Vex4冗余驱动并联机构的动力学建模、力优化及力位混合控制

并联机构引入冗余驱动可消除机构奇异位型，提高刚度和负载能力。但冗余驱动造成驱动力求解不唯一，可能引起内力对抗，造成能量损耗甚至机构损坏。因此冗余驱动并联机构的动力学建模与控制必须考虑驱动力分配和优化。应用自然正交补(NOC)法对Vex4三自由度冗余驱动并联机构进行动力学建模，采用右Moore-Penrose广义逆矩阵通过QR分解转置系数矩阵得到最小驱动力优化解。为平衡驱动力并跟踪轨迹，在力位混合即非冗余支链位置控制、冗余支链力(矩)控制基础上，采用动力学差分提出一种位控、力控支链驱动力同步优化方法，设计同步优化力位混合控制器实现轨迹跟踪控制。搭建Vex4冗余驱动并联机构样机开展轨迹跟踪试验，验证了所提优化和控制方法的有效性。

Dynamics Modeling,Force Optimization and Force/Position Hybrid Control for a Vex4 Redundantly Actuated Parallel Robot

Introducing actuation redundancy in parallel kinematic machines can avoid singularities, improve stiffness and load. Redundant actuation, however, poses challenges to dynamics modeling and controller designing regarding internal force distribution and optimization. In order to solve the above problems, taking a Vex4 3-DOF parallel robot as an example, dynamics model is established based on the natural orthogonal complement method. Then, by resorting to the right Moore-Penrose generalized inverse, the solution of the minimum-actuating-force is obtained based on QR decomposition of coefficient matrix. To balance actuator-force and track trajectory, a synchronous optimization method is first proposed and then integrated into a force-position hybrid controller with non-redundant branch controlled by position law and redundant branch by force law. Finally, a prototype of Vex4 is built to test and verify the proposed modeling and controller designing approach.