In this paper, we show that the free configuration space of a Kirchhoff elastic rod is path-connected. By free configuration space, we mean the set of all equilibrium configurations of the rod that are stable (i.e. locally minimize elastic potential energy) and do not experience self-intersections. We also provide semi-analytical expressions for paths in the free configuration space that connect any two stable equilibrium configurations that do not contain self-intersections. These results are applied to the problem of manipulation planning for deformable objects.

We consider the manipulation planning problem of an extensible elastic rod in collision-free or contact space. We assume the rod can be handled by grippers either at both or at only one of its extremities and during the manipulation, the grasped end may change. We show that the use of both quasi-static and dynamic models can be coupled efficiently with sampling-based methods. By sampling directly on the submanifold of static equilibrium and contact-free configurations, we can take advantage of the dynamic model to improve the exploration in the state space. We show the necessity of considering contacts for this type of problems with several simulation experiments on various scenarios.

In this paper, we address the problem of estimating the shape of a planar elastic rod (e.g., a thin flexible strip of metal) using images of the rod. This is done by treating configurations of the elastic rod as solutions of a geometric optimal control problem. The necessary conditions for optimality provide coordinates over which to perform inference, and the sufficient conditions provide the gradient of the shape of the rod with respect to these coordinates. This optimal control formulation allows for configurations of the rod to be represented as points in a finite-dimensional space without having to discretize the shape of the rod. We consider the estimation problem with and without fiducial markers attached to the rod. Results from both simulations and hardware experiments demonstrate the ability of our approach to track the shape of a deforming elastic rod.

We consider the problem of manipulating a planar elastic rod using robotic grippers which grasp the rod at multiple points. Building upon previous work that considers a rod held only at its ends, we show that manipulating a rod held by n + 1 grippers is equivalent to planning a path on a smooth 3n-dimensional manifold. Using multiple grippers can be advantageous when manipulating around obstacles. We establish upper and lower bounds on the number of grippers needed for an equilibrium shape of the rod to pass between obstacles in a desired way. Finally, we consider manipulation planning when both ends of the rod are held fixed, and only the grippers located along the interior of the rod can move.