🤖 AI Summary
This study addresses the challenge of high-fidelity, scalable dynamics modeling for serial robots with an arbitrary number of flexible links in three-dimensional space. Building upon screw theory, the authors formulate a partial differential equation model that employs three classes of dual screws to characterize both rigid-body motion and elastic deformation of the links. By rigorously coupling joints through variational principles and constraint forces, they construct an infinitely extensible multibody system. The work presents the first scalable screw-theoretic framework for multibody dynamics synthesis, unifying local and global dynamics, explicitly recovering all dynamic states, and yielding a semi-explicit index-1 differential-algebraic system. The approach fully reconstructs the distributed deformation field and rigid-body motion of flexible arms, establishes well-posedness of the system, and provides a mathematically rigorous yet computationally tractable foundation for modeling high-dimensional flexible robotic systems.
📝 Abstract
This paper presents a novel and scalable screw-theoretic multibody synthesis framework for PDE-based dynamic modeling of serial robotic manipulators with an arbitrary number of flexible links in three-dimensional space. The proposed approach systematically constructs screw-theoretic PDE models for individual flexible links and rigorously enforces holonomic joint constraints through interaction forces. The dynamics of each link are formulated using a set of dual screws expressed in body-fixed coordinates: one describing the motion of the body-fixed frame relative to the inertial frame, a second relating the body-fixed frame to the undeformed configuration, and a third capturing elastic deformations. By expressing the system energy and applying variational principles, the governing dynamics of each link had been previously derived in a unified manner. Synthesizing the individual link models yields an infinitely scalable multibody representation capable of capturing both local (subsystem-level) and global (system-level) dynamics. The framework explicitly recovers all dynamic states, including the motion of each body-fixed frame and the distributed deformation fields of the flexible links. For computational tractability and mathematical rigor, the resulting governing equations are formulated as a semi-explicit index-1 differential-algebraic system. Furthermore, by applying separation of variables, the PDE model is recast as an abstract Cauchy problem, and well-posedness of the resulting system is established.