Research on Fractional Cross-coupling Synchronization Strategy of Manipulators
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摘要: 为了对机械臂各关节间进行高精度同步控制，以提高运动轨迹跟踪精度，针对机械臂单关节，提出了分数阶微积分与滑模控制相结合的位置跟踪控制策略，考虑机械臂各关节之间存在的耦合关系，提出了分数阶滑模交叉耦合控制策略。并对所提的控制策略的渐进稳定性进行了理论证明。以二关节机械臂为研究对象进行了实验验证，结果表明：利用本文提出的位置跟踪控制策略使二关节机械臂角位移调整时间分别为0.53 s、0.58 s，优于传统滑模控制策略的1.31 s、1.24 s,其位置误差的均方根误差相比传统滑模控制策略分别减小了1.6×10−4、6.51×10−4。本文所设计的分数阶滑模交叉耦合控制器使机械臂得到的输出响应的上升时间和稳定时间优于PD交叉耦合控制策略和滑模交叉耦合控制策略，且同步误差的均方根误差分别为0.022 5、0.031 6，优于PD交叉耦合的0.133、0.926和滑模交叉耦合的0.057 3、0.052 3。实验结果说明了本文所提出控制方法的有效性。Abstract: In order to synchronize the joints of the manipulator with high precision and improve the tracking accuracy, position tracking control strategy combining fractional calculus and sliding mode control is proposed for the single joint of the manipulator. Considering the coupling relationship between the joints of the manipulator, a fractional sliding mode cross-coupling control strategy is proposed. The asymptotic stability of the proposed control strategy is proved theoretically. The experimental results show that the angular displacement adjustment time of the two-joint manipulator is 0.53 s and 0.58 s respectively by using the position tracking control strategy proposed in this paper, which is superior to the traditional sliding mode control strategy of 1.31 s and 1.24 s. The root mean square error of the position error is reduced by 1.6×10−4, 6.51×10−4 compared with the traditional sliding mode control strategy. The rise time and stability time of the output response obtained by the manipulator is better than those of the PD cross-coupling control strategy and the sliding mode cross-coupling control strategy, and the root mean square error of the synchronization error is 0.022 5, 0.031 6, which is better than 0.133, 0.926 of PD cross-coupling and 0.057 3, 0.052 3 of sliding mode cross-coupling. The experimental results show the effectiveness of the control method proposed.
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Key words:
- sliding mode control /
- manipulator /
- reaching law /
- cross-coupled control /
- synchronization error
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