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fix error and reorder 02-direct-kin notebook for clarity
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‎3-robot-manipulation/1-kinematics/02-direct-kinematics.ipynb‎

Lines changed: 98 additions & 91 deletions
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@@ -76,44 +76,6 @@
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"[![DH Diagram Wikipedia](https://upload.wikimedia.org/wikipedia/commons/3/3f/Sample_Denavit-Hartenberg_Diagram.png)](https://en.wikipedia.org/wiki/Denavit%E2%80%93Hartenberg_parameters#)"
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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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"import math\n",
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"import numpy as np\n",
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"\n",
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"# The function dh(theta, d, a, alpha)\n",
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"def dh(theta: float, d: float, a: float, alpha: float) -> np.array:\n",
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" \"\"\"\n",
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" This function returns the denavit hartenberg parameter matrix\n",
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" from a given theta, d, a, alpha\n",
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"\n",
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" Args:\n",
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" theta (float): the angle in degrees\n",
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" d (float): the offset in mm\n",
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" a (float): the length in mm\n",
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" alpha (float): the angle in degrees\n",
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"\n",
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" Returns:\n",
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" numpy array: the denavit hartenberg parameter matrix\n",
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" \"\"\"\n",
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"\n",
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" # Convert degrees to radians\n",
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" theta = math.radians(theta)\n",
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" alpha = math.radians(alpha)\n",
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"\n",
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" # return the denavit hartenberg parameter matrix\n",
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" return np.array([\n",
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" [np.cos(theta), -1*np.sin(theta)*np.cos(alpha), np.sin(theta)*np.sin(alpha), a*np.cos(theta)],\n",
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" [np.sin(theta), np.cos(theta)*np.cos(alpha), -1*np.cos(theta)*np.sin(alpha), a*np.sin(theta)],\n",
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" [ 0, np.sin(alpha), np.cos(alpha), d],\n",
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" [ 0, 0, 0, 1]\n",
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" ])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
@@ -139,24 +101,16 @@
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"Suppose a robot manipulator has three joints with DH parameters as follows:\n",
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"\n",
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"- Joint 1: theta=40, d=1000, a=0, alpha=0\n",
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"- Joint 2: theta=10, d=1000, a=0, alpha=0\n",
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"\n",
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"The robot would look like this:\n",
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"\n",
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"> ***Run the below cells to see the 'computer model' of the robot***"
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"- Joint 2: theta=10, d=1000, a=0, alpha=0"
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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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"cell_type": "markdown",
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"metadata": {},
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"outputs": [],
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"source": [
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"# install the robotics toolbox for python\n",
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"# this library is helpful for kinematics and dynamics of robot manipulators\n",
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"# more info at:\n",
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"# https://petercorke.github.io/robotics-toolbox-python/index.html\n",
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"%pip install roboticstoolbox-python"
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"#### Model Function for Direct Kinematics\n",
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"\n",
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"The function `dk` models the two joint manipulator example. The function returns the end effector pose given input joint angles. This model computes direct kinematics. "
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]
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},
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{
@@ -166,47 +120,35 @@
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"outputs": [],
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"source": [
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"import math\n",
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"import roboticstoolbox as rtb # load the robotics toolbox\n",
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"import numpy as np\n",
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"\n",
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"# the robot model can be defined using the the robotics toolbox\n",
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"# The DHRobot object stores the joint information for the robot\n",
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"# RevoluteDH objects can be used to represent each revolute joint in the robot model\n",
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"# DH parameters are used to define the robot joint relationships\n",
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"robot_2dof = rtb.DHRobot(\n",
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" [\n",
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" # the RevoluteDH class represents a revolute joint using DH parameters\n",
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" # this is a list of 2 joints representing 2 degrees of freedom (DOF)\n",
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" rtb.RevoluteDH(\n",
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" d = 0,\n",
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" alpha = 0,\n",
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" a = 1, # note that the dimensions are in m instead of mm\n",
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" # offset = math.radians(0)\n",
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" ),\n",
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" rtb.RevoluteDH(\n",
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" d = 0,\n",
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" alpha = 0,\n",
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" a = 1,\n",
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" # offset = math.radians(0)\n",
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" )\n",
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" ],\n",
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" name = \"Two-Link Manipulator\"\n",
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")\n",
125+
"# The function dh(theta, d, a, alpha)\n",
126+
"def dh(theta: float, d: float, a: float, alpha: float) -> np.array:\n",
127+
" \"\"\"\n",
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" This function returns the denavit hartenberg parameter matrix\n",
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" from a given theta, d, a, alpha\n",
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"\n",
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"# this will print the robot model details\n",
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"print(robot_2dof)\n",
131+
" Args:\n",
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" theta (float): the angle in degrees\n",
133+
" d (float): the offset in mm\n",
134+
" a (float): the length in mm\n",
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" alpha (float): the angle in degrees\n",
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"\n",
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"# this will plot the robot model graphically\n",
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"q = [40.0, 10.0]\n",
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"robot_2dof.plot(q, limits=[-2.0, 2.0, -2.0, 2.0, 0.0, 0.5])"
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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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"#### Model Function for Direct Kinematics\n",
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" Returns:\n",
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" numpy array: the denavit hartenberg parameter matrix\n",
139+
" \"\"\"\n",
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"\n",
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"The function `dk` models the two joint manipulator example. The function returns the end effector pose given input joint angles. This model computes direct kinematics. "
141+
" # Convert degrees to radians\n",
142+
" theta = math.radians(theta)\n",
143+
" alpha = math.radians(alpha)\n",
144+
"\n",
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" # return the denavit hartenberg parameter matrix\n",
146+
" return np.array([\n",
147+
" [np.cos(theta), -1*np.sin(theta)*np.cos(alpha), np.sin(theta)*np.sin(alpha), a*np.cos(theta)],\n",
148+
" [np.sin(theta), np.cos(theta)*np.cos(alpha), -1*np.cos(theta)*np.sin(alpha), a*np.sin(theta)],\n",
149+
" [ 0, np.sin(alpha), np.cos(alpha), d],\n",
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" [ 0, 0, 0, 1]\n",
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" ])"
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]
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},
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{
@@ -234,10 +176,10 @@
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"\n",
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" # Denavit-Hartenberg parameters for the 3 DOF robot\n",
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" # end effector: H10 * H21\n",
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" H10 = dh(t1 + 40, 1000, 0, 0)\n",
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" H21 = dh(t2 + 10, 1000, 0, 0)\n",
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" H10 = dh(t1, 0, 1000, 0)\n",
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" H21 = dh(t2, 0, 1000, 0)\n",
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" # the tool has a length of 100 mm\n",
240-
" Htool3 = dh(0, 100, 0, 0)\n",
182+
" Htool3 = dh(0, 0, 100, 0)\n",
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"\n",
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" # matrix multiplication to get the pose\n",
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" # uses numpy's matrix multiplication\n",
@@ -287,6 +229,71 @@
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"# Try with several values to validate your calculations."
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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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"Using the robotics toolbox, we can visualize the robot manipulator.\n",
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"\n",
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"The robot would look like this:\n",
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"\n",
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"> ***Run the below cells to see the 'computer model' of the robot***"
241+
]
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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": [],
248+
"source": [
249+
"# install the robotics toolbox for python\n",
250+
"# this library is helpful for kinematics and dynamics of robot manipulators\n",
251+
"# more info at:\n",
252+
"# https://petercorke.github.io/robotics-toolbox-python/index.html\n",
253+
"%pip install roboticstoolbox-python"
254+
]
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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": [
262+
"import math\n",
263+
"import roboticstoolbox as rtb # load the robotics toolbox\n",
264+
"\n",
265+
"# the robot model can be defined using the the robotics toolbox\n",
266+
"# The DHRobot object stores the joint information for the robot\n",
267+
"# RevoluteDH objects can be used to represent each revolute joint in the robot model\n",
268+
"# DH parameters are used to define the robot joint relationships\n",
269+
"robot_2dof = rtb.DHRobot(\n",
270+
" [\n",
271+
" # the RevoluteDH class represents a revolute joint using DH parameters\n",
272+
" # this is a list of 2 joints representing 2 degrees of freedom (DOF)\n",
273+
" rtb.RevoluteDH(\n",
274+
" d = 0,\n",
275+
" alpha = 0,\n",
276+
" a = 1, # note that the dimensions are in m instead of mm\n",
277+
" # offset = math.radians(0)\n",
278+
" ),\n",
279+
" rtb.RevoluteDH(\n",
280+
" d = 0,\n",
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" alpha = 0,\n",
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" a = 1,\n",
283+
" # offset = math.radians(0)\n",
284+
" )\n",
285+
" ],\n",
286+
" name = \"Two-Link Manipulator\"\n",
287+
")\n",
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"\n",
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"# this will print the robot model details\n",
290+
"print(robot_2dof)\n",
291+
"\n",
292+
"# this will plot the robot model graphically\n",
293+
"q = [40.0, 10.0]\n",
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"robot_2dof.plot(q, limits=[-2.0, 2.0, -2.0, 2.0, 0.0, 0.5])"
295+
]
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},
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{
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"cell_type": "markdown",
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"metadata": {},

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