School of Engineering and Applied Sciences, SUNY at Buffalo

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 ]

Professor Venkat N. Krovi

Course Info

Course Organization

Course Description




SOAR Description


Schedule (including notes) 









(716) 645-2593, x2236


1012 Furnas Hall, North Campus

Office Hours:



Course Description

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 serial-chain and parallel-chain manipulators, wheeled mobile robots (and hybrid combinations of these systems). A preliminary outline of topics that will be covered is shown below:









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



Non-holonomic 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



D-H 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






Redundancy and Redundancy resolution methods



High Level motion planning



Advanced control techniques



Differential Geometry and Lie Group-based approaches to robot analysis


See tentative schedule for a detailed list of topics covered.

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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 Newton's laws and their application to particles in two and three dimensions.

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.

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Text & References:

The recommended (but not required) text is:

[1] Sciavicco, L., and Siciliano, B., Modelling and Control of Robot Manipulators, 2nd Ed.,
Springer-Verlag Advanced Textbooks in Control and Signal Processing Series, London, UK, 2000

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, Addison-Wesley, Reading, MA, 1986.

[3] Canudas de Wit, Siciliano and Bastin, Theory of Robot Control, Springer-Verlag 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.

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Reading assignments, problem sets, laboratory assignments and projects will be announced in class or via e-mail, 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 1-2 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 mid-term 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:






Survey paper/Software Project


Final Examination


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