Gauss optimization method for the dynamics of unilateral contact of rigid multibody systems

Abstract

The discontinuous dynamical problem of multi-point contact and collision in multi-body system has always been a hot and difficult issue in this field. Based on the Gauss’ principle of least constraint, a unified optimization model for multibody system dynamics with multi-point contact and collision is established. The paper presents the study of the numerical solution scheme, in which particle swarm optimization method is used to deal with the corresponding optimization model. The article also presents the comparison of the Gauss optimization method (GOM) and the hybrid linear complementarity method (i.e. combining differential algebraic equations (DAEs) and linear complementarity problems (LCP)), commonly used to solve the dynamic contact problem of multibody systems with bilateral constraints. The results illustrate that, the GOM has the same advantage of dynamical modelling with LCP and when the redundant constraint exists, the GOM always has a unique solution and so no additional processing is needed, whereas the corresponding DAE-LCP method may have singular cases with multiple solutions or no solutions. Using numerical examples, the GOM is verified to effectively solve the dynamics of multibody systems with redundant unilateral and bilateral constraints without additional redundancy processing. The GOM can also be applied to the optimal control of systems in the future and combined with the parameter optimization of systems to handle dynamic problems. The work given provides the dynamics and control of the complex system with a new train of thought and method. The paper establishes a unified optimization model and the corresponding numerical solution scheme for multibody system dynamics with multi-point contact and collision based on Gauss’ principle of least constraint. Comparisons between Gauss optimization method (GOM) and the hybrid linear complementarity method (HLCM) are carried out through theoretical analysis and numerical examples, which show that GOM has the same advantage of dynamical modelling as HLCM and when redundant constraints exist, GOM has unique solutions without additional processes, whereas HLCM may have singular cases with multiple or no solutions.