6-DoF Shape Servoing of Deformable Objects in Co-Rotated Space of Modal Graph

Shape control of deformable objects under both rotational and translational deformations is important for versatile robotic applications. However, deformation control with full 6-degree-of-freedom (DoF) manipulation is an open problem, since modeling and describing rotational deformations lead to significant challenges. To tackle the problem, this paper proposes a novel method by introducing a co-rotated space for the modal graph representation of objects with unknown physical and geometric models. In this space, we design new deformation features that can encode local rotations while preserving a compact and low-frequency shape representation. Moreover, these features can be mapped analytically to the robot manipulation, enabling the design of adaptive control laws with guaranteed stability for unmodeled objects. Experiments on complex volumetric objects demonstrate the effectiveness and advantage of our method with raw, noisy, and unregistered point clouds. The results highlight the importance of integrating co-rotated features to address rotational deformations.