摘要
基于Udwadia和Kalaba方程的伺服约束控制理论可以较好地应用在机械系统的轨迹跟踪控制中。在伺服约束控制中,对约束系统动力学模型的数值积分过程会产生对低阶约束的违约,同时还存在初始值不相容引起的控制偏差甚至系统不稳定问题。利用系统广义质量矩阵的乔利斯基分解,将描述系统的广义虚位移向量经过变换,在约束流形上分解为约束方向与约束允许方向,从而分离出速率约束及坐标约束违约部分,在此基础上推导出修正公式。以二自由度机械臂为仿真对象,在伺服约束轨迹控制中的应用进行了仿真研究。结果表明,基于虚位移分解的方法可以对伺服控制中的约束违约进行抑制,同时也可以解决系统初始条件不相容引起的问题。
The servo constraint control theory based on Udwadia and Kalaba equations can be applied in the tracking control of mechanical systems. The numerical solutions under servo constraint control may violate the lowerorder constraint equations,together with the inconsistent initial conditions,which result in control error even unstable problem. In this paper, using the Cholesky decomposition of the generalized mass matrix and the coordinates transformation,the generalized virtual displacements is decomposed in constrained directions and admissible directions,thus the constraint violation of the generalized velocity and configuration are separated,and the modified equations are obtained. Finally,the simulation study of a mechanical manipulator with two degrees of freedom is made and the results show that the algorithm can eliminate the constraint violation and solve the problem caused by inconsistent initial conditions under servo constraint trajectory control.
出处
《机械科学与技术》
CSCD
北大核心
2014年第12期1811-1814,共4页
Mechanical Science and Technology for Aerospace Engineering
基金
国家自然科学基金项目(51205029)
中央高校基本科研业务费专项基金项目(CHD2011TD016)
教育部留学回国人员科研启动基金项目(20101174)资助
关键词
虚位移分解
约束违约
初始条件
伺服约束控制
算法
algorithms
computer simulation
constraint violation
control
decomposition of virtual displacement
degrees of freedom（mechanics）
initial value
initial value problems
Jacobian matrices
manipulators
mathematical operators
mathematical transformations
MATLAB
servo constraint control
trajectories
velocity
