multibody dynamics modeling

This work addresses the challenge of simulating rigid multibody dynamics involving multiple closed kinematic loops, hard unilateral contacts, Coulomb friction, and restitutional impacts. We propose a unified nonlinear complementarity problem (NCP) modeling and solution framework based on maximal coordinates. Methodologically, the approach integrates forward-dynamics decomposition, implicit time integration, and exact frictional contact modeling, while systematically benchmarking against multiple state-of-the-art physics engine solvers. Our key contribution is the first standardized benchmarking framework specifically designed for closed-loop multibody systems, enabling both qualitative and quantitative evaluation. Extensive experiments across diverse, highly coupled closed-loop scenarios reveal, for the first time, the absolute and relative performance boundaries—across accuracy, stability, and convergence—of prevailing solvers. These empirical findings provide critical evidence for the accuracy–stability trade-off in complex contact-rich simulations.

This work addresses the critical influence of configuration space selection on constraint satisfaction accuracy in numerical simulations of fully constrained rigid body dynamics. From a geometric perspective, the study proposes a differential-algebraic equation (DAE) formulation and geometric integration scheme based on the Lie group SE(3). It demonstrates that when kinematic constraints correspond to subgroups of SE(3), these constraints can be preserved exactly over time. The approach elucidates the intrinsic relationship between SE(3) subgroup structures and lower-pair joints, establishing that employing SE(3) as the configuration space enables strict enforcement of constraints. This result provides both a theoretical foundation and numerical guarantees for high-fidelity simulation of rigid multibody systems.

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.

This work addresses the challenge of preserving energy structure and ensuring long-term stability in multibody dynamics simulations by proposing a port-Hamiltonian framework equivalent to the classical ideal joint model. Built upon Lagrange’s equations, the approach employs singularity-free directional vectors to represent rigid body rotations, incorporates variational principles for index reduction, and solves the resulting index-2 differential-algebraic equations using a structure-preserving midpoint integrator. The resulting model rigorously satisfies both position- and velocity-level constraints while exactly conserving total energy and angular momentum. This exact preservation significantly enhances the accuracy and stability of long-duration simulations and provides a solid theoretical foundation and numerical advantage for energy-based control design.

This work addresses the challenge of precise end-effector localization of slender, deformable objects—such as cables—in high-speed dynamic scenarios, transcending conventional quasi-static and massless assumptions. It pioneers the integration of soft robotics dynamic modeling principles into linear object manipulation. We propose a fully model-driven control framework based on functional strain parameterization, enabling analytically verifiable Lyapunov-based closed-loop stability and steady-state convergence of shape regulation. The method synergistically combines nonlinear feedback shaping with real-time 7-DoF robotic arm closed-loop control, achieving high-accuracy in-plane end-position-and-orientation regulation across six distinct cable types. Experiments demonstrate substantial improvements in both dynamic responsiveness and steady-state accuracy for deformable object manipulation under non-quasi-static conditions. To our knowledge, this is the first theoretically provable and engineering-deployable model-driven solution for complex compliant object manipulation in embodied intelligence systems.

This study addresses the challenge posed by time-varying configurations in sliding beam systems, where conventional fixed modal coordinates become invalid and online-updated modal bases often suffer from semantic drift. To overcome this, the authors propose a global reduced-order basis method tailored for sliding beams: a unified low-dimensional basis is extracted via Proper Orthogonal Decomposition (POD) from a snapshot matrix of modal responses and embedded within a constrained multibody dynamics framework to accommodate continuous sliding motion. This approach preserves essential dynamic characteristics while eliminating inconsistencies in modal coordinate interpretation. Numerical simulations under highly flexible beam conditions, time-varying loads, and active sliding demonstrate approximately 90% reduction in computational time, with root-mean-square displacement errors maintained below 2%.

This study addresses the challenge of accurately modeling the dynamics of flexible two-degree-of-freedom robotic arms, where rigid-body assumptions fail to capture link flexibility and unmodeled residual dynamics. To overcome this limitation, the authors propose a semi-parametric hybrid dynamical modeling framework that augments rigid-body dynamics with a Gaussian Mixture Model (GMM) to learn residual terms, while employing a purely data-driven kinematic regression as a baseline. This approach synergistically integrates physical priors with data-driven mechanisms, transcending the constraints of conventional fully parametric models in flexible systems. Experimental results on an open-source dataset demonstrate that the data-driven component—combined with regularization and least-squares estimation—significantly enhances torque prediction accuracy, thereby validating the efficacy and superiority of the proposed hybrid model.

This study addresses the challenging problem of partial differential equation (PDE)-based control for spatially arbitrary-configured flexible multi-body robotic arms by proposing a modular, subsystem-based control framework. Leveraging screw theory within the se(3) Lie algebra, the approach unifies the modeling of rigid motion, elastic deformation, and internal forces, while introducing a strain-based PDE formulation to eliminate distributed elastic acceleration terms. An inverse kinematics solution compensating for deformation is integrated with task-space end-effector trajectory generation to design both nominal and adaptive controllers. Exploiting the frame invariance of power pairings on se(3) and Newton’s third law, the method achieves exact cancellation of inter-link interaction power, enabling the first proof of global exponential stability for flexible arms of arbitrary length. Theoretical analysis guarantees exponential convergence of twist and parameter estimation errors and bounded elastic deformation, with simulations confirming physical consistency and superior control performance.

This study addresses the ambiguity and inaccuracies in existing definitions of interaction forces and internal loads in redundantly actuated parallel mechanisms, which have led to erroneous force analyses and control deviations. To resolve this issue, the work rigorously clarifies these two concepts and proposes a unified dynamic modeling framework based on null-space torque decomposition and joint torque vector synthesis. The resulting formulation provides a clear and unambiguous analytical foundation specifically tailored for such mechanisms. Validation through representative case studies demonstrates that the proposed method effectively corrects erroneous results reported in the literature and significantly enhances force control accuracy in both balancing and manipulation tasks for redundantly actuated parallel mechanisms.