S41_logistics_state.ipynb

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   "source": [
    "<a href=\"https://colab.research.google.com/github/gtbook/robotics/blob/main/S41_logistics_state.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,
   "metadata": {
    "id": "JoW4C_OkOMhe",
    "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,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "from numpy.random import default_rng\n",
    "rng = default_rng()\n",
    "\n",
    "import plotly.graph_objects as go\n",
    "try:\n",
    "    import google.colab\n",
    "except:\n",
    "    import plotly.io as pio\n",
    "    pio.renderers.default = \"png\"\n",
    "\n",
    "import gtsam\n",
    "from gtbook import logistics\n"
   ]
  },
  {
   "attachments": {},
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   "metadata": {
    "id": "nAvx4-UCNzt2"
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   "source": [
    "```{index} state; continuous state\n",
    "```\n",
    "\n",
    "# Continuous State\n",
    "\n",
    "> The motion of our warehouse robots is restricted to translation in the 2D plane (i.e., there is no rotational motion).\n",
    "\n",
    "<img src=\"Figures4/S41-Warehouse_robots-07.jpg\" alt=\"Splash image with warehouse robot in two different states\" width=\"40%\" align=center style=\"vertical-align:middle;margin:10px 0px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imagine a vast warehouse, with rows of storage, a flat concrete floor, and many people operating alongside robots to fulfill orders and replenish inventory. \n",
    "In logistics applications of this kind, the main job of the robot is to transport items from one location\n",
    "to another. An accurate and complete map of the warehouse layout is typically available, and the motion\n",
    "of the robot is fairly simple, often restricted to translation in directions that are parallel to coordinate\n",
    "axes defined by the arrangement of storage shelves. \n",
    "Such motions can be achieved by a robot equipped with omni-wheels, which allow instantaneous\n",
    "motion in any direction.\n",
    "Because the robot's motion is limited to pure translation, the orientation of the robot\n",
    "does not change, and need not be considered when defining the robot state.\n",
    "Furthermore, because these robots typically move at relatively low speeds, we need not consider forces\n",
    "(or wheel torques) that are required to effect these motions.\n",
    "\n",
    "For this special case of robots that translate in the plane, and whose instantaneous\n",
    "velocity is the command input, the state space is merely the location of the robot\n",
    "in the world with respect to some global coordinate frame:\n",
    "\n",
    "$$x\\in {\\cal D} \\subset \\mathbb{R}^2$$\n",
    "\n",
    "In the remainder of this chapter, we will consider a rectangular warehouse\n",
    "that is 100 by 50 meters, a good size warehouse, similar to a typical DIY store.\n",
    "In this case, $ {\\cal D} = [0,100] \\times [0,50]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In previous chapters, we considered discrete state spaces (categories of objects, rooms in a house). Here, the\n",
    "state space is continuous, which brings a need for more sophisticated methods for dealing with uncertainty.\n",
    "We can broadly divide these approaches into two categories: \n",
    "directly using exact, parameterized probability density functions (pdf's),\n",
    "and using discrete approximations to probability distributions.\n",
    "When using exact pdf's, we will restrict our attention to the multivariate (in our case, bivariate) Gaussian distribution\n",
    "to characterize uncertainty in state.\n",
    "We have previously used univariate Gaussians to model weight for our trash sorting robot,\n",
    "and the extension to the 2D case is not so difficult.\n",
    "In the of approximate representations of probability distributions,\n",
    "we will introduce two complementary methods: a finite element method, and a sampling-based method.\n",
    "In the former, we approximate the state space by a two-diminsional grid, and keep track of the\n",
    "probability mass in each individual grid cell. This is \n",
    "In the latter, we represent a pdf by a weighted collection of samples.\n",
    "This representation is particularly amenable to propagating uncertainties that arise during\n",
    "robot motion."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Densities\n",
    "\n",
    "As we have seen with the trash sorting robot, a one-dimensional Gaussian density can be used\n",
    "to represent continuous random variables.\n",
    "The Gaussian probability density function (pdf) is defined by\n",
    "\n",
    "$$\\mathcal{N}(x;\\mu,\\sigma^2) \\doteq \\frac{1}{k} \\exp\\{ - \\frac{1}{2} \\frac{(x-\\mu)^2}{\\sigma^2} \\}$$\n",
    "\n",
    "where $\\mu$ is the mean, $\\sigma^2$ is the variance, and $k=\\sqrt{2\\pi}\\sigma$ is a normalization constant.\n",
    "It is instructive to consider the term in the exponent.\n",
    "1. The term $x-\\mu$ is the signed distance from $x$ to the mean.\n",
    "2. The term $(x-\\mu)^2$ is the squared distance from $x$ to the mean.\n",
    "3. The term $\\sigma^{-2}(x-\\mu)^2$ is a weighted squared-distance to the mean.\n",
    "\n",
    "Thus, we can interpret the negative log of a 1D Gaussian as a simple quadratic error or \"energy\" function. This fact is worth emphasizing: *a Gaussian density is the probability density associated with a quadratic error function with zero error at the mean $\\mu$ and variance $\\sigma^2$.* We suggestively write this quadratic below as\n",
    "\n",
    "$$\\mathcal{E}(x;\\mu,\\sigma^2) \\doteq \\frac{1}{2} (x-\\mu)\\sigma^{-2}(x-\\mu)$$"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{index} covariance matrix, multivariate Gaussian density",
    "```",
    "The energy analogy can be extended to the multivariate case.\n",
    "In the 1D case, the mean and variance are scalars.\n",
    "For the $n$-dimensional case when $x\\in\\mathbb{R}^n$, the mean is a vector,  $\\mu\\in\\mathbb{R}^n$,\n",
    "and the concept of variance is extended to define a \n",
    "**covariance matrix** $\\Sigma\\in\\mathbb{R}^{n\\times n}$,\n",
    "a symmetric, positive definite matrix that characterizes the \"spread\" of a quadratic in multiple dimensions. \n",
    "This allows us to generalize the 1D error function above to the $n$-dimensional case as\n",
    "\n",
    "$$\\mathcal{E}(x;\\mu,\\Sigma) \\doteq \\frac{1}{2} (x-\\mu)^T\\Sigma^{-1}(x-\\mu)$$\n",
    "\n",
    "We define a **multivariate Gaussian density** using the error function $\\mathcal{E}(x;\\mu,\\Sigma)$\n",
    "as follows\n",
    "\n",
    "$$\\mathcal{N}(x;\\mu,\\Sigma) \\doteq \\frac{1}{k} \\exp\\{ - \\frac{1}{2} (x-\\mu)^T\\Sigma^{-1}(x-\\mu) \\}$$\n",
    "\n",
    "The (non-obvious) normalization constant k can be written very elegantly in terms of the determinant of $2\\pi\\Sigma$:\n",
    "\n",
    "$$k=\\sqrt{(2\\pi)^{n}|\\Sigma|}=\\sqrt{|2\\pi\\Sigma|}.$$\n",
    "\n",
    "Another name for multivariate Gaussian probability density is the multivariate normal distribution. We prefer to use *density* to denote its continuous nature, and Gaussian instead of \"normal\", but it is good to be aware of both nomenclatures."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To better understand the multivariate Gaussian pdf, consider a simple two-dimensional example,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mu &= \\begin{bmatrix} 4 \\\\ 10 \\end{bmatrix} \\\\\n",
    "\\\\\n",
    "\\Sigma &= \\begin{bmatrix} \n",
    "\\sigma^2_{xx} & 0 \\\\\n",
    "0 & \\sigma^2_{yy} \n",
    "\\end{bmatrix}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "If we evaluate $\\mathcal{E}(x;\\mu,\\Sigma)$ for this case, we obtain\n",
    "\n",
    "$$\\mathcal{E}(x;\\mu,\\Sigma) = \\frac{1}{\\sigma^2_{xx}}(x - 4)^2 + \\frac{1}{\\sigma^2_{yy}}(y - 10)^2\n",
    "$$\n",
    "\n",
    "which is the familiar equation of an axis-aligned ellipse in the plane with center at $(4, 10)$.\n",
    "This form gives a nice geometric interpretation to the Gaussian pdf.\n",
    "For any constant $k$,\n",
    "the value of  $\\mathcal{N}(x;\\mu,\\Sigma)$ is constant for all $x$ that satisfy \n",
    "$\\mathcal{E}(x;\\mu,\\Sigma) = k$.\n",
    "For a 2D Gaussian, the level sets $\\{ x \\; | \\; \\mathcal{E}(x;\\mu,\\Sigma) = k \\}$ always take the form\n",
    "of a concentric ellipses (centered at $\\mu$) whose axes are determined by the covariance matrix $\\Sigma$.\n",
    "When illustrating 2D Gaussian pdf's, it is typical to show a few level sets (as in the example below),\n",
    "which is why there are so many ellipses in the figures below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " In python, none of the packages we rely on for this book define a Gaussian, but it is easy enough to do in code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gaussian(x:np.array, mean=np.zeros((2,)), cov=np.eye(2)):\n",
    "    \"\"\"Evaluate multivariate Gaussian at x of shape(m,n), yields (m,) vector.\"\"\"\n",
    "    assert x.shape[-1]==2, f\"error: x has shape {x.shape}\"\n",
    "    k = math.sqrt(np.linalg.det(2*math.pi*cov))\n",
    "    e = x - mean\n",
    "    E = np.sum(0.5 * (e @ np.linalg.inv(cov) * e), axis=-1)\n",
    "    return np.exp(-E)/k\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simple code above has limitations: it *only* works for dimensionality $n\\geq2$.  In this chapter we will be working in 2D, so below we show the effect of mean and covariance as density contour plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: Some example Gaussian densities in 2D.\n",
    "#| label: fig:example_gaussians\n",
    "means = [gtsam.Point2(x,y) for x,y in [(20,25),(70,40),(50,15)]]\n",
    "covariances = [np.diag([sx**2,sy**2]) for sx,sy in [(5,10),(20,5)]]\n",
    "covariances.append(np.array([[40,35],[35,40]]))\n",
    "\n",
    "data = [go.Contour(z=gaussian(logistics.map_coords, mean, cov), contours_coloring='lines',\n",
    "        line_width=2, showscale=False) for mean,cov in zip(means,covariances)]\n",
    "fig = go.Figure(data=data); fig.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first two Gaussians above are *axis-parallel*, and the covariance matrices simply contain the squared standard deviations of the $x$ and $y$ dimensions on their diagonals. The third Gaussian shows off the case where $x$ and $y$ are positively correlated, around a mean of $(50,15)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One advantage of the Gaussian as a probability density is that it is easy to specify and to compute with. A disadvantage is that it provides a very restricted class of densities: in particular, it is a *unimodal* density, meaning that it only has a single maximum. Hence, we will never be able to represent two equally probable locations in space, for example. One way to get around this limitation is to use a *mixture* of Gaussian densities. This is a well known technique, and has its merits, but is outside the scope of this book."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Finite Element Method\n",
    "\n",
    "Representing uncertainty using multivariate Gaussians has the appeal of providing\n",
    "an exact representation that depends on only a small number of parameters (the mean and covariance matrix).\n",
    "However, as mentioned above, multivariate Gaussians suffer from several limitations,\n",
    "including the inability to easily deal with multimodal distributions (e.g.,\n",
    "if the robot thinks it could be in any one of several aisles,\n",
    "but is fairly sure that it is located halfway down the aisle).\n",
    "A second limitation of Gaussians is that they are... Gaussians, and therefore they\n",
    "are of limited utility when uncertainty does not conform to the normal distribution.\n",
    "\n",
    "One way to deal with these limitations is to introduce approximate, grid-based representations\n",
    "of uncertainty.\n",
    "With this approach, each grid cell contains an associated probability mass.\n",
    "As the robot moves in the environment, the probabilities assigned to each grid cell\n",
    "are updated based on uncertainty in the motion model (as we'll see in the next section).\n",
    "When sensor data are available, perception algorithms can be used to reduce uncertainty,\n",
    "thereby concentrating probability mass in grid cells associated with higher likelihood\n",
    "values (as we'll see in the section on perception).\n",
    "Because this approximation does not rely on a parameterization of the pdf (e.g., it is\n",
    "not specified by a mean and covariance matrix), it can be used to approximate any pdf,\n",
    "with accuracy that depends on the number of cells in the grid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grid-based representations embody the classical trade-off between accuracy and complexity.\n",
    "The accuracy of the representation depends on the resolution along the grid coordinate\n",
    "axes, but the number of cells in the grid grows exponentially (with the dimension of the space)\n",
    "as a function of this resolution.\n",
    "Choosing the *resolution* for our discretization scheme is therefore a key design decision.\n",
    "For example, if we pick 1x1 meter cells, we are looking at $100\\times50=5000$ cells. But $1m^2$ seems a bit coarse for navigating with a robot. Could we get away with $10cm$ resolution? \n",
    "Here we immediately see difficulty that arises due to the exponential complexity associated to grids. In our case, increasing the resolution by 10, from 1 meter to 10cm, increases the number of cells needed by $10^2=100$, from 5000 to $1000\\times500=500k$.\n",
    "This difficulty, while significant in the 2D case, rapidly becomes untenable as the dimensionality of the problem\n",
    "increases.\n",
    "\n",
    "Below we show what the 1x1 meter discretization looks like for our warehouse example, using the same three Gaussian densities from above to illustrate a multimodal density:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: A finite element representation of the example Gaussian densities.\n",
    "#| label: fig:example_gaussians_finite\n",
    "probabilities = np.zeros((50,100))\n",
    "for mean,cov in zip(means,covariances):\n",
    "    probabilities += gaussian(logistics.map_coords, mean, cov)\n",
    "logistics.show_map(probabilities/np.max(probabilities))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7I_e7Iloge5i"
   },
   "source": [
    "## A Sampling-based representation.\n",
    "\n",
    "Sampling-based methods offer a simple, efficient alternative. \n",
    "Grid-based representations can be remarkably inefficient:\n",
    "regardless of how the probability mass is distributed over the state space, the number of cells\n",
    "remains fixed, and each cell must be considered when propagating uncertainty.\n",
    "Instead of discretizing the space and keeping track of the probability mass assigned to each grid cell,\n",
    "we can discretize the probability mass, and keep track of how that probability mass moves through\n",
    "the state space as uncertainty is propagated forward in time.\n",
    "Sampling-based approaches do exactly this.\n",
    "\n",
    "In sampling-based methods the density $p(x)$ is represented by a set of N random *samples* or,\n",
    "often called *particles,* $S=\\{s^{(i)};i\\in1..N\\}$ drawn from $p(x)$. \n",
    "We are able to do this because of the essential duality between the samples and the density from which they are generated: from the samples we can always approximately reconstruct the density, e.g. using a histogram.\n",
    "\n",
    "Sampling-based approaches can be significantly more efficient than grid-based approaches.\n",
    "First, the number of samples need not grow exponentially with the dimension of the space.\n",
    "Second, because we (attempt to) keep only samples that represent significant concentrations of probability\n",
    "mass, the number of samples will be small in areas that are unlikely.\n",
    "Finally, sampling-based approaches lend themselves to computationally efficient simulation schemes,\n",
    "and these can form the basis for perception algorithms used in localization (as we shall see shortly).\n",
    "\n",
    "Below, we use a numpy random number generator (`rng`, defined in preamble) to sample from the three Gaussians we defined above, and display the resulting sets of samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| caption: A sampling-based representation of the example Gaussian densities.\n",
    "#| label: fig:example_gaussians_samples\n",
    "N=500\n",
    "samples = [rng.multivariate_normal(mean, cov, size=N)\n",
    "           for mean,cov in zip(means,covariances)]\n",
    "data = [go.Scatter(x=sample[:,0],y=sample[:,1], mode=\"markers\",\n",
    "        marker=dict(size=3), name=i+1) for i, sample in enumerate(samples)]\n",
    "fig = go.Figure(data=data); fig.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing Probabilities\n",
    "\n",
    "In general, for continuous random variables, probability mass is computed by integrating probability density\n",
    "over a domain.\n",
    "In the 2D case,  we can find the probability of the state $x$ being contained in any finite region ${\\cal R}$ by integrating the pdf over ${\\cal R}$:\n",
    "\n",
    "$$P(x\\in {\\cal R}) = \\int_{x\\in {\\cal R}} p(x) dx$$\n",
    "\n",
    "In the case of Gaussian pdfs, it is not possible to compute this integral in closed form, but\n",
    "thanks to the nice geometric properties of the level sets of Gaussian pdfs, there\n",
    "are efficient numerical methods to do so.\n",
    "\n",
    "In the case of grid-based approximations, computing the probability mass assigned to a specific\n",
    "region amounts to summing the probabilities associated to the grid cells that define that region.\n",
    "\n",
    "For sampling-based approximations, a set of weighted samples can be used to construct\n",
    "histogram-style representation of the probability distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GTSAM 101\n",
    "\n",
    "> The GTSAM concepts used in this section, explained.\n",
    "\n",
    "We really used only one concept from GTSAM above, which is `gtsam.Point2`. For maximal compatibility with numpy, in python this is just a function that creates a 2D, float numpy array. Inside GTSAM, it is represented as an Eigen vector, where Eigen is the C++ equivalent of numpy."
   ]
  },
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    "## GTbook 101\n",
    "\n",
    "> About the support code we use throughout this book\n",
    "\n",
    "Because in this chapter we will use the same code over and over again, we defined some of the key functions in the `gtbook` library accompanying this book. In particular, above we used the following:\n",
    "- `logistics.map_coords`: a numpy array of shape (50, 100, 2) with x and y coordinates for every cell in the map, at 1m resolution.\n",
    "- `logistics.show_map`: takes a probability image and plots it using plotly's `imshow` function\n",
    "\n",
    "As always, you can get help on functions by calling `help`:"
   ]
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     "text": [
      "Help on function show_map in module gtbook.logistics:\n",
      "\n",
      "show_map(image=None, markers=None, file: str = None, marker={})\n",
      "    Show image on warehouse map, possibly with markers\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(logistics.show_map)\n"
   ]
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