基于Gromov-Hausdorff近似的多查询机器人操作臂任务排序
Multi-query Robotic Manipulator Task Sequencing with Gromov-Hausdorff Approximations
AI总结：
本文针对机器人任务排序问题，提出一种基于ε-Gromov-Hausdorff近似的多查询方法，通过子空间分解实现路径平滑拼接，在复杂仿真中实现规划速度提升3倍、轨迹加加速度降低5倍。
摘要：
机器人操作臂应用通常需要高效的在线运动规划。在完成多个任务时，任务执行顺序和目标构型的选择会对规划性能产生显著影响。这一问题被称为机器人任务排序问题（RTSP）。现有的通用RTSP算法在可用计算时间受限时，容易产生低质量解或完全失败。我们提出了一种新的多查询任务排序方法，旨在包含静态和非静态障碍物组合的半结构化环境中运行。我们的方法有意在任务空间通用性与规划效率之间进行权衡。给定一个用户定义的包含静态障碍物的任务空间，我们计算其子空间分解。核心思想是建立被称为ε-Gromov-Hausdorff近似的近似等距关系，以识别在任务空间和构型空间中彼此接近的点。重要的是，我们证明了这些子空间内路径长度的有界次优性保证。这些边界关系进一步表明，同一子空间内的路径可以被平滑拼接，我们展示了这对于确定高效的任务序列是有用的。我们在一个复杂的仿真环境中使用多种运动学构型评估了我们的方法，与基线相比，运动规划速度最高提升3倍，最大轨迹加加速度降低5倍。
英文摘要：
Robotic manipulator applications often require efficient online motion planning. When completing multiple tasks, sequence order and choice of goal configuration can have a drastic impact on planning performance. This is well known as the robot task sequencing problem (RTSP). Existing general-purpose RTSP algorithms are susceptible to producing poor-quality solutions or failing entirely when available computation time is restricted. We propose a new multi-query task sequencing method designed to operate in semi-structured environments with a combination of static and non-static obstacles. Our method intentionally trades off workspace generality for planning efficiency. Given a user-defined task space with static obstacles, we compute a subspace decomposition. The key idea is to establish approximate isometries known as $ε$-Gromov-Hausdorff approximations that identify points that are close to one another in both task and configuration space. Importantly, we prove bounded suboptimality guarantees on the lengths of paths within these subspaces. These bounding relations further imply that paths within the same subspace can be smoothly concatenated, which we show is useful for determining efficient task sequences. We evaluate our method with several kinematic configurations in a complex simulated environment, achieving up to 3x faster motion planning and 5x lower maximum trajectory jerk compared to baselines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
