Merge branch 'main' of github.com:MarinhoLab/OpenExecutableBooksRobotics

Author: Murilo M. Marinho

lesson3_tutorial.ipynb

@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Forward Kinematics 1\n",
+    "# Forward Kinematics\n",
     "\n",
     "*License: CC-BY-NC-SA 4.0*\n",
     "\n",

lesson4_tutorial.ipynb

@@ -10,7 +10,7 @@
     "\n",
     "*Author: Murilo M. Marinho (murilo.marinho@manchester.ac.uk)*\n",
     "\n",
-    "## Pre-requisites for the leaner\n",
+    "## Pre-requisites for the learner\n",
     "The user of this notebook is expected to have prior knowledge in\n",
     "- All the content and pre-requisites of lessons 1, 2, and 3.\n",
     "\n",
@@ -168,20 +168,20 @@
     "The analytical Jacobian is given by\n",
     "\n",
     "$$ \\mymatrix{J} = \\left[\\begin{array}{ccc}\n",
-    "         \\frac{\\partial p_{x}}{q_0}    & \\frac{\\partial p_{x}}{q_1} \\\\\n",
-    "         \\frac{\\partial p_{y}}{q_0}    & \\frac{\\partial p_{y}}{q_1}  \\\\\n",
-    "         \\frac{\\partial \\phi_{z}}{q_0} & \\frac{\\partial \\phi_{z}}{q_1}                  \n",
+    "         \\frac{\\partial p_{x}}{\\partial q_0}    & \\frac{\\partial p_{x}}{\\partial q_1} \\\\\n",
+    "         \\frac{\\partial p_{y}}{\\partial q_0}    & \\frac{\\partial p_{y}}{\\partial q_1}  \\\\\n",
+    "         \\frac{\\partial \\phi_{z}}{\\partial q_0} & \\frac{\\partial \\phi_{z}}{\\partial q_1}                  \n",
     "        \\end{array}\\right].$$\n",
     "\n",
     "As we did in class, we find each element by calculating the partial derivative of the respective task-space value with respect to the configuration-space value\n",
     "\n",
     "$$\\begin{align}\n",
-    "\\frac{\\partial p_{x}}{q_0} &= -l_{0}\\sin{q_0} - l_{1}\\sin{(q_0 + q_1)} \\\\\n",
-    "\\frac{\\partial p_{x}}{q_1} &= -l_{1}\\sin{(q_0 + q_1)} \\\\\n",
-    "\\frac{\\partial p_{y}}{q_0} &= l_{0}\\cos{q_0} + l_{1}\\cos{(q_0 + q_1)} \\\\\n",
-    "\\frac{\\partial p_{y}}{q_1} &= l_{1}\\cos{(q_0 + q_1)} \\\\\n",
-    "\\frac{\\partial \\phi_{z}}{q_0} &= 1 \\\\\n",
-    "\\frac{\\partial \\phi_{z}}{q_1} &= 1 \n",
+    "\\frac{\\partial p_{x}}{\\partial q_0} &= -l_{0}\\sin{q_0} - l_{1}\\sin{(q_0 + q_1)} \\\\\n",
+    "\\frac{\\partial p_{x}}{\\partial q_1} &= -l_{1}\\sin{(q_0 + q_1)} \\\\\n",
+    "\\frac{\\partial p_{y}}{\\partial q_0} &= l_{0}\\cos{q_0} + l_{1}\\cos{(q_0 + q_1)} \\\\\n",
+    "\\frac{\\partial p_{y}}{\\partial q_1} &= l_{1}\\cos{(q_0 + q_1)} \\\\\n",
+    "\\frac{\\partial \\phi_{z}}{\\partial q_0} &= 1 \\\\\n",
+    "\\frac{\\partial \\phi_{z}}{\\partial q_1} &= 1 \n",
     "\\end{align}$$\n",
     "        \n",
     "resulting in\n",