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Murilo M. Marinho
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Added first version of lesson 4
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Lines changed: 717 additions & 163 deletions

‎Lesson4.png‎

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‎Lesson4.svg‎

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‎cheat_sheet.ipynb‎

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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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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
@@ -26,6 +26,28 @@
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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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"# Macros\n",
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"\n",
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"$\\providecommand{\\myvec}[1]{{\\mathbf{\\boldsymbol{{#1}}}}}$\n",
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"$\\providecommand{\\mymatrix}[1]{{\\mathbf{\\boldsymbol{{#1}}}}}$"
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]
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},
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{
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"cell_type": "raw",
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"metadata": {
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"vscode": {
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"languageId": "raw"
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}
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},
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"source": [
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"\\providecommand{\\myvec}[1]{{\\mathbf{\\boldsymbol{{#1}}}}}\n",
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"\\providecommand{\\mymatrix}[1]{{\\mathbf{\\boldsymbol{{#1}}}}}"
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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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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 14,
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"metadata": {},
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"outputs": [],
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"source": [
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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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"execution_count": 15,
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"metadata": {},
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"outputs": [],
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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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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 16,
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"metadata": {},
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"outputs": [],
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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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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 17,
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"metadata": {},
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"outputs": [],
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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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"# 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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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"If you're having problems comparing matrices with \"similar\" dimesions, try to use `numpy.squeeze` when applicable. \n",
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"\n",
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"To understand the problem, see $\\myvec{v}_1$ and $\\myvec{v}_2$ below"
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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": 18,
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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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"Shapes are not equal, notice that in v1 we have [] and in v2 we have [[]].\n",
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"So, v1.shape=(2,) and v2.shape=(1, 2).\n",
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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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"from math import pi, sin, cos\n",
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"\n",
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"v1 = np.array([sin(pi/2), cos(pi/2)])\n",
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"v2 = np.array([[sin(pi/2), cos(pi/2)]])\n",
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"\n",
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"print(f\"Shapes are not equal, notice that in v1 we have [] and in v2 we have [[]].\")\n",
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"print(f\"So, v1.shape={v1.shape} and v2.shape={v2.shape}.\")\n",
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"\n",
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"print(np.allclose(v1, v2))"
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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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"To compare, we do"
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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": 19,
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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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"# Compare v1 and v2\n",
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"print(np.allclose(np.squeeze(v1), np.squeeze(v2)))"
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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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"display_name": ".venv",
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"language": "python",
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"name": "python3"
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},

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