Efficient motion planning for quasi-static elastic rods using geometry neighborhood approximation

We present a motion planning algorithm for a quasi-static Kirchhoff elastic rod in complex environments. As the set of quasi-static deformations defines a finite dimensional manifold that can be parameterized by a single chart, the configuration space formulation extends nicely to this deformation space. This parameterization is computationally expensive and our algorithm takes advantage of its linearization to perform fast collision checking in its neighborhood. In the context of physically realistic deformable rods, the efficiency of this approximation can be coupled with motion planning techniques to obtain significant performance improvements. We demonstrate the effectiveness of our approach on various toy and industrial scenarios.