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).

中文翻译：

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使用接触的弹性杆的运动规划


本文的贡献是提出了一种利用与环境接触来解决可伸展弹性杆的运动规划问题的方法。我们首先展示如何通过将准静态和动态杆模型与基于采样的方法相结合来完成可变形杆的运动规划。直接在静态平衡和无接触配置的子流形中采样可以利用动态模型来改进状态空间的探索。然后，借助接触信息（点、力、方向和接触数量），可以改进快速探索随机树（RRT）方法的探索。我们提出了一种新的 RRT-SLIDE 算法，该算法基于人类推理的一些原理，通过滑动接触模式来指导路线图扩展。我们证明我们的方法在概率上是完整的。我们还通过多个模拟实验证明了考虑复杂场景下接触的必要性。除了其性能之外，我们的算法不需要针对新场景进行进一步的调整阶段。从业者须知——本文是在工业项目 Flecto 下完成的。它的目的是解决杆的组装/拆卸任务，同时满足数字模型中其材料的弹性参数。对于工业应用，解决时间是一个关键点。一方面，概率运动规划方法需要有效地构建有效杆配置的路线图。另一方面，精确的杆建模意味着使用基于有限元法 (FEM) 的模拟器。然而，路线图的尺寸非常大，导致对模拟器的大量调用，这与 FEM 模拟的高计算成本相冲突。 为了克服这个问题，一种解决方案是减少模拟器调用的数量。这可以通过使用有效的参数化对自由空间进行采样以及将模拟器的使用限制为自由空间或接触空间中的路线图扩展来实现。我们引入基于模拟器返回的联系信息的启发式方法，以显着减少计算时间。我们算法的主要优点之一是它不需要针对每个场景进行任何调整阶段。尽管我们没有解决更一般的夹具操纵规划问题，但这种方法可以用作计算夹具运动之前的第一步。在我们的项目框架中，我们没有考虑意味着解开杆结的拆卸操作。因此，我们的方法中不考虑摩擦（摩擦模拟对于处理结是必要的）。