Merge pull request #91 from gtbook/frank/sept_10

Remove problematic aligns

S11_models.ipynb

@@ -131,6 +131,9 @@
    "id": "dcf88139",
    "metadata": {},
    "source": [
+    "```{index} action\n",
+    "```\n",
+    "\n",
     "## Actions\n",
     "> By executing actions, robots change the state of the world, as well as their own state.\n",
     "\n",
@@ -168,6 +171,9 @@
    "id": "bd6579ba",
    "metadata": {},
    "source": [
+    "```{index} sensor\n",
+    "```\n",
+    "\n",
     "## Sensors\n",
     "> Actions allow the robot to affect the world. Sensors allow the robot to perceive the world.\n",
     "\n",

S12_reasoning.ipynb

@@ -30,6 +30,9 @@
    "id": "9e999b46",
    "metadata": {},
    "source": [
+    "```{index} perception\n",
+    "```\n",
+    "\n",
     "##  Perception\n",
     "> Perception uses sensor data to drive inference about the world.\n",
     "\n",
@@ -61,7 +64,10 @@
    "id": "d3ff7da9",
    "metadata": {},
    "source": [
-    "##    Planning\n",
+    "```{index} planning\n",
+    "```\n",
+    "\n",
+    "## Planning\n",
     "> Planning is the process of determining which actions to execute in order to effect desired changes in the world.\n",
     "\n",
     "Planning can mean very different things, depending on the complexity of the task, the time scale for actions,\n",
@@ -136,6 +142,9 @@
    "id": "8ea67598",
    "metadata": {},
    "source": [
+    "```{index} learning\n",
+    "```\n",
+    "\n",
     "## Learning\n",
     "> By learning from data we can make robots smarter.\n",
     "\n",

S26_sorter_learning.ipynb

@@ -86,6 +86,9 @@
     }
    },
    "source": [
+    "```{index} learning; density estimation\n",
+    "```\n",
+    "\n",
     "# Learning\n",
     "\n",
     "> We can learn prior and sensor models from data we collect.\n",

S36_vacuum_RL.ipynb

@@ -81,6 +81,9 @@
     "id": "nAvx4-UCNzt2"
    },
    "source": [
+    "```{index} learning; reinforcement learning\n",
+    "```\n",
+    "\n",
     "# Learning to Act Optimally\n",
     "\n",
     "> Learning to act optimally in a stochastic world.\n",

S42_logistics_actions.ipynb

@@ -370,11 +370,9 @@
     "that maps a desired robot velocity $v=(v_x,v_y)$ to the appropriate commanded wheel velocities:\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
     "\\begin{pmatrix}\\omega^1 \\\\ \\omega^2 \\\\ \\omega^3 \\end{pmatrix} \n",
     "= \\frac{1}{r} \\begin{pmatrix}- \\sin\\theta^1 & \\cos\\theta^1 \\\\ - \\sin\\theta^2 & \\cos\\theta^2 \\\\ - \\sin\\theta^3 & \\cos\\theta^3 \\end{pmatrix}\n",
     "\\begin{pmatrix}v_x \\\\ v_y \\end{pmatrix}\n",
-    "\\end{align}\n",
     "$$\n",
     "\n",
     "in which the $3\\times2$ matrix is called the **Jacobian matrix**.\n",

S46_logistics_learning.ipynb

@@ -65,6 +65,9 @@
     "id": "nAvx4-UCNzt2"
    },
    "source": [
+    "```{index} learning; system identification\n",
+    "```\n",
+    "\n",
     "# Some System Identification\n",
     "\n",
     "> We can \"learn\" measurement and motion models.\n",

S53_diffdrive_sensing.ipynb

@@ -647,11 +647,9 @@
     "we can now completely reconstruct the location of the point $P$ in (left) camera coordinates:\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
     "\\begin{bmatrix}X\\\\Y\\\\Z\\end{bmatrix}\n",
     "= \\begin{bmatrix}Z(u_L-u_0)/f\\\\Z(v_L-v_0)/f\\\\B f/d\\end{bmatrix}\n",
     "= B \\frac{f}{d} \\begin{bmatrix}(u_L-u_0)/f\\\\(v_L-v_0)/f\\\\1\\end{bmatrix}\n",
-    "\\end{align}\n",
     "$$\n",
     "\n",
     "Stereo cameras are used very often on robotics platforms because of this ability to reconstruct the world in 3D, at least in principle. This is akin to our own (human) ability to perceive depth by virtue of having two eyes, a feature we have in common with many animals - primarily predators, who need accurate depth vision to hunt prey. In practice, using a stereo camera is not as easy, as it has to be carefully calibrated and finding *correspondences* between left and right cameras is not always straightforward. However, the latter has been alleviated quite a bit by recent advances in neural networks, which we will discuss below."

S56_diffdrive_learning.ipynb

@@ -84,6 +84,9 @@
     "id": "nAvx4-UCNzt2"
    },
    "source": [
+    "```{index} learning; deep learning\n",
+    "```\n",
+    "\n",
     "# Deep Learning\n",
     "\n",
     "> Stochastic gradient descent and the like.\n",

S61_driving_state.ipynb

@@ -461,7 +461,6 @@
     "We can write the above coordinate transformation as a matrix equation:\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
     "\\begin{bmatrix}\n",
     "P^0 \\\\ 1\n",
     "\\end{bmatrix}\n",
@@ -473,7 +472,6 @@
     "\\begin{bmatrix}\n",
     "P^1 \\\\ 1\n",
     "\\end{bmatrix}\n",
-    "\\end{align}\n",
     "$$\n",
     "\n",
     "in which $0_2$ denotes the row vector $[0~ 0]$.\n",

S66_driving_DRL.ipynb

@@ -62,6 +62,9 @@
     "id": "nAvx4-UCNzt2"
    },
    "source": [
+    "```{index} learning; deep reinforcement learning\n",
+    "```\n",
+    "\n",
     "# Deep Reinforcement Learning\n",
     "\n",
     "> Deep Q-learning and policy gradient.\n",
@@ -105,6 +108,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "```{index} pair: DQN; deep reinforcement learning\n",
+    "```\n",
+    "\n",
     "## Deep Q-Learning\n",
     "\n",
     "> DQN is an early deep learning RL method akin to Q-learning.\n",
@@ -160,6 +166,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "```{index} pair: policy optimization; deep reinforcement learning\n",
+    "```\n",
+    "\n",
     "## Policy Optimization\n",
     "\n",
     "> Policy optimization takes a black box optimization approach to a deep policy.\n",
@@ -233,7 +242,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Policy Gradient\n",
+    "```{index} pair: policy gradient methods; deep reinforcement learning\n",
+    "```\n",
+    "\n",
+    "## Policy Gradient Methods\n",
     "\n",
     "> Policy gradient methods are akin to policy iteration, with a neural flavor.\n",
     "\n",

S67_driving_summary.ipynb

@@ -62,7 +62,8 @@
     "information (encoded by the rightmost column).\n",
     "Thus, these matrices have the form\n",
     "\n",
-    "$$T^0_1 =\n",
+    "$$\n",
+    "T^0_1 =\n",
     "\\begin{bmatrix}\n",
     "R_{1}^{0} & d_{1}^{0}\\\\\n",
     "0_{2} & 1\n",
@@ -85,7 +86,6 @@
     "matrix equation:\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
     "\\begin{bmatrix}\n",
     "P^0 \\\\ 1\n",
     "\\end{bmatrix}\n",
@@ -97,7 +97,6 @@
     "\\begin{bmatrix}\n",
     "P^1 \\\\ 1\n",
     "\\end{bmatrix}\n",
-    "\\end{align}\n",
     "$$\n",
     " \n",
     "Finally, composition of homogeneous transformations requires nothing more than simple\n",

S71_drone_state.ipynb

@@ -207,12 +207,10 @@
     "matrices in $SE(3)$ by embedding the rotation and translation into a $4\\times4$ invertible matrix defined as\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
     "T_{b}^{n}=\\begin{bmatrix}\n",
     "R_{b}^{n} & t_{b}^{n}\\\\\n",
     "0 & 1\n",
     "\\end{bmatrix}.\n",
-    "\\end{align}\n",
     "$$\n",
     "\n",
     "Again, as in the previous chapter, we can implement the group operation as simple matrix multiplication.\n",
@@ -221,7 +219,6 @@
     "a 3D homogeneous transformation as\n",
     "\n",
     "$$\n",
-    "\\begin{align}\n",
     "\\begin{bmatrix}\n",
     "R_{b}^{n} & t_{b}^{n}\\\\\n",
     "0 & 1\n",
@@ -234,7 +231,6 @@
     "R_{b}^{n}p^{b}+t_{b}^{n}\\\\\n",
     "1\n",
     "\\end{bmatrix}\n",
-    "\\end{align}\n",
     "$$\n",
     "\n",
     "Note that both ways of defining and applying 3D rigid transformations are equivalent: sometimes it is more convenient to use one over the other. It should be apparent from the context as to which flavor we use."

S76_drone_learning.ipynb

@@ -92,6 +92,9 @@
     "id": "nAvx4-UCNzt2"
    },
    "source": [
+    "```{index} pair: learning; neural radiance fields\n",
+    "```\n",
+    "\n",
     "# Neural Radiance Fields for Drones\n",
     "\n",
     "> Learning 3D scene representations from images.\n",
@@ -103,6 +106,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "```{index} pair: neural radiance fields; NeRF\n",
+    "```\n",
+    "\n",
     "## What is a NeRF?\n",
     "\n",
     "> NeRFs represent 3D scenes to render new views.\n",