MAE 493/593:
Mathematical Methods in Robotics Fall 2005 (The course was formerly known as MAE405/505:
Robotics) [ University
at Buffalo]  [ College of
Engineering ]  [ MAE Department
]

MAE 493/593 Mathematical Methods in Robotics is intended to be a mathematical introduction to modeling, analysis and control of robotic systems. The first part of the course deals with the theoretical frameworks for modeling, analysis (kinematics and dynamics) and control of generic robotic mechanical systems, rooted in rich traditions of mechanics and geometry. The rest of the course will examine many of these issues in the context of serialchain and parallelchain manipulators, wheeled mobile robots (and hybrid combinations of these systems). A preliminary outline of topics that will be covered is shown below:
No. 

Topics 

Introduction 



Robotics and automation. 

Mathematical Preliminaries 



Rigid Body Motions, Homogeneous coordinates, lines, Plucker coordinates 


Transformation of points, displacements, rotation matrices, spherical displacements 


Composition of transformations and displacements, relative displacements, representations for finite rotations, Euler angles, Chasles Theorem 


Infinitesimal screw displacements, twist and wrenches, transformation of lines 


Principle of Virtual Work 


Nonholonomic constraints 


Lagrange’s equations of motion, application to robot dynamics 

CASE STUDY: Planar Serial Chain and Parallel chain Manipulators 



Kinematic modeling of single degree of freedom axial joints 


DH parameters, Example of the PUMA robot 


Workspace Analysis 


Direct and Inverse kinematics of planar manipulators. 


Manipulator Jacobians. Singularities in manipulator control 


Principle of Virtual Work: Static analysis of robot manipulators 


Dynamics and control of robot manipulators. 

CASE STUDY: Mobile Robots 



Modeling of NH Wheeled Mobile Robots 


Kinematics and Dynamics of NH Wheeled Mobile Robots 


Simulation and control of NH systems 

ADDITIONAL TOPICS: 



Redundancy and Redundancy resolution methods 


High Level motion planning 


Advanced control techniques 


Differential Geometry and Lie Groupbased approaches to robot analysis 
See tentative schedule for a detailed list of topics covered.
This course is open to all mechanical engineering graduate students. If you are not a graduate student in mechanical engineering or if you are an undergraduate student, you must talk to me before registering for the course.
1. Students
are expected to have studied kinematics and kinetics in a sophomore level
course and must be familiar with
2. We will assume that everybody is familiar with vector analysis (vectors & matrix manipulation) and linear algebra (matrix solution of linear systems), and has had a basic course in ordinary differential equations.
3. Finally, a basic degree of computer literacy is absolutely essential. We will make extensive use of MATLAB and MAPLE (or Mathematica) to solve examples.
[1] Sciavicco,
L., and Siciliano, B., Modelling
and Control of Robot Manipulators, 2nd Ed.,
SpringerVerlag Advanced Textbooks in Control and Signal Processing
Series,
These other textbooks are intended to
serve as references:
[1] Asada, H. and Slotine,
J.J. E., Robot Analysis and Control, J. Wiley and Sons, 1986.
[2] Craig, J.,
Introduction to Robotics: Mechanics and Control, AddisonWesley, Reading, MA,
1986.
[3] Canudas de Wit, Siciliano and Bastin, Theory of
Robot Control, SpringerVerlag London Limited, 1996.
[4] Murray, R., Li,
Z. and Sastry, S. A mathematical
introduction to robotic manipulation. CRC Press, 1994.
[5] Spong, M. W. and Vidyasagar, M.
Robot dynamics and control. J. Wiley, 1989.
[6] Tsai, L.W,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley &
Sons, 1999.
Reading assignments, problem sets, laboratory assignments and projects will be announced in class or via email, and be available through the web (see Lectures, labs, and homeworks).
All homeworks and projects will be done by students in groups of two. There will be approximately one homework assignment every 12 weeks. Problem sets will be due one week after they are assigned. Only selected problems from each set will be graded. No credit will be given for late assignments (demonstrations or reports). Under special circumstances, exceptions may be made, but only if prior arrangements are made with me at least 3 days in advance of the due date.
At the current time, only one midterm exam (worth 20% of the grade) is planned. A survey paper/software project (worth 20% of the grade) is also planned – however I reserve the right to substitute it with a second midterm based on the progress during the semester.
The preliminary grading scheme breakdown is as follows:
Homeworks 
20% 
Midterm 
20% 
Survey paper/Software Project 
20% 
Final Examination 
40% 