Scale-invariant tracking improves shape matching across different robots
Scale-Invariant Manipulability Shape Tracking Across Heterogeneous Manipulators
Robotics
Summary
When copying how one robot moves or exerts force to another robot with a different size or shape, it can be tricky to match the exact scale of movements. The authors found that it’s often enough to match the shape and orientation rather than the exact size. They developed a method that ignores scale differences and focuses only on matching shape, making transfers between very different robots more accurate and easier. Tests showed their technique keeps shape errors very low without extra tuning, improving how human movement is copied by robots of various types.
What this means in practice
- •For industrial robot programmers: Enable robots with different hardware to more accurately copy each other’s force and motion behaviors without manual scaling adjustments.
- •For robotic prosthesis developers: Improve how artificial limbs mimic human arm movements by focusing on shape consistency rather than exact size matching across users.
Authors
Geunwoo Kwon, Dong-gyu Lee, Kai Li, Soonwoong Hwang, Wansoo Kim
Abstract
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.