Optimization and Systems Theory Seminar
Friday, May 18, 2001, 11.00-12.00, Room 3721, Lindstedtsv. 25

Claudio Altafini
Optimization and Systems Theory
E-mail: claudio.altafini@math.kth.se

Modeling and control of redundant robotic chains on Riemannian manifolds

This talk will overview the first two papers of my doctoral thesis "Geometric control methods for nonlinear systems and robotic applications".

For redundant robotic chains composed of simple one-degree of freedom joints or links, the forward kinematic map from joint space to the workspace of the end-effector is interpreted geometrically in terms of Riemannian submersions. Several properties of redundant robots then admit clear geometric characterizations, the most remarkable being that the Moore-Penrose pseudoinverse normally used in Robotics coincides with the horizontal lift of the Riemannian submersion. The end-effector of the robot leaves on the Special Euclidean group in 3 dimension. On SE(3), the dynamical equations of the robotic chain look like a set of controlled Euler-Lagrange equations, or Euler-Poincare' equations after reduction by group symmetry. Variational methods are used to generate a geometric spline for such equations and the extra complications of the corresponding reduction, due to the semidirect product structure of SE(3), are analyzed. The loop is closed in workspace using a PD controller which is then pulled back to joint space by means of the horizontal lift, all respecting the different geometric structures of the two underlying model spaces.

Calendar of seminars
Last update: May 9, 2001 by Anders Forsgren, anders.forsgren@math.kth.se.