.I_xy\n",
    "        self.wb[2] += net_tau[2] * dt / self.I_z\n",
    "        \n",
    "        # Call super's integrate method for kinematics\n",
    "        super().integrate(dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "NXJ4FVRUmwWj",
   "metadata": {},
   "source": [
    "We can verify that with just enough upward thrust ($f=9.81$) and zero torque, we attain a perfect hover:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "x-oVEdKVCy_4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Dynamics simulation of a drone hovering.\n",
    "#| label: fig:drone_dynamics\n",
    "zero = lambda : gtsam.Point3(0, 0, 0)\n",
    "drone = Drone(rn=zero(), vn=zero(), nRb=gtsam.Rot3(), wb=zero())\n",
    "fig = px.scatter_3d(x=[0], y=[0], z=[0])\n",
    "fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "for k in range(10):\n",
    "    drone.integrate(9.81, zero(), dt=1)\n",
    "    fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "fig.update_layout(showlegend=False, scene_aspectmode='data').show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2i__WDR8Y2to",
   "metadata": {},
   "source": [
    "Because we model drag, for a given non-zero linear velocity the drone keeps moving because of inertia but slows down as time goes on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "M5qX7HosCvmr",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final velocity: [0.69 0.   0.  ]\n"
     ]
    }
   ],
   "source": [
    "#| caption: Dynamics simulation of a drone floating forward.\n",
    "#| label: fig:drone_dynamics_forward\n",
    "drone = Drone(rn=zero(), vn=gtsam.Point3(1, 0, 0), nRb=gtsam.Rot3(), wb=zero())\n",
    "fig = px.scatter_3d(x=[0], y=[0], z=[0])\n",
    "fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "for k in range(10):\n",
    "    drone.integrate(9.81, zero(), dt=1)\n",
    "    fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "fig.update_layout(showlegend=False, scene_aspectmode='data').show()\n",
    "print(\"final velocity:\", np.round(drone.vn, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "agM2CDsuLoBw",
   "metadata": {},
   "source": [
    "We can also execute fully dynamic maneuvers. Here we show the forward flight condition we discussed above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ws5R9ORHUoYZ",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Dynamics simulation of a drone accelerating through pitching.\n",
    "#| label: fig:drone_dynamics_pitch\n",
    "pitch = math.radians(10)\n",
    "f = 9.81 / math.cos(pitch)\n",
    "drone = Drone(rn=zero(), vn=zero(), nRb=gtsam.Rot3.Pitch(pitch), wb=zero())\n",
    "fig = px.scatter_3d(x=[0], y=[0], z=[0])\n",
    "scale, labels = 10, [\"F\", \"L\", \"U\"]\n",
    "fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "for k in range(10):\n",
    "    drone.integrate(f, zero(), dt=1)\n",
    "    fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "fig.update_layout(showlegend=False, scene_aspectmode='data').show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aTc3-HNV2GU5",
   "metadata": {},
   "source": [
    "Note the drone speeds up from hover but fairly quickly reaches terminal velocity because of drag.\n",
    "\n",
    "Finally, if we input a small moment, we can make the drone changes direction. However, one's first instinct of rotating around the body Up/$z$-axis will not actually make the drone's trajectory curved! Indeed, in the body frame, rotating around the $z$-axis leaves the direction of the $z$-axis unchanged, and hence also the thrust exerted by the motors. While the \"Forward\" direction of the drone will change, only a change in the direction of thrust can make the center of mass move along a curve. A small moment \"roll\" around the Forward/$x$-axis will do the trick:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "jaYo_xW3QVgl",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Dynamics simulation of a drone curving left.\n",
    "#| label: fig:drone_dynamics_left\n",
    "drone = Drone(rn=zero(), vn=zero(), nRb=gtsam.Rot3.Pitch(pitch), wb=zero())\n",
    "fig = px.scatter_3d(x=[0], y=[0], z=[0])\n",
    "scale, labels = 10, [\"F\", \"L\", \"U\"]\n",
    "fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "for k in range(10):\n",
    "    drone.integrate(f, gtsam.Point3(-0.0001,0,0), dt=1)\n",
    "    fig.add_traces(axes(drone.pose(), scale, labels))\n",
    "fig.update_layout(showlegend=False, scene_aspectmode='data').show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "BqYYxxqs9OIx",
   "metadata": {},
   "source": [
    "### Exercises:\n",
    "\n",
    "- In this last scenario, is the drone curving the correct way? Think about the sign of the roll moment.\n",
    "- What happens if you extend the simulation? Form a hypothesis first, then try it. Does the drone keep turning? Explain."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "S72_drone_actions.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3.8.12 ('gtbook')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  },
  "latex_metadata": {
   "affiliation": "Georgia Institute of Technology",
   "author": "Frank Dellaert and Seth Hutchinson",
   "title": "Introduction to Robotics"
  },
  "vscode": {
   "interpreter": {
    "hash": "9f7376ced4243bb13dfcffa8a3ba834e0602aa8334cd3a1d8ba8d285f4628083"
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