Violation elimination of nominal models for manipulators constructed with Udwadia-Kalaba equation
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摘要:
采用Udwadia-Kalaba方程构建的操作臂轨迹跟踪控制器名义模型中，初始条件难以满足约束方程，数值求解过程产生误差累积造成的约束违约是亟待解决的问题。通过在数值求解过程所产生位置和速度项上添加修正项直接消除违约误差的方法，对该问题进行了研究。根据Udwadia-Kalaba建模思想，构建了期望轨迹下三杆操作臂的动力学名义模型并进行轨迹跟踪仿真。分别利用传统的Baumgarte约束稳定法与所提出误差直接消除法对仿真数值结果进行了修正。结果显示，所提误差直接消除法可更加快速直接地将约束违约控制在更小范围，更适用于操作臂动力学名义模型修正的使用。
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关键词:
- 机器人操作臂 /
- 动力学建模 /
- 违约消除 /
- 约束流形 /
- Udwadia-Kalaba方程
Abstract:In the nominal model of the manipulator trajectory tracking controller constructed by Udwadia-Kalaba equation, the initial conditions are difficult to satisfy the constraint equations, and the constraint violation is generated by the accumulation of errors in the process of numerical solution, which are all problems to be solved at present. Problems are solved by the method of eliminating violation errors directly. This method adds correction items to position and speed terms which are produced by the numerical solution process. The dynamic nominal model of the three-link manipulator is constructed, and the trajectory tracking simulation is carried out under the desired trajectory based on the Udwadia-Kalaba modeling idea. The simulation numerical results are corrected by using the traditional Baumgarte stability method and the proposed error direct elimination method. The results show that the direct elimination method can control the constraint violation in a smaller range more quickly, and is more suitable for the use of trajectory correction to manipulator dynamic nominal model.
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图 2 操作臂各关节角度随时间变化曲线
Figure 2. Curves of each manipulator joint's angle changing with time
图 3 操作臂各关节角速度随时间变化曲线
Figure 3. Curves of each manipulator joint's angular velocity changing with time
图 4 操作臂末端在Cartesian空间运动轨迹
Figure 4. Motion trajectories of end point of manipulator in Cartesian space
图 5 修正后工作空间操作臂末端轨迹
Figure 5. Corrected trajectories of end point of spatial manipulator
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