Trajectory tracking control of Mecanum wheel omnidirectional mobile robot based on power reaching law
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摘要:
针对基于一般滑模的麦克纳姆轮全向移动机器人在轨迹跟踪过程中收敛速度慢、耗时长及控制存在抖振等问题，提出一种利用多幂次趋近律实现系统快速收敛的滑模控制. 通过控制4个麦克纳姆轮的角速度实现机器人3个自由度的位置变化，完成3输入4输出的控制，根据所建的数学模型，使用多幂次趋近律在系统趋近滑模面的不同阶段进行针对性调节保证收敛速度，用双曲正切函数替换趋近律中的符号函数改善抖振问题，利用Lyapunov理论证明3输入4输出控制系统的稳定性，最后 通过仿真验证所提出算法的有效性.
Abstract:Aiming at problems of slow convergence and long time consuming in trajectory tracking, and chattering problem exists in the control of Mecanum wheel omnidirectional mobile robot based on general sliding mode, a sliding mode control method was proposed to realize the rapid convergence of the system by using the multi power reaching law. The position change of three degrees of freedom of robot was realized by controlling the angular velocity of four Mecanum wheels, and the control of three inputs and four outputs was completed. According to the mathematical model established, the multi power reaching law was used to adjust the convergence speed at different stages of the system approaching sliding mode surface, and the hyperbolic tangent function was used to replace the sign function in the reaching law to improve the chattering problem. The stability of the three inputs and four outputs control system was proved by Lyapunov theory. Finally, the control effect of the proposed algorithm was illustrated by simulation and comparison analysis.
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Key words:
- Mecanum wheel /
- trajectory tracking /
- sliding mode control /
- multi power reaching law
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表 1 MP-SMC仿真参数设置表
Table 1. Simulation parameters setting table of MP-SMC
参数 值 a/m 0.25 b/m 0.35 r/m 0.05 ${I_0}/({\rm{kg}}{\rm{\cdot} }{ {\rm{m} }^{\rm{2} } })$ 0.09 ${\eta _0}/({\rm{N}}{\rm{\cdot m\cdot s\cdot rad^{-1} } })$ 0.2 $ \alpha $ 10 $ \beta $ 0.2 $ \delta $ diag{12,12,12} $\lambda $ diag{10,10,10} $ \sigma $ diag{100,100,100} $ \varepsilon $ diag{30,30,30} k diag{30,30,30} 
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