Scalable Screw-Theoretic Synthesis for PDE-Based Dynamic Modeling of Multibody Flexible Manipulators

TL;DR

This paper introduces a scalable screw-theoretic framework for PDE-based dynamic modeling of flexible multibody robotic manipulators, enabling detailed local and global dynamic analysis.

Contribution

It develops a systematic, scalable method to construct PDE models for flexible links in multibody systems, incorporating holonomic constraints and elastic deformations.

Findings

Framework explicitly recovers all dynamic states.

Models formulated as semi-explicit index-1 differential-algebraic systems.

Established well-posedness of the PDE-based dynamic models.

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.