The material covered in class is scattered in several books and recent papers. As we proceed you'll find here as well as in the course's page more references and links to relevant publications.

 For basic robotics, see

J.J. Craig
Introduction to Robotics
3nd Edition, Pearson Prentice Hall, 2005.

 For robot motion planning, see

A classical book:
J.-C. Latombe,
Robot Motion Planning
Kluwer Academic Publishers, 1991.

newer books:

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 The MIT Press, 2005.

S.M. LaValle,
Planning Algorithms
Cambridge University Press, 2006

 Basic techniques of computational geometry can be found in the following book:

M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications
2nd Edition, Springer, 2000.

 Survey papers in:

CRC Handbook of Discrete and Computational Geometry
J.E. Goodman and J. O'Rourke (eds.),
2nd Edition, Chapman and Hall/CRC, 2004,
(1) Algorithmic Motion Planning (Chapter 47), M. Sharir
(2) Robotics (Chapter 48), D. Halperin, L.E. Kavraki, and J.-C. Latombe
(3) Collision and Proximity Queries (Chapter 35), M.C. Lin, and D. Manocha
(4) Shortest Paths and Networks (Chapter 27), J.S.B. Mitchell

 Davenport-Schinzel sequences, single face results

M. Sharir and P.K. Agarwal
Davenport-Schinzel Sequences and Their Geometric Applications
Cambridge University Press, New York, 1995