Roy's Teaching Materials

The materials on this page are available for anyone to use for the purpose of self education. For any other purpose, you must seek Roy's permission first.

Materials for Courses Taught at IIT, May 2022

This year, like last year, the courses will be taught via Microsoft Teams. As usual, they are open to everyone. However, in order for you to participate, it will be necessary for you to contact Roy via his IIT email (roy.featherstone@iit.it) if you wish to attend because the links for the classes will not be made public. Do this at least two days before the start of the course. University of Genoa students wishing to earn credits for taking these courses should both register in the usual way via the University's website and send an email to Roy. Students at other universities who wish to earn credits must discuss the matter with their own course coordinator in order to obtain approval, but, of course, are welcome to attend anyway. Attendance certificates will be issued to those who need them.

Introduction to Spatial (6D) Vectors

Course Notes 2022: slides, notes, question and answer sheets.
Official Course Description 2022
Lesson Schedule
Aulaweb link for University of Genoa students.
If you have access to IEEE documents then you are recommended to get a copy of the Tutorial for Beginners part 1 and part 2.

Computational Robot Dynamics

Course Notes 2022: slides, notes, question and answer sheets.
Official Course Description 2022
Lesson Schedule
Aulaweb link for University of Genoa students.
You should also download the spatial arithmetic library Spatial_v2.

In both courses, you will be expected to solve problems during the classes, so remember to have pen/pencil and paper ready. In the second course, you will also be expected to write a few small Matlab (or GNU Octave) functions using the library Spatial_v2.

A Tutorial for Beginners

A Beginner's Guide to 6-D Vectors (Part 1) and A Beginner's Guide to 6-D Vectors (Part 2). This two-part tutorial (available via IEEE Xplore) leads the reader gently through the basic concepts of spatial vectors, contrasting them with 3-D vectors, and explains how to implement the recursive Newton-Euler, composite-rigid-body and articulated-body algorithms in Matlab code.

Some Books and Papers

Robot Dynamics Algorithms (1987). [DOI]. This is the original book on dynamics algorithms and spatial vectors. Although it is still worth reading, it has been superceded by the book below. The treatment of spatial vectors in this book is a little different from the modern treatment.
Rigid Body Dynamics Algorithms (2008). [DOI]. This is the new book on dynamics algorithms and spatial vectors. It is the main reference on these two topics.
Springer Handbook of Robotics (2008, 2016). Chapter 2 in the first edition [DOI] and Chapter 3 in the second edition [DOI] (they are almost identical) cover the basics of spatial vector algebra and recursive dynamics algorithms, as well as providing a bit of history and an extensive list of references.
Robot Dynamics: Equations and Algorithms (2000). This is a survey paper on robot dynamics. It contains a brief description of spatial vector algebra and the most important algorithms.
Plücker Basis Vectors (2006). This paper discusses Plücker coordinates, Plücker basis vectors and rigid-body acceleration using a mathematical tool called a basis mapping.

More Stuff on Spatial Vectors and Dynamics

A Short Course on Spatial Vector Algebra
This is an old introductory course (written in 2008) that takes approximately one or two days, depending on how much you already know. The materials are intended to be suitable for self study.
a one-hour seminar on spatial vectors which is even older than the short course, but gets to the point very quickly in order to fit into just one hour
a 2-body worked example comparing the solution of a simple rigid-body dynamics problem using 3D vectors with the solution of the same problem using spatial vectors:
- solution using 3D vectors (long and complicated)
- solution using spatial vectors (much shorter and easier)