ME 449 Assignment 1 - Revision history

Lynch: /* Part 1: Chapter 2 */

2025-09-24T13:48:30Z

Part 1: Chapter 2

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	C. For the task of erasing a whiteboard (the eraser moves in flat contact with the board), how many degrees of freedom does the task space have? Describe the topology of this task space.		C. For the task of erasing a whiteboard (the eraser moves in flat contact with the board), how many degrees of freedom does the task space have? Describe the topology of this task space.

	D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do ~~those~~ joints offer? (They are not typical robot joints!) And, if you are interested in anatomy, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?		D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged as shown in the image? How many total freedoms must these joints offer, as indicated by Grubler? (They are not typical robot joints!) And, if you are interested in anatomy, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?

	==Part 2: CoppeliaSim Simulation and Exploration==		==Part 2: CoppeliaSim Simulation and Exploration==

Lynch: /* Part 2B: Exploring the UR5 Scene 1 */

2025-09-24T13:47:05Z

Part 2B: Exploring the UR5 Scene 1

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	'''Your task:'''		'''Your task:'''
	Modify the UI_Script to change an aspect of the scene, and you will use this modified scene for ~~Part~~ 2, below. For example, you can choose to change the Custom UI layout, change the titles and words of the Custom UI, or change font sizes in the Custom UI. Some example changes include:		Modify the UI_Script to change an aspect of the scene, and you will use this modified scene for part 3, below. For example, you can choose to change the Custom UI layout, change the titles and words of the Custom UI, or change font sizes in the Custom UI. Some example changes include:

	*Changing the layout: consult the XML syntax and change <group layout="vbox"> to another type (hbox,form, grid, none). Using line 257, changing <group layout="vbox"> to <group layout="hbox"> changes the orientation of the items in the group containing "Configuration Entry", "Current configuration", and "Messages" on the "Enter Config and SE(3) Value" tab of the Custom UI from vertically arranged to horizontal.		*Changing the layout: consult the XML syntax and change <group layout="vbox"> to another type (hbox,form, grid, none). Using line 257, changing <group layout="vbox"> to <group layout="hbox"> changes the orientation of the items in the group containing "Configuration Entry", "Current configuration", and "Messages" on the "Enter Config and SE(3) Value" tab of the Custom UI from vertically arranged to horizontal.

Lynch at 13:45, 24 September 2025

2025-09-24T13:45:24Z

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	D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do those joints offer? (They are not typical robot joints!) And, if you are interested in anatomy, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?		D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do those joints offer? (They are not typical robot joints!) And, if you are interested in anatomy, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?


	==Part 2: CoppeliaSim Simulation and Exploration==		==Part 2: CoppeliaSim Simulation and Exploration==

Lynch at 13:44, 24 September 2025

2025-09-24T13:44:55Z

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	All assignments will be graded based on correctness, how clearly you organize your homework (the grader should easily find all of your solutions), and how well you follow the instructions. You will lose points if you don't follow the instructions or if the assignment is difficult for the grader to grade.		All assignments will be graded based on correctness, how clearly you organize your homework (the grader should easily find all of your solutions), and how well you follow the instructions. You will lose points if you don't follow the instructions or if the assignment is difficult for the grader to grade.

	==Part 1: ~~CoppeliaSim~~ ~~Simulation and Exploration~~==		==Part 1: Chapter 2==

⚫	In part 1, you will explore some of the functionality and built-in models for CoppeliaSim. Go to [http://hades.mech.northwestern.edu/index.php/Getting_Started_with_the_CoppeliaSim_Simulator this page] for a refresher on getting started with CoppeliaSim.
		⚫	A. Use Grubler's formula to find the number of degrees of freedom of the mechanism in Figure 2.18(d).

		⚫	B. Use Grubler's formula to find the number of degrees of freedom of the mechanism in Figure 2.21(a).

		⚫	C. For the task of erasing a whiteboard (the eraser moves in flat contact with the board), how many degrees of freedom does the task space have? Describe the topology of this task space.

		⚫	D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do those joints offer? (They are not typical robot joints!) And, if you are interested in anatomy, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?


			==Part 2: CoppeliaSim Simulation and Exploration==
		⚫	In part 2, you will explore some of the functionality and built-in models for CoppeliaSim. Go to [http://hades.mech.northwestern.edu/index.php/Getting_Started_with_the_CoppeliaSim_Simulator this page] for a refresher on getting started with CoppeliaSim.

	A CoppeliaSim scene may include [https://www.coppeliarobotics.com/helpFiles/en/objects.htm objects] (like [https://www.coppeliarobotics.com/helpFiles/en/shapes.htm shapes], [https://www.coppeliarobotics.com/helpFiles/en/joints.htm joints], or sensors) and one or more [https://www.coppeliarobotics.com/helpFiles/en/models.htm models]. A model consists of a number of objects connected to each other.		A CoppeliaSim scene may include [https://www.coppeliarobotics.com/helpFiles/en/objects.htm objects] (like [https://www.coppeliarobotics.com/helpFiles/en/shapes.htm shapes], [https://www.coppeliarobotics.com/helpFiles/en/joints.htm joints], or sensors) and one or more [https://www.coppeliarobotics.com/helpFiles/en/models.htm models]. A model consists of a number of objects connected to each other.
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	A scene also includes a [https://www.coppeliarobotics.com/helpFiles/en/mainScript.htm main script], which handles the simulation loop. At each simulation step, the main script calls (a) "actuation" functions that simulate the motion of the system and (b) "sensing" functions that simulate the sensors. Generally this main script should not be edited.		A scene also includes a [https://www.coppeliarobotics.com/helpFiles/en/mainScript.htm main script], which handles the simulation loop. At each simulation step, the main script calls (a) "actuation" functions that simulate the motion of the system and (b) "sensing" functions that simulate the sensors. Generally this main script should not be edited.

	===Part 1A: Building a world for a mobile robot===		===Part 2A: Building a world for a mobile robot===

	In this part, you will explore the CoppeliaSim model browser and learn how to create your own scene using the default models. Anything in the model browser can be dragged and dropped onto the checkerboard floor of the scene. It can then be moved or reoriented using the '''Object/item shift''' and the '''Object/item rotate''' buttons in the top toolbar (the cubes with the arrows around them). Also try using the controls at the top of the window to zoom the camera in and out, pan the camera, etc.		In this part, you will explore the CoppeliaSim model browser and learn how to create your own scene using the default models. Anything in the model browser can be dragged and dropped onto the checkerboard floor of the scene. It can then be moved or reoriented using the '''Object/item shift''' and the '''Object/item rotate''' buttons in the top toolbar (the cubes with the arrows around them). Also try using the controls at the top of the window to zoom the camera in and out, pan the camera, etc.
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	* Take a screen recording video of the robot moving through your world and interacting with at least three walls. In the video, use the zoom, pan, and other buttons to move the camera view while the robot is moving. You can change the robot's default speed in its child script to make it easier to capture your video with the moving camera. (If you don't know how to take a screen recording, you can check out [http://hades.mech.northwestern.edu/index.php/CoppeliaSim_Introduction CoppeliaSim Introduction].)		* Take a screen recording video of the robot moving through your world and interacting with at least three walls. In the video, use the zoom, pan, and other buttons to move the camera view while the robot is moving. You can change the robot's default speed in its child script to make it easier to capture your video with the moving camera. (If you don't know how to take a screen recording, you can check out [http://hades.mech.northwestern.edu/index.php/CoppeliaSim_Introduction CoppeliaSim Introduction].)

	===Part 1B: Exploring the UR5 Scene 1===		===Part 2B: Exploring the UR5 Scene 1===

	Open Scene 1 for interactive manipulation of the Universal Robots UR5 robot, a popular 6R robot. (You can go to the [http://hades.mech.northwestern.edu/index.php/CoppeliaSim_Introduction CoppeliaSim Introduction] to download Scene 1 and the other scenes used in this course). In this scene, there is a model of a UR5 robot, which consists of a collection of [https://www.coppeliarobotics.com/helpFiles/en/joints.htm joints] connecting shapes (links), from the base out to the end-effector.		Open Scene 1 for interactive manipulation of the Universal Robots UR5 robot, a popular 6R robot. (You can go to the [http://hades.mech.northwestern.edu/index.php/CoppeliaSim_Introduction CoppeliaSim Introduction] to download Scene 1 and the other scenes used in this course). In this scene, there is a model of a UR5 robot, which consists of a collection of [https://www.coppeliarobotics.com/helpFiles/en/joints.htm joints] connecting shapes (links), from the base out to the end-effector.
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	-->		-->

	==Part 2: Joint Angle Calculations==		==Part 3: Joint Angle Calculations==

	The 6R UR5 robot is shown below at its home configuration. Eight frames are defined: the fixed frame {s} at the base, frames {1} through {6} attached to links 1 through 6, and the end-effector frame {b} which is fixed relative to link 6. (The frame {b} is not shown in the image.) The red arrow is the x-axis, the green arrow is the y-axis, and the blue arrow is the z-axis. Frames {s} and {1}-{6} are aligned when the robot is at its home configuration, i.e., each rotation matrix <math>R_{ij}</math> (where <math>i, j</math> could be <math>s</math> or any number 1 through 6) is the identity matrix.		The 6R UR5 robot is shown below at its home configuration. Eight frames are defined: the fixed frame {s} at the base, frames {1} through {6} attached to links 1 through 6, and the end-effector frame {b} which is fixed relative to link 6. (The frame {b} is not shown in the image.) The red arrow is the x-axis, the green arrow is the y-axis, and the blue arrow is the z-axis. Frames {s} and {1}-{6} are aligned when the robot is at its home configuration, i.e., each rotation matrix <math>R_{ij}</math> (where <math>i, j</math> could be <math>s</math> or any number 1 through 6) is the identity matrix.
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	* Enter the joint angles you found into your modified Scene1_UR5 in CoppeliaSim to see the configuration of the robot.		* Enter the joint angles you found into your modified Scene1_UR5 in CoppeliaSim to see the configuration of the robot.
	* Calculate ''R<sub>sb</sub>'' using the information given, and verify that your joint angle vector <math>\theta</math> is correct by entering the joint angles into the scene and comparing your ''R<sub>sb</sub>'' to the rotation matrix portion of the ''T<sub>sb</sub>'' calculated by the scene under the "Enter Config and SE(3) Value" tab.		* Calculate ''R<sub>sb</sub>'' using the information given, and verify that your joint angle vector <math>\theta</math> is correct by entering the joint angles into the scene and comparing your ''R<sub>sb</sub>'' to the rotation matrix portion of the ''T<sub>sb</sub>'' calculated by the scene under the "Enter Config and SE(3) Value" tab.

	==Part 3: Chapter 2==

⚫	A. Use Grubler's formula to find the number of degrees of freedom of the mechanism in Figure 2.18(d).

⚫	B. Use Grubler's formula to find the number of degrees of freedom of the mechanism in Figure 2.21(a).

⚫	C. For the task of erasing a whiteboard (the eraser moves in flat contact with the board), how many degrees of freedom does the task space have? Describe the topology of this task space.

⚫	D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do those joints offer? (They are not typical robot joints!) And, if you are interested in anatomy, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?

	==What to Submit via Canvas==		==What to Submit via Canvas==
	Turn in a single zip file. The file name should be FamilyName_GivenName_asst1.zip (for me, it would be Lynch_Kevin_asst1.zip). This file should have:		Turn in a single zip file. The file name should be FamilyName_GivenName_asst1.zip (for me, it would be Lynch_Kevin_asst1.zip). This file should have:
⚫	* Part 1A: A single video file showing a screen recording of your Pioneer_p3dx robot moving through your custom scene. NOTE: make sure your video is in a common format and reasonably sized (e.g., less than 20 MB).
	* A single pdf file including:		* A single pdf file including:
		⚫	** Part 1: Solutions to A-D.
	** Part 1B: A screenshot of your changed code in the child script. Explain what you changed about the scene/UI. (A small change suffices.)
	** Part ~~1B & 2~~: A screenshot of ~~the~~ ~~scene,~~ ~~clearly~~ ~~showing~~ the ~~modified~~ ~~UI,~~ ~~the~~ ~~SE(3)~~ ~~calculation,~~ ~~and~~ the ~~robot~~ at ~~the~~ ~~correct configuration.~~		** Part 2B: A screenshot of your changed code in the child script. Explain what you changed about the scene/UI. (A small change suffices.)
			** Part 2B & 3: A screenshot of the scene, clearly showing the modified UI, the SE(3) calculation, and the robot at the correct configuration.
	** Part 2: The list of the six joint angles and ''R<sub>sb</sub>'' you calculated and a brief explanation of the method (including your code, which likely calls the MR code) you used to calculate them.		** Part 3: The list of the six joint angles and ''R<sub>sb</sub>'' you calculated and a brief explanation of the method (including your code, which likely calls the MR code) you used to calculate them.
⚫	** Part 3: Solutions to A-D.
		⚫	* Part 2A: A single video file showing a screen recording of your Pioneer_p3dx robot moving through your custom scene. NOTE: make sure your video is in a common format and reasonably sized (e.g., less than 20 MB).

	The contents of your zip file should look like what you see below (with your name substituted):		The contents of your zip file should look like what you see below (with your name substituted):

Lynch at 13:42, 24 September 2025

2025-09-24T13:42:57Z

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			<!--
	In Chapter 4, we will study the forward kinematics problem for open-chain robots: finding the configuration of the robot's end-effector <math>T_{sb}(\theta) \in SE(3)</math> given the vector of joint positions <math>\theta</math>. The forward kinematics problem is easy to solve using a formula called the "product of exponentials," which uses the matrix exponential of this chapter. In this project, CoppeliaSim will solve the forward kinematics for you.		In Chapter 4, we will study the forward kinematics problem for open-chain robots: finding the configuration of the robot's end-effector <math>T_{sb}(\theta) \in SE(3)</math> given the vector of joint positions <math>\theta</math>. The forward kinematics problem is easy to solve using a formula called the "product of exponentials," which uses the matrix exponential of this chapter. In this project, CoppeliaSim will solve the forward kinematics for you.

	The goal of this project is to test your understanding of the matrix log for rotations, to give you a little practice using the MR library of functions, and to familiarize you with CoppeliaSim.		The goal of this project is to test your understanding of the matrix log for rotations, to give you a little practice using the MR library of functions, and to familiarize you with CoppeliaSim.
			-->

	You will submit '''a single zip file''' that includes '''a single pdf file and one video (make sure we can play it)''' to Canvas. The file name should be FamilyName_GivenName_asst1.zip (for me, it would be Lynch_Kevin_asst1.zip). You will have to concatenate all your responses and screenshots into a single pdf file. The video should be only a few MB; don't submit an overly long, hi-res video.		You will submit '''a single zip file''' that includes '''a single pdf file and one video (make sure we can play it)''' to Canvas. The file name should be FamilyName_GivenName_asst1.zip (for me, it would be Lynch_Kevin_asst1.zip). You will have to concatenate all your responses and screenshots into a single pdf file. The video should be only a few MB; don't submit an overly long, hi-res video.

Lynch: /* Part 3: Chapter 2 */

2025-09-24T13:37:20Z

Part 3: Chapter 2

← Older revision		Revision as of 08:37, 24 September 2025
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	C. For the task of erasing a whiteboard (the eraser moves in flat contact with the board), how many degrees of freedom does the task space have? Describe the topology of this task space.		C. For the task of erasing a whiteboard (the eraser moves in flat contact with the board), how many degrees of freedom does the task space have? Describe the topology of this task space.

	D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do those joints offer? (They are not typical robot joints!) And, if you are ~~feeling~~ ~~ambitious~~, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?		D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do those joints offer? (They are not typical robot joints!) And, if you are interested in anatomy, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?

	==What to Submit via Canvas==		==What to Submit via Canvas==

Lynch: /* Part 3: Chapter 2 */

2025-09-24T13:36:57Z

Part 3: Chapter 2

← Older revision		Revision as of 08:36, 24 September 2025
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	C. For the task of erasing a whiteboard (the eraser moves in flat contact with the board), how many degrees of freedom does the task space have? Describe the topology of this task space.		C. For the task of erasing a whiteboard (the eraser moves in flat contact with the board), how many degrees of freedom does the task space have? Describe the topology of this task space.

	D. Answer Part 2 of [[DOF of the Human Arm]]. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do those joints offer? (They are not typical robot joints!) And, if you are feeling ambitious, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?		D. Answer Part 2 of [[DOF of the Human Arm]], the total number of constraints provided by joints in the arm. BONUS (you don't need to answer): how many total joints might there be, considering how the five rigid bodies (ground, humerus, ulna, radius, hand) are arranged? How many total freedoms do those joints offer? (They are not typical robot joints!) And, if you are feeling ambitious, how are these joints enforced by biological tissue, and what are the anatomical names of these joints?

	==What to Submit via Canvas==		==What to Submit via Canvas==

Lynch: /* What to Submit via Canvas */

2025-09-24T13:35:43Z

What to Submit via Canvas

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	** Part 1B & 2: A screenshot of the scene, clearly showing the modified UI, the SE(3) calculation, and the robot at the correct configuration.		** Part 1B & 2: A screenshot of the scene, clearly showing the modified UI, the SE(3) calculation, and the robot at the correct configuration.
	** Part 2: The list of the six joint angles and ''R<sub>sb</sub>'' you calculated and a brief explanation of the method (including your code, which likely calls the MR code) you used to calculate them.		** Part 2: The list of the six joint angles and ''R<sub>sb</sub>'' you calculated and a brief explanation of the method (including your code, which likely calls the MR code) you used to calculate them.
			** Part 3: Solutions to A-D.

	The contents of your zip file should look like what you see below (with your name substituted):		The contents of your zip file should look like what you see below (with your name substituted):

Lynch at 13:32, 24 September 2025

2025-09-24T13:32:30Z

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 * Enter the joint angles you found into your modified Scene1_UR5 in CoppeliaSim to see the configuration of the robot.
 * Calculate ''R<sub>sb</sub>'' using the information given, and verify that your joint angle vector <math>\theta</math> is correct by entering the joint angles into the scene and comparing your ''R<sub>sb</sub>'' to the rotation matrix portion of the ''T<sub>sb</sub>'' calculated by the scene under the "Enter Config and SE(3) Value" tab.
 ==What to Submit via Canvas==

Lynch: /* Part 1B: Exploring the UR5 Scene 1 */

2025-09-24T13:15:35Z

Part 1B: Exploring the UR5 Scene 1

← Older revision		Revision as of 08:15, 24 September 2025
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	When you run this scene you will see a window with two tabs: "Enter Config and SE(3) Value" and "Joint Angle Sliders". Go to the "Joint Angle Sliders" tab, move the sliders corresponding to the six joints, and watch how the robot moves.		When you run this scene you will see a window with two tabs: "Enter Config and SE(3) Value" and "Joint Angle Sliders". Go to the "Joint Angle Sliders" tab, move the sliders corresponding to the six joints, and watch how the robot moves.

		⚫	Make sure your scene 1 simulation is stopped so you can open up a script. Find the script "UI_Script" in the Scene hierarchy at the left. Double-click the folded paper icon to open it. You will see a script written in the Lua programming language. Early in the file, you might notice that some functions look similar to functions written in the Modern Robotics Library. For example, ''so3andp2se3(R,p)'' in this script resembles ''RpToTrans(R,p)'' in the Modern Robotics Library.
	Make sure your scene 1 simulation is stopped so you can open up a script.

	[[File:CoppeliaSim_scripts.PNG]]

⚫	Find the script "UI_Script" in the Scene hierarchy at the left. Double-click the folded paper icon to open it. You will see a script written in the Lua programming language. Early in the file, you might notice that some functions look similar to functions written in the Modern Robotics Library. For example, ''so3andp2se3(R,p)'' in this script resembles ''RpToTrans(R,p)'' in the Modern Robotics Library.

	Scroll down to line 242. From here to the end of the file, this code examines the type of "call" to the child script by the main script and performs the appropriate functions. For example, if the sim_call_type is sim.syscb_init, the simulation has started and the user interface should be generated. (There is a lot of XML code here defining the user interface.) If the sim_call_type is sim.syscb_actuation, then the joint angles entered by the user in the UI are applied to the UR5 model, the UI is updated, and the transformation matrix for the end-effector is calculated. If the sim_call_type is sim.syscb_sensing, nothing happens, and if it is sim.syscb_cleanup, the UI is destroyed as the simulation ends.		Scroll down to line 242. From here to the end of the file, this code examines the type of "call" to the child script by the main script and performs the appropriate functions. For example, if the sim_call_type is sim.syscb_init, the simulation has started and the user interface should be generated. (There is a lot of XML code here defining the user interface.) If the sim_call_type is sim.syscb_actuation, then the joint angles entered by the user in the UI are applied to the UR5 model, the UI is updated, and the transformation matrix for the end-effector is calculated. If the sim_call_type is sim.syscb_sensing, nothing happens, and if it is sim.syscb_cleanup, the UI is destroyed as the simulation ends.