Mobile Manipulation Capstone - Revision history

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

2026-04-07T13:02:15Z

Introduction, and the CSV Mobile Manipulation youBot CoppeliaSim Scene

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

2026-04-07T13:00:36Z

Introduction, and the CSV Mobile Manipulation youBot CoppeliaSim Scene

Lynch: /* Kinematics of the youBot */

2026-04-07T03:07:33Z

Kinematics of the youBot

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

2026-04-07T03:06:13Z

Introduction, and the CSV Mobile Manipulation youBot CoppeliaSim Scene

Lynch: /* Kinematics of the youBot */

2026-04-07T03:04:16Z

Kinematics of the youBot

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

2026-04-07T03:01:42Z

Introduction, and the CSV Mobile Manipulation youBot CoppeliaSim Scene

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

2026-04-07T02:55:34Z

Milestone 1: youBot Kinematics Simulator and csv Output

Lynch: /* Milestones and Details */

2026-04-07T02:49:53Z

Milestones and Details

Lynch: /* Milestones and Details */

2026-04-07T02:47:57Z

Milestones and Details

Lynch: /* Kinematics of the youBot */

2026-04-07T02:46:21Z

Kinematics of the youBot

@@ Line 15: / Line 15: @@
 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]]''' (from Course 1 of the [https://www.coursera.org/specializations/modernrobotics Coursera specialization]).  [[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.  (Even if you have downloaded it before, download it again before you begin your project, to make sure you have the most up-to-date version of this scene.) Leave the block's initial and goal configurations as the default.  The default initial block configuration is at
+'''[[Getting_Started_with_the_CoppeliaSim_Simulator|Make sure you have a working CoppeliaSim installation]]''' (from Course 1 of the [https://www.coursera.org/specializations/modernrobotics Coursera specialization]).  [[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.  (Even if you have downloaded it before, download it again before you begin your project, to make sure you have the most up-to-date version of this scene.) 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>
-<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>.

@@ Line 19: / Line 19: @@
 (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>.
+and the final block configuration is at <math>(x,y,\theta)=(0\text{m},-1\text{m},-\pi/2\text{rad})</math>.
 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 and ODE, but ODE is the default for Scene 6.

@@ Line 101: / Line 101: @@
 The configuration of the frame {b} of the mobile base, relative to the frame {s} on the floor, is described by the 3-vector
-<math>q = (\phi,x,y)
+<math>q=(\phi,x,y)
 </math>
 or the

@@ Line 19: / Line 19: @@
 (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>.
+and the final block configuration is at <math>(x,y,\theta)=(0~\text{m},-1~\text{m},-\pi/2~\text{rad})</math>.
 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 and ODE, but ODE is the default for Scene 6.

@@ Line 96: / Line 96: @@
 meters and the side-to-side distance between wheels is <math>2w = 0.3</math> meters.  The radius of each wheel is <math>r = 0.0475</math> meters.  The forward driving and "free sliding" direction <math>\gamma</math> of each wheel is indicated.]]
-[[image:Youbot-gripper.png|right|300px|thumb|The gripper and the end-effector frame {e}, which has an origin midway between the fingers of the gripper.  The minimum opening distance of the gripper is <math>d_{1,\text{min}} = 2</math> cm, 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.  The axis <math>\hat{\text{x}}_{\text{e}}</math> is into the screen.]]
+[[image:Youbot-gripper.png|right|300px|thumb|The gripper and the end-effector frame {e}, which has an origin midway between the fingers of the gripper.  The minimum opening distance of the gripper is <math>d_{1,\text{min}} = 2</math> cm, 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.  The axis <math>\hat{\text{x}}_{\text{e}}</math> is into the screen.]]
 [[image:Block-capstone.png|right|300px|thumb|The object being manipulated is a cube, 5 cm x 5 cm x 5 cm.  The cube's frame {c} is at its center, and the axes are aligned with the edges of the cube.]]

@@ Line 206: / Line 206: @@
 u
 </math>
-(4 variables) and the arm joint speeds <math>\dot{\theta}</math> (5 variables).
+(4 variables) and the arm joint speeds
+<math>
+\dot{\theta}
+</math>
+(5 variables).
 * A timestep <math>\Delta t</math>.
 * A positive real value indicating the maximum angular speed of the arm joints and the wheels.  For example, if this value is 12.3, the angular speed of the wheels and arm joints is limited to the range [-12.3 radians/s, 12.3 radians/s].  Any speed in the 9-vector of controls that is outside this range will be set to the nearest boundary of the range.  If you don't want speed limits, just use a very large number.  If you prefer, your function can accept separate speed limits for the wheels and arm joints.

@@ Line 202: / Line 202: @@
 '''Input:'''
 * A 12-vector representing the current configuration of the robot (3 variables for the chassis configuration, 5 variables for the arm configuration, and 4 variables for the wheel angles).
-* A 9-vector of controls indicating the wheel speeds <math>u</math> (4 variables) and the arm joint speeds <math>\dot{\theta}</math> (5 variables).
+* A 9-vector of controls indicating the wheel speeds
+<math>
+u
+</math>
+(4 variables) and the arm joint speeds <math>\dot{\theta}</math> (5 variables).
 * A timestep <math>\Delta t</math>.
 * A positive real value indicating the maximum angular speed of the arm joints and the wheels.  For example, if this value is 12.3, the angular speed of the wheels and arm joints is limited to the range [-12.3 radians/s, 12.3 radians/s].  Any speed in the 9-vector of controls that is outside this range will be set to the nearest boundary of the range.  If you don't want speed limits, just use a very large number.  If you prefer, your function can accept separate speed limits for the wheels and arm joints.

@@ Line 213: / Line 213: @@
 * 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.

@@ Line 90: / Line 90: @@
 [[image:Yb-book.png|right|500px|thumb|This figure illustrates the arm at its home configuration (all joint angles zero) and the frames {s}, {b}, {0}, and {e}.  For the image on the right, joint axes 1 and 5 (not shown) point upward and joint axes 2, 3, and 4 are out of the screen.  Click to make the image bigger.]]
-[[image:Yb-base-capstone.png|right|300px|thumb|A top view of the omnidirectional mobile base.  The forward-backward distance between the wheels is <math>2l = 0.47</math> meters and the side-to-side distance between wheels is <math>2w = 0.3</math> meters.  The radius of each wheel is <math>r = 0.0475</math> meters.  The forward driving and "free sliding" direction <math>\gamma</math> of each wheel is indicated.]]
+[[image:Yb-base-capstone.png|right|300px|thumb|A top view of the omnidirectional mobile base.  The forward-backward distance between the wheels is
+<math>
+l = 0.47
+</math>
+meters and the side-to-side distance between wheels is <math>2w = 0.3</math> meters.  The radius of each wheel is <math>r = 0.0475</math> meters.  The forward driving and "free sliding" direction <math>\gamma</math> of each wheel is indicated.]]
 [[image:Youbot-gripper.png|right|300px|thumb|The gripper and the end-effector frame {e}, which has an origin midway between the fingers of the gripper.  The minimum opening distance of the gripper is <math>d_{1,\text{min}} = 2</math> cm, 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.  The axis <math>\hat{\text{x}}_{\text{e}}</math> is into the screen.]]