Manipulating deformable linear objects (DLOs) to achieve desired shapes in constrained environments with obstacles is a meaningful but challenging task. Global planning is necessary for such a highly-constrained task; however, accurate models of DLOs required by planners are difficult to obtain owing to their deformable nature, and the inevitable modeling errors significantly affect the planning results, probably resulting in task failure if the robot simply executes the planned path in an open-loop manner. In this paper, we propose a coarse-to-fine framework to combine global planning and local control for dual-arm manipulation of DLOs, capable of precisely achieving desired configurations and avoiding potential collisions between the DLO, robot, and obstacles. Specifically, the global planner refers to a simple yet effective DLO energy model and computes a coarse path to find a feasible solution efficiently; then the local controller follows that path as guidance and further shapes it with closed-loop feedback to compensate for the planning errors and improve the task accuracy. Both simulations and real-world experiments demonstrate that our framework can robustly achieve desired DLO configurations in constrained environments with imprecise DLO models, which may not be reliably achieved by only planning or control.

翻译：在存在障碍物的受限环境中操纵可变形线性物体（DLO）以实现期望形状，是一项有意义但极具挑战性的任务。全局规划对于这种高度受限的任务是必要的；然而，由于DLO的可变形特性，规划器所需的精确模型难以获取，且不可避免的建模误差会显著影响规划结果，若机器人仅以开环方式执行规划路径，可能导致任务失败。本文提出了一种从粗到精的框架，将全局规划与局部控制相结合用于DLO的双臂操纵，能够精确实现期望构型，并避免DLO、机器人与障碍物之间的潜在碰撞。具体而言，全局规划器采用一种简单而有效的DLO能量模型，计算粗略路径以高效寻找可行解；随后局部控制器以此路径为指导，通过闭环反馈进一步修正形状，以补偿规划误差并提高任务精度。仿真与真实实验均表明，在DLO模型不精确的受限环境中，该框架能稳健地实现期望DLO构型，而仅靠单一规划或控制方法可能无法可靠达成此目标。