This paper presents a formulation of Lagrangian dynamics of constrained mechanical systems in terms of reduced quasi-velocities and quasi-forces that can be used for simulation, analysis, and control purposes. In this formulation, a Cholesky decomposition of the mass matrix in conjunction with adequate orthogonal matrices is used to define reduced-quasi-velocities, input quasi-forces, and constraint quasi-forces which possess natural metric. The new state and input variables always have homogeneous units despite the generalized coordinates may involve in both translational and rotational components and the constraint wrench may involve in both force and moment components. Therefore, this formulation is inherently invariant with respect to changes in dimensional units without requiring weighting matrices. Moreover, in this formulation the equations of motion are completely decoupled from those of the constrained force. This allows the possibility of a simple force control action that is totally independent of the motion control action facilitating a hybrid force/motion control. The properties of the new dynamics formulation are investigated and subsequently force/motion tracking control and regulation of constrained multibody systems based on quasi-velocities and quasi-forces are presented.

本文根据可用于模拟、分析和控制目的的降低的准速度和准力，提出了受约束机械系统的拉格朗日动力学公式。在这个公式中，质量矩阵的 Cholesky 分解结合适当的正交矩阵用于定义具有自然度量的约简准速度、输入准力和约束准力。尽管广义坐标可能涉及平移和旋转分量，并且约束扳手可能涉及力和力矩分量，但新的状态和输入变量始终具有齐次单位。因此，该公式对于维度单位的变化是固有不变的，而不需要加权矩阵。而且，在这个公式中，运动方程与受约束力的方程完全分离。这允许完全独立于运动控制动作的简单力控制动作的可能性，促进混合力/运动控制。研究了新动力学公式的性质，随后介绍了基于准速度和准力的受约束多体系统的力/运动跟踪控制和调节。