Invariant Descriptors of Motion and Force Trajectories for Interpreting Object Manipulation Tasks in Contact

TL;DR

This paper develops invariant descriptors for force trajectories in contact tasks by leveraging motion-force duality, enabling robust task representation unaffected by sensor or frame calibration, with applications in object manipulation recognition.

Contribution

It introduces the first invariant descriptors for force trajectories, extending motion invariants to contact tasks using duality principles and optimal control methods.

Findings

Invariant descriptors are robust to sensor noise.

Descriptors enable calibration-independent task recognition.

Methods are validated on human demonstration tasks.

Abstract

Invariant descriptors of point and rigid-body motion trajectories have been proposed in the past as representative task models for motion recognition and generalization. Currently, no invariant descriptor exists for representing force trajectories, which appear in contact tasks. This paper introduces invariant descriptors for force trajectories by exploiting the duality between motion and force. Two types of invariant descriptors are presented depending on whether the trajectories consist of screw or vector coordinates. Methods and software are provided for robustly calculating the invariant descriptors from noisy measurements using optimal control. Using experimental human demonstrations of 3D contour following and peg-on-hole alignment tasks, invariant descriptors are shown to result in task representations that do not depend on the calibration of reference frames or sensor locations. The tuning process for the optimal control problems is shown to be fast and intuitive. Similar to motions in free space, the proposed invariant descriptors for motion and force trajectories may prove useful for the recognition and generalization of constrained motions, such as during object manipulation in contact.