S45_logistics_planning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github",
    "tags": [
     "no-tex"
    ]
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/gtbook/robotics/blob/main/S45_logistics_planning.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": {
    "id": "10-snNDwOSuC",
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.random import default_rng\n",
    "rng = default_rng()\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 gtsam\n",
    "from gtbook import logistics\n",
    "from gtbook.display import show, pretty\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "id": "nAvx4-UCNzt2"
   },
   "source": [
    "# Planning for Logistics\n",
    "\n",
    "> Our warehouse robot needs to know its location in the warehouse with more precision than the vacuuming robot.\n",
    "\n",
    "<img src=\"Figures4/S45-Warehouse_robots-05.jpg\" alt=\"Splash image with warehouse robot thinking\" width=\"40%\" align=center style=\"vertical-align:middle;margin:10px 0px\">\n",
    "\n",
    "In Chapter 3, we modeled a robot system as an MDP, and saw how to compute both\n",
    "the optimal value function and the corresponding optimal policy.\n",
    "The state space in Chapter 3 was very simple, having only five states.\n",
    "For our vacuuming robot, it was sufficient to know the room in which the\n",
    "robot was located, but this level of detail is not sufficient for our warehouse\n",
    "robot.\n",
    "In order to position itself accurately with respect to the shelves that\n",
    "contain inventory, the warehouse robot needs a quantitative description\n",
    "of its location, namely, coordinates in a warehouse coordinate frame.\n",
    "Therefore, for our warehouse robot, we represent\n",
    "the state space by a discrete grid, whose coordinates\n",
    "define the location of the robot.\n",
    "This representation has significantly more states than for the vacuuming robot.\n",
    "In this section, we show how to perform value iteration on such a grid, and\n",
    "briefly discuss the implications of estimating the state using sensor data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Value Iteration in 2D\n",
    "\n",
    "> It works, but can be slow."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that value iteration starts with an initial guess, $V^0$, and at each iteration we update\n",
    "our approximation of the value function by the update rule:\n",
    "\n",
    "$$\n",
    "V^{k+1}(x) \\leftarrow \\max_a \\left\\{ \\bar{R}(x,a) + \\gamma \\sum_{x'} P(x'|x, a) V^k(x')   \\right\\}\n",
    "= \\max_a Q(x, a; V^k)\n",
    "$$\n",
    "\n",
    "This can be *very* expensive if applied naively, when the number of states is large. Indeed, if we use the 5000-state finite element discretization of the warehouse, the conditional probability table (CPT) above contains $5k \\times 4 \\times 5k = 100M$ entries.\n",
    "\n",
    "There are ways to deal with this, computationally. Indeed, most transitions have zero probability, and hence we could store the CPT in a *sparse* multi-dimensional array instead. Alternatively, we can implement the Q value calculation as a *function*. This is what we will do below, and we will also immediately switch to using the 2D coordinates $(i,j)$ for the discretized cells:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "goal = 35, 50\n",
    "proximity = logistics.base_map + logistics.proximity_map_on\n",
    "\n",
    "def Q_value(x, a, V):\n",
    "    \"\"\"Given a state x=(i,j) action a, and value image, calculate Q value.\"\"\"\n",
    "    i, j = x\n",
    "    if x==goal: return 0 # only reward when *first* arriving at goal\n",
    "    if logistics.base_map[i,j]: return 0 # invalid state\n",
    "    if a == 0: next = (i,j-1) if j>0 else x # LEFT\n",
    "    if a == 1: next = (i,j+1) if j<99 else x # RIGHT\n",
    "    if a == 2: next = (i-1,j) if i>0 else x # UP\n",
    "    if a == 3: next = (i+1,j) if i<49 else x # DOWN\n",
    "    reward = 100 if next==goal else 0\n",
    "    r, c = next\n",
    "    if logistics.proximity_map_on[i,j]: reward -= 50 # in proximity is bad!\n",
    "    if logistics.proximity_map_on[r,c]: reward -= 50 # as is going in proximity.\n",
    "    return reward + 0.975 * V[r,c]\n",
    "\n",
    "def update_V(x, V):\n",
    "    \"\"\"Given a state x=(i,j) and value image, calculate updated value.\"\"\"\n",
    "    Q_x = [Q_value(x, a, V) for a in range(4)]\n",
    "    return max(Q_x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note above we assumed actions were *deterministic*, but the function can be easily adapted to non-deterministic actions. We awarded 100 points upon reaching the goal, but make sure that happens only once, or otherwise the value of that state will be infinite. In addition, when the state is near an obstacle (we use the `proximity_map_on` likelihood image from Section 4.3), the agent gets punished by 100 points. Below, we do value iteration using a brute force loop, which is still remarkably fast:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after 86 iterations, error = 0.0\n",
      "CPU times: user 1.95 s, sys: 15.4 ms, total: 1.97 s\n",
      "Wall time: 1.99 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "I, J = np.meshgrid(range(50), range(100), indexing='ij')\n",
    "states = np.dstack((I, J)).reshape(5000,2)\n",
    "k = 0\n",
    "V_k = np.full((50,100), 0.0)\n",
    "error = float('inf')\n",
    "while error>1e-5:\n",
    "    V_plus = np.empty((50,100), float)\n",
    "    for i,j in states:\n",
    "        V_plus[i,j] = update_V((i,j), V_k)\n",
    "    error = np.max(np.abs(V_plus-V_k))\n",
    "    V_k = V_plus\n",
    "    k += 1\n",
    "print(f\"after {k} iterations, error = {error}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.imshow(V_k, color_continuous_scale='Turbo',origin=\"upper\", aspect='equal')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the *gradient* of the value function determines the optimal policy: at any cell, we can just look around in all 4 directions and move to the cell with the largest value.\n",
    "\n",
    "### Thought Exercise\n",
    "\n",
    "Why might the algorithm terminate after 86 iterations?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Intuition behind Value Iteration\n",
    "\n",
    "> Costs and rewards propagate.\n",
    "\n",
    "It is instructive to look at an animation for how the value function evolves in successive iterations of the value iteration algorithm:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<figure id=\"fig:value\">\n",
    "<img src=\"https://github.com/gtbook/robotics/blob/main/Figures4/value.gif?raw=1\" style=\"width:14cm\" alt=\"\">\n",
    "<figcaption>The <b>value iteration</b> algorithm, animated.</figcaption>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most prominent phenomenon that one can make out in the animation above is that the reward from reaching the goal state, in the middle of the warehouse, gradually propagates towards every location. It gradually decreases in value because of the discount factor. It also does not penetrate the obstacles in the map, because those states simply have a value of zero.\n",
    "\n",
    "There is a deep connection between value iteration and the all-source-shortest-path algorithm that you might have seen in an algorithms class.\n",
    "Deterministic actions set up a graph, and while in this case we have no penalty to moving in the the graph, the discount factor plays the same role in practice.\n",
    "In fact, if we set the discount factor to zero and give actions a cost, both algorithms will return identical results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Closing the Loop\n",
    "\n",
    "> Adding a state estimator closes the sense-think-act loop.\n",
    "\n",
    "When the robot acts in the world, it senses, estimates its state, and executes a policy. We can take any of the algorithms from the last section and use them to estimate the robot's current state. The value function gives us a policy, which the robot can then execute. After that, repeat.\n",
    "\n",
    "To calculate the policy, we should take into account the uncertainty in actions. The policy we calculated above for the warehouse may not be optimal, because we assumed deterministic actions in the calculation of the Q values. In Section 3.5 we saw how to account for uncertain, Gaussian actions.\n",
    "We could do the same here to potentially obtain a better policy.\n",
    "In particular, the robot will be more cautious and stay even further away from obstacles,\n",
    "since the robot does not always perfectly execute commands.\n",
    "\n",
    "### Thought Exercise\n",
    "\n",
    "Estimating a single location for the robot is not always possible: posterior densities can be *multi-modal*, and so do not know any better than that we are in one of a number of possible locations. What should we do in that case?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partially Observable MDPs\n",
    "\n",
    "> POMDPs facilitate planning to sense.\n",
    "\n",
    "To *really* calculate the optimal policy, we would need to know how future actions\n",
    "will affect sensing. Even when we take into account the uncertainty in the actions, there is something we have not taken into account: uncertain *sensing*. Indeed, when calculating the optimal policy we have assumed that we have perfect knowledge of the state. The probabilistic model that takes into account uncertain sensing is called a **partially observable Markov decision process**, or POMDP. \n",
    "\n",
    "While out of scope for this book, it is important to be aware of this limitation of the MDP framework. A POMDP policy could improve on this by planning to sense: for example, the robot could deliberately move closer to an RFID beacon on purpose, to re-localize the robot when it is not very certain about its location. \n",
    "\n",
    "POMDPs are computationally incredibly expensive, because the state is no longer simply *where* we are, but also *what we believe* the state is. Hence, POMDPs are about planning in the *belief space*, which is a very high-dimensional concept."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "S45_logistics_planning.ipynb",
   "provenance": []
  },
  "interpreter": {
   "hash": "c6e4e9f98eb68ad3b7c296f83d20e6de614cb42e90992a65aa266555a3137d0d"
  },
  "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": "3.8.12"
  },
  "latex_metadata": {
   "affiliation": "Georgia Institute of Technology",
   "author": "Frank Dellaert and Seth Hutchinson",
   "title": "Introduction to Robotics"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}