Explicit equations of motion for U-K equations and its associated deformations in constrained multibody systems

Wanxin Man; Xinhong Li; Zhibin Zhang; Gangxuan Hu; Guohui Zhang

doi:10.1117/12.2678972

25 May 2023 Explicit equations of motion for U-K equations and its associated deformations in constrained multibody systems

Wanxin Man, Xinhong Li, Zhibin Zhang, Gangxuan Hu, Guohui Zhang

Author Affiliations +

Proceedings Volume 12712, International Conference on Cloud Computing, Performance Computing, and Deep Learning (CCPCDL 2023); 1271202 (2023) https://doi.org/10.1117/12.2678972
Event: International Conference on Cloud Computing, Performance Computing, and Deep Learning (CCPCDL 2023), 2023, Huzhou, China

Abstract

The U-K approach provides a new, general solution for the explicit motion equations of complex constrained mechanics systems. These equations are suitable for constraint forms such as holonomic or nonholonomic, ideal or non-ideal, scleronomic or rheonomic. In the resolution process, the constraint forces and accelerations can be achieved without introducing Lagrange multipliers. At present, this approach has been applied to the trajectory tracking of robotic arms, structural dynamics control, and the motion of swarm robotic systems. The process of resolving the U-K equations involves two key problems. (1) The introduction of generalized inverse matrix brings great difficulties to the actual solution. (2) The mass matrix in the representation is positive definite, but the mass matrix described by the redundant minimum number of generalized coordinates may be singular, which causes the equations can not be used. For the U-K method and the above problems, we firstly uses the Lagrange method to get the dynamic equation of the constrained multibody system. The constraint equations of Lagrange multipliers and the method of additional constraint forces are imposed to express the transformation process of the unconstrained system to constrained system. Then, three different methods are respectively introduced to replace the generalized inverse representation in the original U-K equations. In the situation of singular mass matrix, the Udwadia-Phohomsiri form of generalized inverse representation and the explicit dynamics represented by null space form are introduced. Then, by adding auxiliary systems, we get two representations that respond to both the U-K equations and the Udwadia-Phohomsiri form.

Citation Download Citation

Wanxin Man, Xinhong Li, Zhibin Zhang, Gangxuan Hu, and Guohui Zhang "Explicit equations of motion for U-K equations and its associated deformations in constrained multibody systems", Proc. SPIE 12712, International Conference on Cloud Computing, Performance Computing, and Deep Learning (CCPCDL 2023), 1271202 (25 May 2023); https://doi.org/10.1117/12.2678972

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KEYWORDS

Matrices

Deformation

Mechanics

Control systems

Complex systems

Modeling

Dynamical systems

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