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SymPyBotics - Coriolis matrix
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{ | |
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"name": "", | |
"signature": "sha256:88622d1d8a89808cba9b9b0be646204c86509a691507964b7c2e19cd428bc075" | |
}, | |
"nbformat": 3, | |
"nbformat_minor": 0, | |
"worksheets": [ | |
{ | |
"cells": [ | |
{ | |
"cell_type": "heading", | |
"level": 1, | |
"metadata": {}, | |
"source": [ | |
"SymPyBotics - Coriolis matrix" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"--------" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"import sympy\n", | |
"import numpy\n", | |
"import sympybotics\n", | |
"\n", | |
"rbtdef = sympybotics.RobotDef('Example Robot', # robot name\n", | |
" [('-pi/2', 0, 0, 'q+pi/2'), # list of tuples with Denavit-Hartenberg parameters\n", | |
" ( 'pi/2', 0, 0, 'q-pi/2')], # (alpha, a, d, theta)\n", | |
" dh_convention='standard' # either 'standard' or 'modified'\n", | |
" )\n", | |
"rbtdef.frictionmodel = {'Coulomb', 'viscous'} # options are None or a combination of 'Coulomb', 'viscous' and 'offset'\n", | |
"\n", | |
"rbt = sympybotics.RobotDynCode(rbtdef, verbose=True)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating geometric model\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating kinematic model\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating inverse dynamics code\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating gravity term code\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating coriolis term code\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating coriolis matrix code\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating inertia matrix code\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating regressor matrix code\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"generating friction term code\n" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"done\n" | |
] | |
} | |
], | |
"prompt_number": 1 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"from numpy import cos, sin, random\n", | |
"rand_dynp = random.rand(rbt.dyn.n_dynparms)\n", | |
"rand_q = random.rand(rbt.dof)\n", | |
"rand_dq = random.rand(rbt.dof)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 2 | |
}, | |
{ | |
"cell_type": "heading", | |
"level": 2, | |
"metadata": {}, | |
"source": [ | |
"Coriolis and centripetal forces vector $c(q, \\dot{q})$" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"exec(sympybotics.robotcodegen.robot_code_to_func('python', rbt.c_code, 'c', 'coriolis_vector', rbtdef))" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 3 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"c = coriolis_vector(rand_dynp, rand_q, rand_dq)\n", | |
"c = numpy.matrix(c).T\n", | |
"c" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 4, | |
"text": [ | |
"matrix([[ 0.06027864],\n", | |
" [-0.01747512]])" | |
] | |
} | |
], | |
"prompt_number": 4 | |
}, | |
{ | |
"cell_type": "heading", | |
"level": 2, | |
"metadata": {}, | |
"source": [ | |
"Coriolis and centripetal forces matrix $C(q, \\dot{q})$" | |
] | |
}, | |
{ | |
"cell_type": "heading", | |
"level": 2, | |
"metadata": {}, | |
"source": [ | |
"$C(q, \\dot{q})\\,\\dot{q} = c(q, \\dot{q})$" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"exec(sympybotics.robotcodegen.robot_code_to_func('python', rbt.C_code, 'C', 'coriolis_matrix', rbtdef))" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 5 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"C = coriolis_matrix(rand_dynp, rand_q, rand_dq)\n", | |
"C = numpy.matrix(C).reshape((rbt.dof, rbt.dof))\n", | |
"C" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 6, | |
"text": [ | |
"matrix([[ 0. , 0.19423486],\n", | |
" [-0.07206067, 0. ]])" | |
] | |
} | |
], | |
"prompt_number": 6 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"C * numpy.matrix(rand_dq).T" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 7, | |
"text": [ | |
"matrix([[ 0.06027864],\n", | |
" [-0.01747512]])" | |
] | |
} | |
], | |
"prompt_number": 7 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"c - C * numpy.matrix(rand_dq).T" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 8, | |
"text": [ | |
"matrix([[ 6.93889390e-18],\n", | |
" [ -3.46944695e-18]])" | |
] | |
} | |
], | |
"prompt_number": 8 | |
} | |
], | |
"metadata": {} | |
} | |
] | |
} |
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