PC7 Model: Dynamics of Expanding and Contracting Soft Robots using Piece-wise Constant 7D Deformation Based on Similarity Transformation Group

Abstract:This paper proposes a novel soft robot model named piece-wise constant 7D deformation (PC7) model that can represent expanding and contracting deformation of, for example, artificial muscle actuator. In the proposed model, we newly define the 7D deformation vector based on SIM(3) - 3D similarity transformation group - whereas a 6D deformation vector was defined for Cosserat rod based on SE(3) - the special Euclid group - in the piece-wise constant strain (PCS) model proposed in the previous study. The additional dimension of the 7D deformation vector represents expanding and contracting deformation, which comes from the scaling parameter in SIM(3). Common mathematical properties between SE(3) and SIM(3) allow us to directly extend the kinematics and dynamics of the PCS model to those of the PC7 model. In particular, we derive the dynamical equation of the PC7 model based on Euler-Poincare equation in a mathematically precise manner. We validate the proposed model through dynamical simulations assuming a thin cylinder structure or McKibben-type artificial muscle actuator.

Robotics (cs.RO)

arXiv:2610.14586 [cs.RO]

(or arXiv:2610.14586v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2610.14586 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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