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Murilo M. Marinho
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Added cheatsheet
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‎cheat_sheet.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Cheatsheet\n",
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"\n",
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"*License: CC-BY-NC-SA 4.0*\n",
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"\n",
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"*Author: Murilo M. Marinho (murilo.marinho@manchester.ac.uk)*\n",
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"\n",
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"## Installation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%%capture\n",
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"%pip install numpy\n",
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"%pip install roboticstoolbox-python\n",
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"%pip install numpy --break-system-packages\n",
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"%pip install roboticstoolbox-python --break-system-packages"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Imports"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import spatialmath as sm\n",
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"from math import pi"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Converting from `spatialmath` to `numpy`\n",
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"\n",
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"### SE(2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 38,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m-1 \u001b[0m \u001b[38;5;4m 1 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;1m 1 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;4m 2 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 1 \u001b[0m \u001b[0m\n",
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"\n",
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"The original SE(2) object was \n",
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" \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m-1 \u001b[0m \u001b[38;5;4m 1 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;1m 1 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;4m 2 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 1 \u001b[0m \u001b[0m\n",
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"\n",
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" and can be converted to: \n",
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"\tA rotation matrix \n",
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"[[ 6.123234e-17 -1.000000e+00]\n",
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" [ 1.000000e+00 6.123234e-17]]\n",
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" that has size = (2, 2).\n",
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"\tA position vector \n",
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"[1. 2.]\n",
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" that has size = (2,).\n",
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"\tA homogenous transformation matrix \n",
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"[[ 6.123234e-17 -1.000000e+00 1.000000e+00]\n",
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" [ 1.000000e+00 6.123234e-17 2.000000e+00]\n",
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" [ 0.000000e+00 0.000000e+00 1.000000e+00]]\n",
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" that has size = (3, 3).\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"import spatialmath as sm\n",
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"from math import pi\n",
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"\n",
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"# SE(2)\n",
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"HA = sm.SE2(1,2,pi/2)\n",
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"print(HA)\n",
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"\n",
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"# Useful conversions\n",
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"# Rotation\n",
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"RA_np = HA.R\n",
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"# Position\n",
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"pA_np = HA.t\n",
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"# (full) Transformation\n",
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"HA_np = HA.A\n",
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"\n",
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"print(f\"The original SE(2) object was \\n{HA}\\n and can be converted to: \")\n",
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"print(f\"\\tA rotation matrix \\n{RA_np}\\n that has size = {RA_np.shape}.\")\n",
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"print(f\"\\tA position vector \\n{pA_np}\\n that has size = {pA_np.shape}.\")\n",
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"print(f\"\\tA homogenous transformation matrix \\n{HA_np}\\n that has size = {HA_np.shape}.\")\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### SE(3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m-1 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;4m 1 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;1m 1 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;4m 2 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m 1 \u001b[0m \u001b[38;5;4m 3 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 1 \u001b[0m \u001b[0m\n",
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"\n",
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"The original SE(2) object was \n",
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" \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m-1 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;4m 1 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;1m 1 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;4m 2 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m 0 \u001b[0m \u001b[38;5;1m 1 \u001b[0m \u001b[38;5;4m 3 \u001b[0m \u001b[0m\n",
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" \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 0 \u001b[0m \u001b[38;5;244m 1 \u001b[0m \u001b[0m\n",
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"\n",
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" and can be converted to: \n",
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"\tA rotation matrix \n",
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"[[ 6.123234e-17 -1.000000e+00 0.000000e+00]\n",
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" [ 1.000000e+00 6.123234e-17 0.000000e+00]\n",
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" [ 0.000000e+00 0.000000e+00 1.000000e+00]]\n",
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" that has size = (3, 3).\n",
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"\tA position vector \n",
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"[1. 2. 3.]\n",
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" that has size = (3,).\n",
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"\tA homogenous transformation matrix \n",
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"[[ 6.123234e-17 -1.000000e+00 0.000000e+00 1.000000e+00]\n",
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" [ 1.000000e+00 6.123234e-17 0.000000e+00 2.000000e+00]\n",
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" [ 0.000000e+00 0.000000e+00 1.000000e+00 3.000000e+00]\n",
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" [ 0.000000e+00 0.000000e+00 0.000000e+00 1.000000e+00]]\n",
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" that has size = (4, 4).\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"import spatialmath as sm\n",
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"from math import pi\n",
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"\n",
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"# SE(3)\n",
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"HB = sm.SE3(1,2,3) * sm.SE3().Rz(pi/2)\n",
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"print(HB)\n",
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"\n",
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"# Useful conversions\n",
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"# Rotation\n",
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"RB_np = HB.R\n",
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"# Position\n",
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"pB_np = HB.t\n",
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"# (full) Transformation\n",
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"HB_np = HB.A\n",
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"\n",
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"print(f\"The original SE(2) object was \\n{HB}\\n and can be converted to: \")\n",
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"print(f\"\\tA rotation matrix \\n{RB_np}\\n that has size = {RB_np.shape}.\")\n",
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"print(f\"\\tA position vector \\n{pB_np}\\n that has size = {pB_np.shape}.\")\n",
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"print(f\"\\tA homogenous transformation matrix \\n{HB_np}\\n that has size = {HB_np.shape}.\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Comparing `numpy` matrices\n",
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"\n",
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"Owing to floating point limitations of computers, use, in general, `numpy.allclose`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 40,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"True\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"import spatialmath as sm\n",
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"from math import pi, sin, cos\n",
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"\n",
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"# SE(2) with spatialmath\n",
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"HC = sm.SE2(1,2,pi/2)\n",
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"\n",
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"# SE(2) directly from numpy\n",
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"HC_np = np.array(\n",
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" [[cos(pi/2), -sin(pi/2), 1],\n",
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" [sin(pi/2), cos(pi/2), 2],\n",
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" [0, 0, 1]]\n",
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")\n",
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"\n",
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"# Compare HC.A and HC_np\n",
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"print(np.allclose(HC.A, HC_np))"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.9"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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