An SE(3)-based formulation of the shape servoing problem

The art of controlling the shape of deformable
objects autonomously, a.k.a. shape servoing, remains a challenging task for robots today. While some current works devoted
attention to improving controllers, we propose to reconsider the
formulation of the problem itself, under the theory of Lie groups.
This results in a new representation of the state of the object
and leads to a new definition of the shape error. In return,
results obtained from simulations demonstrate that the approach
can achieve better performance for large deformations tasks. In
addition, mobile frame definitions reduce the non-linearity of the
problem. Importantly, this approach is not tied to the algorithm
developed here and can therefore be easily extended to other
types of controllers.