Controllability analysis of mechanical multibody dynamics control systems based on lie symmetry

To quantitatively characterize the dynamic controlled performance of mechanical multibody systems and design collaborative control strategies, this paper investigates the controllability of mechanical multibody dynamic control systems. Firstly, under the affine connection framework of Lagrange mechanical control systems, we establish the Euler-Poincaré equations of unconstrained mechanical multibody dynamics control systems by differential geometry method; Further, we transform the Euler-Poincaré equations into the classical state space form of nonlinear control systems by augmented vector method; Secondly, by introducing Lie group representation theory, the definition and the solution of generalized Lie symmetry for mechanical multibody dynamics control systems are given, and the necessary and sufficient conditions for state controllability (local controllability) are given by using Lie symmetry; Finally, an application example of dynamic control of a single degree of freedom manipulator with basic vibration is provided, it explains the effectiveness and correctness of the Lie symmetry method in this paper. The research has shown that using Lie symmetry to analyze the controllability problem of mechanical multibody dynamics control systems can be transformed into its low-dimensional quotient space analysis, and if the quotient space is controllable at a point, then the system can be controllable for all points on the orbit where that point at.