University of Pennsylvania
School of Engineering and Applied Science
Department of Mechanical Engineering

MEAM 620: Robotics and Motion Planning
Spring 2007

Table of Contents

General Info






Tentative Schedule




Schedule and notes


Related notes and codes

Grading Policy








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General Information

Meam 620 is a graduate level course in robotics, focusing on robot kinematics and motion planning. The first part of this course will cover kinematics from a differential geometric viewpoint. In the second and third parts of this course, students will also learn to use and develop algorithms to solve motion planning problems. This course is open to all engineering graduate students. Undergraduate and masters students should visit A more detailed description of the course is available here.


1.      HW 6 is online and due Apr. 11, 2007

2.      Project presentations are on April 16 & 18. Presentation order will  be announced

3.      Project review is on April 4

4.      HW 5 is online and due on Mar. 26, 2007

5.      Two lectures in the week of Feb. 26-Mar. 2 will be given by Savvas.

6.      Programming assignment 2 is available and due on Mar. 16, 2007.

7.      Programming assignment 1 is online (see "Assignments/Homeworks" section) and due on Mar. 1, 2007.

8.      A half page course project proposal is due on Mar. 1, 2007.

9.      HW 2 is online and due on Feb. 19, 2007.

10.  No class on Jan 15 because of the Dr. Martin Luther King holiday.

11.  HW1 is now due on Jan 29, 2007 instead of Jan 22, 2007.

12.  HW1 is online. Access a pdf version here along with the data files for Problem 3.

13.  Access references for the course here using the username and password emailed to you earlier.



Time and Location:

          Monday & Wednesday, 1:30 – 3:00 pm, Towne 303


Dr. Sachin Chitta,    Lectures 1-7                         Office: Levine 403,              Email:

Dr. Peng Cheng,      Lectures 9-15                       Office: Levine 403,              Email:

Dr. Savvas Loizou, Lectures 17-23                     Office: Levine 465,              Email:

Ethan Stump,            Lectures 8, 16                      Office: TBA,                         Email:


Office Hours

Mondays 3-4 pm, Thursdays 3-4 pm in Levine 457 or e mail the instructor for an appointment.


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[MLS 94] Murray, R., Li, Z. and Sastry, S., A mathematical introduction to robotic manipulation. CRC Press, 1994. Comments: A group theoretic and differential geometric approach to robot kinematics and dynamics.

[LaValle 05] LaValle, S., Planning Algorithms. Cambridge University Press, 2006. Free at .


[1] Craig, J., Introduction to Robotics: Mechanics and Control, Addison-Wesley, Reading, MA, 1986. Comments: Easy reading, good introduction.

[2] Mason, M. and Salisbury, K., Robot Hands and the Mechanics of Manipulation, M.I.T. Press, 1985. Comments: The first book dealing with the mechanics of multifingered grasping and modeling of contacts, applications of screw theory.

[3] McCarthy, J.M., Introduction to Theoretical Kinematics, M.I.T. Press, 1990. Comments: The most readable account of theoretical kinematics. Moderately priced.

[4] Spong, M. W. and Vidyasagar, M., Robot dynamics and control. J. Wiley, 1989. Comments: A good text for robot control.

[5] Strang, G., Linear algebra and its applications. Academic press, 1980. Comments: A basic book on linear algebra. If you don't know this material, you might have trouble in this course.

[6] Handbook of Industrial Robotics,  Ed. S. Nof,  1999.  Comments: A comprehensive reference to the latest work and the state of the art in robotics research and practice.

[7] Paul, R., Robot Manipulators, Mathematics, Programming and Control, The MIT Press, Cambridge, 1981. The first text and still one of the best texts.

[8] H. Choset, K. M. Lynch, S. Hutchinson, G. Kantor, W. Burgard, L. E. Kavraki and S. Thrun, Principles of Robot Motion: Theory, Algorithms, and Implementations, MIT Press, Boston, 2005.

[9] Jean-Paul Laumond (Editor), Robot Motion Planning and Control, Springer, 1998.

[10] J.C. Latombe, Robot Motion Planning, Kluwer Academic Publishers, Boston, MA, 1991.


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Course Information

Course Description

This course deals with the robot kinematics and motion planning. After this class, people will be expected to use and develop algorithms to solve motion planning problems. See tentative schedule.

Students are expected to have a basic background in physics and must have had basic courses in algorithms, ordinary differential equations, linear algebra and multivariable calculus. We expect students from diverse background, but with a basic level of mathematical maturity. In addition, some familiarity with one of the topic areas: robotics, dynamics, control, vision or graphics is expected.

Lectures will be complemented by discussions and presentations by the students in the class. These discussion sessions will help in problem solving.

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Tentative Schedule



Reading materials


Lec. 1


[MLS 94], 
Chapter 2
Introduction to kinematics, Rigid body motion, Rotations, SO(3), Euler's theorem,
exponential map.

Lec. 2


[MLS 94], Chapter 2

Homeogeneous transformation matrices, SE(3), Twists, Exponential map from se(3) to SE(3). 

Lec. 3


[MLS 94], Chapter 2
Twists, Chasles theorem, Screw 

Lec. 4


[MLS 94], 
Chapter 2
Velocity analysis

Lec. 5


[MLS 94], Chapter 3

Inverse Kinematics

Lec. 6


[MLS 94], Chapter 3
Manipulator Jacobian

Lec. 7


[MLS 94], Chapter 3
Wrenches and reciprocal screws, Visual servoing, 
Parallel manipulators - cable manipulator

Lec. 8



Lec. 9


[LaValle 05], II-Overview
Overview of motion planning: motivation, application, general algorithm principle

Lec. 10


[LaValle 05], II-Chapter 4 
Configuration space - I: concept, examples of configuration space, mathematical representation, 

Lec. 11


[LaValle 05], II-Chapter 4
Configuration space - II: representation of shape of robots, computation of configuration space 
obstacles, abstraction of path planning problems

Lec. 12


[LaValle 05], I-Chapter 2
Discrete planning overview: problem formulation, discrete search methods, discrete optimal planning

Lec. 13


[LaValle 05], II-Chapter 6
Combinatorial planning algorithms - I : visibility-based complete planning, simplicial complex decomposition

Lec. 14


[LaValle 05], II-Chapter 6

Combinatorial planning algorithms - II: cylindrical decomposition methods, Canny's algorithm

Lec. 15


[LaValle 05], II-Chapter 5
Sampling-based path planning algorithms: basic concepts and methods in configuration space sampling, 
common sampling sequences, sampling-based algorithms

 Lec. 16




Lec. 17


[LaValle 05], II-Chapter 7
Extensions of the Basic Motion Planning Problem

Lec. 18


[LaValle 05], II-Chapter 8
Planning in discrete state spaces

Lec. 19


[LaValle 05], IV-Chapter 13
Planning with differential constraints
Velocity constraints, Phase space representations

Lec. 20


[LaValle 05], IV-Chapter 15
Stability, Lyapunov methods, controllability

Lec. 21


[LaValle 05], II-Chapter 8
Feedback motion Planning 
Vector fields on R^n, Smooth Manifolds 

Lec. 22


[LaValle 05], II-Chapter 8
Complete methods for continuous spaces, Acceleration based control,
velocity/acceleration constraints, Harmonic Potential functions

Lec. 23


[LaValle 05], II-Chapter 8
Navigation Functions (Rimon-Koditschek)

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Jan 8, 2007

Introduction, Rotations

Lecture1.ppt, Lecture1.pdf



Jan 10, 2007

Rotations – exponential formulation, Euler’s theorem, Homogeneous transformations – composition, similarity transformation

Lecture2.ppt, Lecture2.pdf



Jan 10, 2007

Introduction of Motion Planning









Feb 26, 2007

Extensions of the Basic Motion Planning Problem

Lecture17a, Lecture17b



Feb 28, 2007

Navigation Functions










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1.      There will be three homeworks for every 8 lectures. Homework assignments will be posted on the web site. Reading assignments, and homework problem sets will be announced  through the web (see Lectures and homeworks). Problem sets will be assigned at least one week before they are due. You may consult your colleagues or talk to the instructors before doing the homework problems. No late homework will be accepted without special permission from one of the instructors.

2.      All students will be required to do a term paper/project. This will involve independent research (for example, read and critique one or more journal articles on material that is relevant to the class). Original work will be encouraged and suitably rewarded.




Due dates



Data for Problem 3, Part 1 (littledog_accel.txt)

Data for Problem 3, Part 2 (littledog_gyro.txt)


Jan 29, 2007.




Feb 19, 2007.


Programming assignment 1


Mar 1, 2007.


Programming assignment 2


Mar 16, 2007.




Mar 26, 2007




Apr 11, 2007



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Grading Policy

The tentative grading policy is as follows:






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Project work for research track


1.      Survey of different methods for representing rigid body rotations and translations (e.g., quaternions plus vectors, homogeneous transforms) from the point of view of robot kinematic transformations.

2.      Survey of motion planning algorithms:  scientific basis, methodology, algorithms, and implementations.

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Maple code



Robotics Links


2.      Service Industry

3.      Manufacturing

4.      Research Labs

5.      Medical Robotics

6.      Humanoid Robots

7.      Other useful robotics links

Under construction.....  Please send me links that you'd like to see here.

Other Useful Links

1.      Penn Online Directory

2.     Penn Libraries Homepage

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