update jupyter docs

Author: AtsushiSakai

PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.ipynb

@@ -12,7 +12,21 @@
   {
    "cell_type": "markdown",
    "source": [
-    "## Quintic polynomials for one dimension robot motion\n",
+    "## Quintic polynomials for one dimensional robot motion\n",
+    "\n",
+    "We assume a dimensional robot motion $x(t)$ at time $t$ is formulated as a quintic polynomials based on time as follows:\n",
+    "\n",
+    "$x(t) = a_0+a_1t+a_2t^2+a_3t^3+a_4t^4$\n",
+    "\n",
+    "a_0, a_1. a_2, a_3 are parameters of the quintic polynomial.\n",
+    "\n",
+    "So, when time is 0,\n",
+    "\n",
+    "$x(0) = a_0 = x_s$\n",
+    "\n",
+    "x_s is a start x position.\n",
+    "\n",
+    "\n",
     "\n",
     "$e^{i\\pi} + 1 = 0$\n",
     "\n",