Mobile Manipulation Capstone 2024 - Revision history

Lynch: /* Milestone 3: Feedforward Control */

2024-11-13T00:24:18Z

Milestone 3: Feedforward Control

← Older revision		Revision as of 19:24, 12 November 2024
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	If you don't get these results (within reasonable roundoff error), you should correct your program before moving on.		If you don't get these results (within reasonable roundoff error), you should correct your program before moving on.

	'''Singularities:''' If the 6x9 Jacobian matrix <math>J_e</math> is singular (i.e., its rank drops below 6) or nearly singular, the pseudoinverse algorithm may generate a pseudoinverse <math>J_e^\dagger</math> with unreasonably large entries, which could lead to unacceptably large commanded joint speeds if we ask for even a very small component of a twist in a direction that the near-singularity nearly prevents. A better behavior for the robot would be to essentially ignore any requested twist components in directions that the near-singularity renders difficult to achieve. To achieve this ~~in MATLAB and Mathematica~~, you may wish to explore the tolerance options for the pseudoinverse algorithm. The tolerance option allows you to specify how close to zero a singular value must be to be treated as zero. By treating small singular values (that are greater than the default tolerance) as zero, you will avoid having pseudoinverse matrices with unreasonably large entries. A MATLAB example is shown below:		'''Singularities:''' If the 6x9 Jacobian matrix <math>J_e</math> is singular (i.e., its rank drops below 6) or nearly singular, the pseudoinverse algorithm may generate a pseudoinverse <math>J_e^\dagger</math> with unreasonably large entries, which could lead to unacceptably large commanded joint speeds if we ask for even a very small component of a twist in a direction that the near-singularity nearly prevents. A better behavior for the robot would be to essentially ignore any requested twist components in directions that the near-singularity renders difficult to achieve. To achieve this, you may wish to explore the tolerance options for the pseudoinverse algorithm in MATLAB, Mathematica, or NumPy. The tolerance option allows you to specify how close to zero a singular value must be to be treated as zero. By treating small singular values (that are greater than the default tolerance) as zero, you will avoid having pseudoinverse matrices with unreasonably large entries. A MATLAB example is shown below:

	>> M = [[2,0];[0,0.00001]] % a matrix that's nearly singular		>> M = [[2,0];[0,0.00001]] % a matrix that's nearly singular

Lynch: /* Milestone 2: Reference Trajectory Generation */

2024-11-12T23:42:20Z

Milestone 2: Reference Trajectory Generation

← Older revision		Revision as of 18:42, 12 November 2024
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	'''Output:'''		'''Output:'''
	* A representation of the <math>N</math> configurations of the end-effector along the entire concatenated eight-segment reference trajectory. Each of these <math>N</math> reference points represents a transformation matrix <math>T_{se}</math> of the end-effector frame {e} relative to {s} at an instant in time, plus the gripper state (0 or 1). For example, if your entire eight-segment trajectory takes 30 seconds~~, for example~~, you will have approximately <math>N \approx 30k/0.01</math> sequential reference configurations (perhaps one or a few more, depending on how you treat boundary conditions), each separated by <math>0.01/k</math> seconds in time. These reference configurations will be used by your controller. Your representation of the reference configurations could be anything you want. If you use an <math>N \times 13</math> matrix, for example, each of the <math>N</math> rows would represent a configuration of the end-effector frame {e} relative to {s} at that instant in time. Twelve of the 13 entries of a matrix row are the top three rows of the transformation matrix <math>T_{se}</math> at that instant of time, i.e., <math>r_{11}, r_{12}, r_{13}, r_{21}, r_{22}, r_{23}, r_{31}, r_{32}, r_{33}, p_x, p_y, p_z</math> from		* A representation of the <math>N</math> configurations of the end-effector along the entire concatenated eight-segment reference trajectory. Each of these <math>N</math> reference points represents a transformation matrix <math>T_{se}</math> of the end-effector frame {e} relative to {s} at an instant in time, plus the gripper state (0 or 1). For example, if your entire eight-segment trajectory takes 30 seconds, you will have approximately <math>N \approx 30k/0.01</math> sequential reference configurations (perhaps one or a few more, depending on how you treat boundary conditions), each separated by <math>0.01/k</math> seconds in time. These reference configurations will be used by your controller. Your representation of the reference configurations could be anything you want. If you use an <math>N \times 13</math> matrix, for example, each of the <math>N</math> rows would represent a configuration of the end-effector frame {e} relative to {s} at that instant in time. Twelve of the 13 entries of a matrix row are the top three rows of the transformation matrix <math>T_{se}</math> at that instant of time, i.e., <math>r_{11}, r_{12}, r_{13}, r_{21}, r_{22}, r_{23}, r_{31}, r_{32}, r_{33}, p_x, p_y, p_z</math> from

	<math> T_{se} = \left[\begin{array}{cccc} r_{11} & r_{12} & r_{13} & p_x \\ r_{21} & r_{22} & r_{23} & p_y \\ r_{31} & r_{32} & r_{33} & p_z \\ 0 & 0 & 0 & 1 \end{array}\right], </math>		<math> T_{se} = \left[\begin{array}{cccc} r_{11} & r_{12} & r_{13} & p_x \\ r_{21} & r_{22} & r_{23} & p_y \\ r_{31} & r_{32} & r_{33} & p_z \\ 0 & 0 & 0 & 1 \end{array}\right], </math>

Lynch: /* Milestone 1: youBot Kinematics Simulator and csv Output */

2024-11-12T23:30:58Z

Milestone 1: youBot Kinematics Simulator and csv Output

← Older revision		Revision as of 18:30, 12 November 2024
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	* new chassis configuration is obtained from odometry, as described in Chapter 13.4		* new chassis configuration is obtained from odometry, as described in Chapter 13.4

	'''Testing the <tt>NextState</tt> function:''' To test your <tt>NextState</tt> function, you should embed it in a program that takes an initial configuration of the youBot and simulates constant controls for one second. For example, you can set <math>\Delta t</math> to 0.01 seconds and run a loop that calls <tt>NextState</tt> 100 times with constant controls <math>(u,\dot{\theta})</math>. Your program should write a csv file, where each line has 13 values separated by commas (the 12-vector consisting of 3 chassis configuration variables, the 5 arm joint angles, and the 4 wheel angles, plus a "0" for "gripper open") representing the robot's configuration after each integration step. Then you should load the csv file into the CSV Mobile Manipulation youBot CoppeliaSim scene and watch the animation of the constant controls to see if your <tt>NextState</tt> function is working properly (and to check your ability to produce a csv file).		'''Testing the <tt>NextState</tt> function:''' To test your <tt>NextState</tt> function, you should embed it in a program that takes an initial configuration of the youBot and simulates constant controls for one second. For example, you can set <math>\Delta t</math> to 0.01 seconds and run a loop that calls <tt>NextState</tt> 100 times with constant controls <math>(u,\dot{\theta})</math>. Your program should write a csv file where each line has 13 values separated by commas (the 12-vector consisting of 3 chassis configuration variables, the 5 arm joint angles, and the 4 wheel angles, plus a "0" for "gripper open") representing the robot's configuration after each integration step. Then you should load the csv file into the CSV Mobile Manipulation youBot CoppeliaSim scene and watch the animation of the constant controls to see if your <tt>NextState</tt> function is working properly (and to check your ability to produce a csv file).

	[[Writing_a_CSV_File\|'''This page''']] has information on writing csv files in Python, MATLAB, and Mathematica.		[[Writing_a_CSV_File\|'''This page''']] has information on writing csv files in Python, MATLAB, and Mathematica.

Lynch: /* Joints in Scene 6 */

2024-11-12T23:24:33Z

Joints in Scene 6

← Older revision		Revision as of 18:24, 12 November 2024
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	'''In Scene 6, all joints are in passive mode, except for the two joints controlling the gripper motion.''' All passive joints kinematically follow the motions commanded in the csv file.		'''In Scene 6, all joints are in passive mode, except for the two joints controlling the gripper motion.''' All passive joints kinematically follow the motions commanded in the csv file.

	All joint limits for the youBot's 5R arm are disabled in Scene 6. This is unrealistic, but ~~respecting~~ joint limits is ~~not part of~~ ~~this~~ ~~capstone~~ ~~project~~.		All joint limits for the youBot's 5R arm are disabled in Scene 6. This is unrealistic, of course, but you can enforce joint limits once you get everything working.

	=== Gripper ===		=== Gripper ===

Lynch: /* Kinematics of the youBot */

2024-11-12T23:12:36Z

Kinematics of the youBot

← Older revision		Revision as of 18:12, 12 November 2024
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	# <math>\mathcal{B}_5 = (\omega_5,v_5)</math> where <math>\omega_5 = (0,0,1), \; v_5 = (0,0,0)</math>		# <math>\mathcal{B}_5 = (\omega_5,v_5)</math> where <math>\omega_5 = (0,0,1), \; v_5 = (0,0,0)</math>

	In this project, for simplicity '''we assume no joint limits on the five joints of the robot arm.''' It is recommended, however, that you choose limits on the wheel and joint velocities. We will come back to this issue later.		In this project, for simplicity '''we assume no joint limits on the five joints of the robot arm.''' (But see "Other Things to Try" at the bottom of this page.) It is recommended, however, that you choose limits on the wheel and joint velocities. We will come back to this issue later.

	The end-effector frame {e} is rigidly attached to the last link and is midway between the tips of the gripper fingers. The minimum opening distance of the gripper is <math>d_{1,\text{min}} = 2</math> cm (i.e., the fingers cannot fully close; they can only get within 2 cm of each other), the maximum opening distance is <math>d_{1,\text{max}} = 7</math> cm, the interior length of the fingers is <math>d_{2} = 3.5</math> cm, and the distance from the base of the fingers to the frame {e} is <math>d_{3} = 4.3</math> cm. When the gripper closes, it closes until it reaches its minimum closing distance or encounters a force large enough to prevent further closing.		The end-effector frame {e} is rigidly attached to the last link and is midway between the tips of the gripper fingers. The minimum opening distance of the gripper is <math>d_{1,\text{min}} = 2</math> cm (i.e., the fingers cannot fully close; they can only get within 2 cm of each other), the maximum opening distance is <math>d_{1,\text{max}} = 7</math> cm, the interior length of the fingers is <math>d_{2} = 3.5</math> cm, and the distance from the base of the fingers to the frame {e} is <math>d_{3} = 4.3</math> cm. When the gripper closes, it closes until it reaches its minimum closing distance or encounters a force large enough to prevent further closing.

Lynch: /* Introduction, and the CSV Mobile Manipulation youBot CoppeliaSim Scene */

2024-11-12T23:01:48Z

Introduction, and the CSV Mobile Manipulation youBot CoppeliaSim Scene

← Older revision		Revision as of 18:01, 12 November 2024
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	'''[[Getting_Started_with_the_CoppeliaSim_Simulator\|Make sure you have a working CoppeliaSim installation]]'''. [[CoppeliaSim_Introduction#Scene_6:_CSV_Mobile_Manipulation_youBot\|'''This project uses Scene 6 (CSV Mobile Manipulation youBot) from the CoppeliaSim Introduction wiki page''']]. You should download it and test it with its sample csv file, to see what a solution looks like. Leave the block's initial and goal configurations as the default. The default initial block configuration is at <math>(x,y,\theta) = (1~\text{m}, 0~\text{m}, 0~\text{rad})</math> and the final block configuration is at <math>(x,y,\theta) = (0~\text{m},-1~\text{m},-\pi/2~\text{rad})</math>. (If the simulation plays too quickly, toggle the "real-time mode" by clicking on the icon that looks like a clock in the top toolbar.)		'''[[Getting_Started_with_the_CoppeliaSim_Simulator\|Make sure you have a working CoppeliaSim installation]]'''. [[CoppeliaSim_Introduction#Scene_6:_CSV_Mobile_Manipulation_youBot\|'''This project uses Scene 6 (CSV Mobile Manipulation youBot) from the CoppeliaSim Introduction wiki page''']]. You should download it and test it with its sample csv file, to see what a solution looks like. Leave the block's initial and goal configurations as the default. The default initial block configuration is at <math>(x,y,\theta) = (1~\text{m}, 0~\text{m}, 0~\text{rad})</math> and the final block configuration is at <math>(x,y,\theta) = (0~\text{m},-1~\text{m},-\pi/2~\text{rad})</math>. (If the simulation plays too quickly, toggle the "real-time mode" by clicking on the icon that looks like a clock in the top toolbar.)

	Unlike previous projects, where we used CoppeliaSim to simply animate the robot's motion, in this project CoppeliaSim will use a physics simulator to simulate the interaction of the youBot ~~with~~ the block. In other words, if the gripper closes on the block in the wrong position or orientation, the block may simply slide out of the grasp. The interaction between the robot and the block is governed by a physics simulator, often called a "physics engine," which approximately accounts for friction, mass, inertial, and other properties. CoppeliaSim has different physics engines which you can select, including Bullet, ODE, and MuJoCo, but ODE is the default for Scene 6.		Unlike previous projects, where we used CoppeliaSim to simply animate the robot's motion, in this project CoppeliaSim will use a physics simulator to simulate the interaction between the youBot's gripper and the block, and between the block and the floor. In other words, if the gripper closes on the block in the wrong position or orientation, the block may simply slide out of the grasp. The interaction between the robot and the block is governed by a physics simulator, often called a "physics engine," which approximately accounts for friction, mass, inertial, and other properties. CoppeliaSim has different physics engines which you can select, including Bullet, ODE, and MuJoCo, but ODE is the default for Scene 6.

	'''The time between each successive configuration in your csv file is 0.01 seconds (10 milliseconds).''' This is an important bit of information, since, unlike the previous visualization scenes which simply animated a csv file with no particular notion of time, the notion of time is critical in a dynamic simulation.		'''The time between each successive configuration in your csv file is 0.01 seconds (10 milliseconds).''' This is an important bit of information, since, unlike the previous visualization scenes which simply animated a csv file with no particular notion of time, the notion of time is critical in a dynamic simulation.

Lynch: /* Introduction, and the CSV Mobile Manipulation youBot CoppeliaSim Scene */

2024-11-12T22:58:12Z

Introduction, and the CSV Mobile Manipulation youBot CoppeliaSim Scene

← Older revision		Revision as of 17:58, 12 November 2024
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	The final output of your software will be a comma-separated values (csv) text file that specifies the configurations of the chassis and the arm, the angles of the four wheels, and the state of the gripper (open or closed) as a function of time. This specification of the position-controlled youBot will then be "played" on the CoppeliaSim simulator to see if your trajectory succeeds in solving the task. [[Writing_a_CSV_File\|'''This page''']] has information on writing csv files in Python, MATLAB, and Mathematica.		The final output of your software will be a comma-separated values (csv) text file that specifies the configurations of the chassis and the arm, the angles of the four wheels, and the state of the gripper (open or closed) as a function of time. This specification of the position-controlled youBot will then be "played" on the CoppeliaSim simulator to see if your trajectory succeeds in solving the task. [[Writing_a_CSV_File\|'''This page''']] has information on writing csv files in Python, MATLAB, and Mathematica.

	'''[[Getting_Started_with_the_CoppeliaSim_Simulator\|Make sure you have a working CoppeliaSim installation]]'''. [[CoppeliaSim_Introduction#Scene_6:_CSV_Mobile_Manipulation_youBot\|'''This project uses Scene 6 (CSV Mobile Manipulation youBot) from the CoppeliaSim Introduction wiki page''']]. You should download it and test it with its sample csv file, to see what a solution looks like. Leave the block's initial and goal configurations as the default. The default initial block configuration is at <math>(x,y,\theta) = (1~\text{m}, 0~\text{m}, 0~\text{rad})</math> and the final block configuration is at <math>(x,y,\theta) = (0~\text{m},-1~\text{m},-\pi/2~\text{rad})</math>.		'''[[Getting_Started_with_the_CoppeliaSim_Simulator\|Make sure you have a working CoppeliaSim installation]]'''. [[CoppeliaSim_Introduction#Scene_6:_CSV_Mobile_Manipulation_youBot\|'''This project uses Scene 6 (CSV Mobile Manipulation youBot) from the CoppeliaSim Introduction wiki page''']]. You should download it and test it with its sample csv file, to see what a solution looks like. Leave the block's initial and goal configurations as the default. The default initial block configuration is at <math>(x,y,\theta) = (1~\text{m}, 0~\text{m}, 0~\text{rad})</math> and the final block configuration is at <math>(x,y,\theta) = (0~\text{m},-1~\text{m},-\pi/2~\text{rad})</math>. (If the simulation plays too quickly, toggle the "real-time mode" by clicking on the icon that looks like a clock in the top toolbar.)

	Unlike previous projects, where we used CoppeliaSim to simply animate the robot's motion, in this project CoppeliaSim will use a physics simulator to simulate the interaction of the youBot with the block. In other words, if the gripper closes on the block in the wrong position or orientation, the block may simply slide out of the grasp. The interaction between the robot and the block is governed by a physics simulator, often called a "physics engine," which approximately accounts for friction, mass, inertial, and other properties. CoppeliaSim has different physics engines which you can select, including Bullet, ODE, and MuJoCo, but ODE is the default for Scene 6.		Unlike previous projects, where we used CoppeliaSim to simply animate the robot's motion, in this project CoppeliaSim will use a physics simulator to simulate the interaction of the youBot with the block. In other words, if the gripper closes on the block in the wrong position or orientation, the block may simply slide out of the grasp. The interaction between the robot and the block is governed by a physics simulator, often called a "physics engine," which approximately accounts for friction, mass, inertial, and other properties. CoppeliaSim has different physics engines which you can select, including Bullet, ODE, and MuJoCo, but ODE is the default for Scene 6.

Lynch: Created page with "x250px This page describes the capstone project for ME 449. [https://youtu.be/Q1CekpBW6Js '''A video summary of this project is given in t..."

2024-11-12T19:17:48Z

Created page with "right|x250px This page describes the capstone project for ME 449. [https://youtu.be/Q1CekpBW6Js '''A video summary of this project is given in t..."

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