A seminar course in topological robotics.

The aim of this course is to study topological aspects of some problems that arise in robotics. We plan to cover following three broad topics:
  1. Moduli spaces of spatial and planar polygons.
  2. Navigational complexity.
  3. Moduli space of distinct points on the projective line.
During this semester long seminar we plan to cover some of the important results in this area that are accessible to graduate students. For example, space of spatial polygons is generically a symplectic manifold. Moreover, its real part is planar polygon space, modulo full isometries. The (co)homology calculations. CW decomposition of the space of planar polygons. Connections with the moduli space of points on P^1.
We will meet twice a week and discuss some of the main results and problems. Details of each meeting will be posted below.


  1. Farber M. Invitation to topological robotics. European Mathematical Society; 2008.
  2. Hausmann JC, Knutson A. Polygon spaces and grassmannians. Enseignement mathématique. 1997;43(1/2):173-98.
  3. Hausmann JC, Knutson A. The cohomology ring of polygon spaces. Annales de l'institut Fourier 1998 Jan 1 (Vol. 48, No. 1, p. 281).
  4. Panina G. Moduli space of planar polygonal linkage: a combinatorial description. arXiv:1209.3241.
  5. Panina G, Zhukova A. Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle. arXiv:1504.05139.
  6. Devadoss S. Combinatorial equivalence of real moduli spaces. Notices of the AMS. 2004 Jun;51:620-8.
  7. Yoshida M. The democratic compactification of configuration spaces of point sets on the real projective line. Kyushu Journal of Mathematics. 1996;50(2):493-512.

Weekly details

Week Material Speaker
13/08/2018 Background and motivation. Basic definitions and complete analysis of moduli spaces of planar 4-gons. Priyavrat
20/8/2018 The smooth structure of moduli spaces. Some explicit homeomorphisms. Priyavrat
27/08/2018 Polygons and Grassmannians - I Sambit
03/09/2018 Polygons and Grassmannians - II Sambit
10/09/2018 Moduli space of points on the real projective line - I Navnath
17/09/2018 Moduli space of points on the real projective line - II Navnath
24/09/2018 Mid semester exam break
01/10/2018 Homology of planar polygon spaces Deepraj
08/10/2018 A cell structure for planar polygon spaces Naagesh
15/10/2018 Introduction to discrte Morse theory Anurag
22/10/2018 Discrte Morse theory for planar polygon spaces Anurag
29/10/2018 Symplectic geometry and polygon spaces Sambit 05/11/2018 No meeting 12/11/2018 Symplectic geometry and polygon spaces Sambit 19/11/2018 Topological complexity Priyavrat