AntiPodal Grasp Sampler.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Notations:\n",
    "* G                    → Gripper frame.\n",
    "\n",
    "* ${purple, red, green}$ → ${z, y, x}$ of the gripper frame G.\n",
    "\n",
    "* $\\vec{p}$            → Randomly chosen point on object surface.\n",
    "\n",
    "* $\\vec{n}$            → Surface normal at point $\\vec{p}$. \n",
    "\n",
    "* $s_{min}$            → distance from gripper origin $\\vec{g}$ to closest on antipodal grasp ray (Stand-off distance)\n",
    "\n",
    "* $\\alpha$             → Angle between the normal $\\vec{n}$ and antipodal grasp ray. \n",
    "\n",
    "* $\\gamma$             → rotation around antipodal grasp ray. \n",
    "\n",
    "##### For generating each sample\n",
    "* sample a point $\\vec{p}$ on the object surface\n",
    "* $\\alpha$ → uniform_sample(0, $\\pi/6$)\n",
    "* $s_{min}$ → 0\n",
    "* $\\gamma$ → uniform_sample(0, $2\\pi$)\n",
    "* Antipodal point $p^{\\prime}$ is choosen such that farthest intersection point along the antipodal grasp ray. \n",
    "* Choose grasp sample $\\hat{G}$ with the center of line segment $\\vec{p}$ $\\vec{p}^\\prime$ + $d$ and rotatated $\\gamma$ w.r.t antipodal grasp ray. \n",
    "* If sample $\\hat{G}$ results in collision with the object or object volume between the fingers is zero, discard the sample."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}