Position and Orientation Control Scheme for End-effector of Redundant Manipulators Based on Data-driven Technology
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摘要: 模型未知的冗余机器人执行任务的过程中会产生较大的控制误差, 其末端执行器的位置与姿态也需要针对不同任务进行修正. 为解决该问题, 提出一种基于数据驱动的冗余机器人末端执行器位置与姿态控制方案. 该方案使用在线学习技术, 能够应用于模型未知的冗余机器人控制. 同时引入四元数表示法将控制机器人末端执行器姿态问题转化为基于四元数表示的控制方法. 随后, 设计一种神经动力学求解器对所提方案进行求解. 相关的理论分析、仿真及对比体现了所提方案的可行性、有效性与新颖性.Abstract: A redundant manipulator with unknown models produces a large control error during a task execution, and the position and orientation of its end-effector need to be corrected for different tasks. To solve this problem, a position and orientation control scheme for the end-effector of a redundant manipulator is proposed based on a data-driven technology. The proposed scheme utilizes an online learning technology, which is able to be applied to control a redundant manipulator with unknown models. By introducing the quaternion representation, the rotation matrix controlling the orientation of the end-effector of a redundant manipulator is transformed into a quaternion representation control method. In addition, a neural dynamics solver is designed to solve the proposed scheme. Theoretical analysis, simulations, and comparisons demonstrate the feasibility, validity, and novelty of the proposed scheme.
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图 1 采用所提方案(14)实现冗余机器人末端执行器位置跟踪与姿态保持的仿真结果
Fig. 1 Simulation results of the redundant manipulator using the proposed scheme (14) to achieve position tracking and orientation maintenance
图 2 采用所提方案(14)实现冗余机器人位置与姿态跟踪的仿真结果
Fig. 2 Simulation results of the redundant manipulator using the proposed scheme (14) to achieve position and orientation tracking
图 3 基于CoppeliaSim平台冗余机器人实现位置与姿态跟踪的对比结果
Fig. 3 Comparison results of the redundant manipulator achieving position and orientation tracking based on CoppeliaSim platform
表 1 所提冗余机器人控制方案的符号含义
Table 1 Definitions of variables of the proposed scheme for redundant manipulators
符号 含义 $ {{\boldsymbol{\theta}}} \in {\bf{R}}^a $ 机器人关节角向量 $ \dot{\boldsymbol{\theta}}\in {\bf{R}}^a $ 机器人关节角速度向量 $ \dot{\boldsymbol{\theta}}^{-}(\dot{\boldsymbol{\theta}}^{+}) $ 关节角速度的下界(上界) $ {\boldsymbol r}\in {\bf{R}}^b $ 末端执行器的位置向量 $ \boldsymbol{r}^{d}\in {\bf{R}}^b $ 末端执行器的期望位置向量 $ \dot{\boldsymbol r}\in {\bf{R}}^b $ 末端执行器的速度向量 $ \dot{\hat{\boldsymbol r}}\in {\bf{R}}^b $ 末端执行器的估计速度向量 $ f(\cdot): {\bf{R}}^a \rightarrow {\bf{R}}^b $ 机器人非线性前向运动学映射 $ J=\dfrac{\partial f({{\boldsymbol{\theta}}})}{\partial {{\boldsymbol{\theta}}}}\in {\bf{R}}^{b\times a} $ 机器人雅可比矩阵 $ \hat{J}\in {\bf{R}}^{b\times a} $ 机器人估计雅可比矩阵 $ {\dot{\hat{J}}}\in {\bf{R}}^{b\times a} $ 机器人估计雅可比矩阵的导数 $ M(\boldsymbol \theta)\in {\bf{R}}^{3\times 3} $ 末端执行器的方向旋转矩阵 $ {\boldsymbol q}_{E}(\boldsymbol \theta)\in {\bf{R}}^{4} $ 末端执行器的方向四元数 $ \boldsymbol{\overline{o}}(\boldsymbol \theta)\in {\bf{R}}^{5} $ 末端执行器的方向向量 $ \tilde{\boldsymbol q}\in {\bf{R}}^{5} $ 末端执行器的期望方向向量 $ H({\boldsymbol \theta})=\dfrac{\partial{\boldsymbol q}_{E}(\boldsymbol \theta)}{\partial{\boldsymbol \theta}}\in {\bf{R}}^{4\times a} $ $ {\boldsymbol q}_{E} $ 的雅可比矩阵 $ G({\boldsymbol{\theta}})=\dfrac{\partial{\boldsymbol{\overline{o}}({\boldsymbol{\theta}}})}{\partial{{\boldsymbol{\theta}}}}\in {\bf{R}}^{5\times a} $ $ \boldsymbol{\overline{o}}({\boldsymbol{\theta}}) $的雅可比矩阵 $ \kappa(\boldsymbol q)=\dfrac{\partial{{\tilde{\boldsymbol q}}}}{\partial{\boldsymbol q}}\in {\bf{R}}^{5\times 4} $ $ \tilde{\boldsymbol q} $ 的雅可比矩阵 $ \boldsymbol{u}\in {\bf{R}}^a $ 方差为极小值的独立同分布零均值随机噪声 ${\boldsymbol{u} }_{0}\in {\bf{R} }^a$ $ \boldsymbol{u} $的上界 $ \hat{\dot{{\boldsymbol{\theta}}}}\in {\bf{R}}^a $ 受噪声驱动的关节角速度 $ \Vert \cdot \Vert_2 $ 向量的二范数 $ \mathrm{tr(\cdot)} $ 矩阵的迹 
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表 2 冗余机器人不同轨迹跟踪控制方案对比
Table 2 Comparison of different trajectory tracking control schemes for redundant manipulators
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