发表机构
Hanyang University; Hanyang University ERICA（汉阳大学; 汉阳大学ERICA校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种尺度不变的可操作性形状跟踪方法，将仅相差正标量的矩阵视为等价，并集成到关节速度二次规划中，在异构机器人转移中实现高精度形状匹配，显著降低位置误差。
AI 中文摘要
当在不同尺寸和运动学结构的系统之间转移可操作性时，如果目标是复现方向性和半轴长度比，匹配绝对椭球尺度可能是不必要的。然而，全矩阵跟踪会同时惩罚形状和绝对尺度差异，即使仅需要形状匹配。因此，我们提出了一种尺度不变的可操作性形状跟踪方法，该方法将仅相差一个正标量因子的矩阵视为等价，并使用其单位行列式代表。我们推导了单位行列式形状代表的微分，以及在仿射不变黎曼度量（AIRM）下切线跟踪残差的正交坐标表示。由此产生的尺度不变目标与位置和末端执行器方向任务集成在一个受约束的关节速度二次规划中。使用四个异构机器人的仿真评估了机器人到机器人和人类到机器人的转移。在三个从动机器人上，所提出的方法在无需尺度调整的情况下实现了端点形状距离为9.30×10^-5。在运动过程中调整了机器人特定目标尺度后，Full方法在KR500和UR20上保留了0.19-0.31的端点轴比误差。对于具有并发任务的人类到达动作，所提出的方法在所有四个机器人上产生了沿X方向拉长的双力形状，类似于人类目标，端点位置误差为参考臂长的2.4-5.6%，而Full方法跟踪原始人类椭球时误差高达75%。
英文摘要
When transferring manipulability across systems with different sizes and kinematic structures, matching absolute ellipsoid scale may be unnecessary when the goal is to reproduce orientation and semi-axis length ratios. Full-matrix tracking, however, penalizes both shape and absolute-scale differences, even when only shape matching is required. We therefore propose a scale-invariant manipulability shape-tracking method that treats matrices differing only by a positive scalar factor as equivalent and uses their unit-determinant representatives. We derive the differential of the unit-determinant shape representative and an orthonormal coordinate representation of the tangent tracking residual under the affine-invariant Riemannian metric (AIRM). The resulting scale-invariant objective is integrated with position and end-effector direction tasks in a constrained joint-velocity quadratic program. Simulations with four heterogeneous robots evaluate robot-to-robot and human-to-robot transfer. On three followers, the proposed method achieves endpoint shape distances of 9.30 x 10^-5 without scale tuning. With robot-specific target scales tuned during motion, the Full method retains endpoint axis-ratio errors of 0.19-0.31 on KR500 and UR20. For human reaching with concurrent tasks, the proposed method yields dual force shapes elongated along X like the human target on all four robots, with endpoint position errors of 2.4-5.6% of reference arm length versus up to 75% for the Full method tracking the original human ellipsoid.
Comments8 pages, 5 figures, 3 tables
