Piecewise Constant Mean Curvature Assumption for Robotic Surfaces

Iwamoto, Noriyasu

doi:10.51094/jxiv.4576

##article.authors##

Iwamoto, Noriyasu Faculty of Textile Science and Technology, Shinshu University https://researchmap.jp/niwamo

DOI:

https://doi.org/10.51094/jxiv.4576

キーワード:

Flexible Robotics、 Soft Robots、 Kinematics、 Robotic Surfaces、 Piecewise Constant Curvature

抄録

We propose a piecewise constant mean curvature (PCMC) surface model for the kinematic representation of robotic surfaces. Inspired by the piecewise constant-curvature assumption for continuum manipulators, the proposed framework represents a deformable surface as an assembly of alternating constant-mean-curvature surface (CMCS) patches and minimal surface (MS) patches. The CMCS patches describe actuator-dominant regions with explicit analytic expressions, whereas the MS patches represent passively deformable membrane regions through boundary value problems. This decomposition provides a compact yet expressive surface representation with a low-dimensional parameter set.

Based on this model, we develop forward kinematics (FK) and inverse kinematics (IK) calculations and a surface-fitting method. For the CMCS patches, we use analytical surface representations, including a Kenmotsu-type formula that unifies cylinders, spheres, unduloids, and nodoids. This yields homogeneous-transformation-based FK and explicit Jacobian computation in a form analogous to that in conventional rigid-body manipulator kinematics. For the MS regions, shapes are efficiently reconstructed by solving a discrete Laplace equation on a triangular mesh. We further show that point-based IK can be solved for both active patches and passive MS regions, the latter through sparse-mesh approximation. Simulations demonstrate efficient whole-surface computation, successful control-point tracking, and applicability to deformable-surface fitting, indicating that the PCMC assumption offers a practical geometric foundation for robotic surface kinematics.

利益相反に関する開示

The author have no conflicts of interest.

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