Motion Planning for an Elastic Rod Using Contacts

The contribution of this article is to propose an approach that solves the motion planning problem for an extensible elastic rod using contacts with the environment. We first show how motion planning for a deformable rod can be done by coupling both quasi-static and dynamic rod models with sampling-based methods. Sampling directly in the submanifold of static equilibrium and contact-free configurations allows to take advantage of the dynamic model to improve the exploration of the state space. Then, thanks to the contact information (point, forces, direction, and the number of contacts), the exploration of the rapidly exploring random tree (RRT) approach can be improved. We present a new RRT-SLIDE algorithm, which guides the roadmap extension with a sliding contact mode based on some principles of human reasoning. We show that our approach is probabilistically complete. We also demonstrate the necessity of considering contacts on complex scenarios with several simulation experiments. Besides its performances, our algorithm does not require further tuning phase for a new scenario. Note to Practitioners-This article was done under the industrial project Flecto. It aims at solving the assembly/disassembly task for a rod while satisfying the elasticity parameters of its material in a digital mockup. For industrial applications, the resolution time is a critical point. On the one hand, probabilistic motion planning methods require to efficiently build a roadmap of valid rod configurations. On the other hand, accurate rod modeling implies the use of a simulator based on the finite-element method (FEM). Nevertheless, the very large size of the roadmap that leads to a high number of calls to the simulator is conflicting with the high computational cost of FEM simulation. To overcome this problem, one solution is to reduce the number of simulator calls. This can be achieved by sampling the free space with an efficient parameterization and by limiting the use of the simulator to roadmap extension in the free space or in the contact space. We introduce heuristics based on contact information returned by the simulator to significantly reduce the computational time. One of the main advantages of our algorithm is that it does not require any tuning phase for each scenario. Although we do not solve the more general gripper manipulation planning problem, this approach could be used as a first step before computing the grippers' motion. In the framework of our project, we did not consider disassembling operations implying undoing rod knots. Consequently, we do not consider friction in our approach (friction simulation is necessary to handle knots).