Abstract: My talk in the language of robotics:
“I will show how to establish an appropriate configuration space for
robotic manipulation of canonical ‘deformable linear objects’ like a
Kirchhoff elastic rod (e.g., a flexible wire). This result leads to
simple algorithms for manipulation and perception that are easy to
implement and that work well in practice.”
My talk in the language of mathematics:
“Any framed curve traced by a Kirchhoff elastic rod in static
equilibrium can be described as a local solution to an optimal control
problem on the special Euclidean group SE(3). By application of
Lie-Poisson reduction, I will show that the set of all normal extremals
for this problem is a smooth manifold of finite dimension that admits a
single global chart. I will also show that the subset of all local
optima is open and is locally diffeomorphic to the space of boundary
conditions.”