Active Disturbance Rejection Trajectory Tracking Control of Omnidirectional Mobile Robot
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摘要: 针对4-Mecanum轮全向移动机器人轨迹跟踪问题,设计了一种自抗扰控制器。首先对机器人的运动学与动力学模型进行分析;其次由反步法设计运动学控制器,并根据机器人在运动过程中受到未知干扰的现象,设计了改进的扩张状态观测器和动力学控制器;最后在不同扰动的作用下进行仿真。对比结果表明该控制器跟踪误差小,收敛速度快,观测器能够快速准确地估计出不确定因素对机器人的扰动并进行实时补偿,验证了该控制器具有较好的抗干扰性和鲁棒性。Abstract: In this paper, an active disturbance rejection trajectory trackingcontroller for a 4-Mecanum wheel omnidirectional mobile robot is presented. Firstly, the kinematic and dynamic model of the robot is analyzed. Secondly, the kinematic controller is designed with the backstepping method. An improved extended state observer and dynamic controller is designed because the disturbances during the robot′s movement remain unknown. Finally, simulation is carried out under the influence of different disturbances. The comparison results show that the controller has smaller tracking error and faster convergence speed. The extended state observer estimates the disturbances quickly and accurately with uncertain factors as well as making real-time compensation, thus verifying that the controller has better anti-interference and robustness.
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表 1 ODMR模型参数与控制器参数
参数 参数值 ODMR $ a{\text{ = }}0.37\;{\text{m}} $;$ b{\text{ = }}0.3\;{\text{m}} $;$ m = 11\;{\text{kg}} $;$ R{\text{ = }}0.04\;{\text{m}} $;
$ {\mu _i}{\text{ = }}0.2 $;${J_{\textit{z}}}{\text{ = } }3.42\;{\text{kg} } \cdot { {\text{m} }^2}$;$ {J_m}{\text{ = }}0.137\;{\text{kg}} \cdot {{\text{m}}^2} $;
${f_i} = 2N,(i = 1,2,3,4)$;控制器 $ {\omega _0}{\text{ = }}20 $;$ {\omega _c}{\text{ = }}30 $;$ \delta {\text{ = }}0.005 $;$ {\alpha _1}{\text{ = }}1 $;$ {\alpha _2}{\text{ = }}0.5 $;
$ {\alpha _3}{\text{ = 0}}{\text{.25}} $;$ {k_1} = 0.8 $;$ {k_2} = 10 $;$ {k_3} = 0.5 $;$ {K_1} = 20 $;
$ {K_2} = 40 $;$ {K_3} = 20 $表 2 直线轨迹评价指标
控制器 ADRC SADRC 0 ~ 10 s $ T({e_{xy}}) $ 0.0357 0.0281 $ T({e_\theta }) $ 0.0155 0.0126 $ {e_{xy}}_{\max } $ 0.0101 0.0021 $ {e_\theta }_{\max } $ 0.0015 0.0019 10 ~ 25 s $ T({e_{xy}}) $ 0.3545 0.1992 $ T({e_\theta }) $ 0.0031 0.0036 $ {e_{xy}}_{\max } $ 0.0539 0.0207 $ {e_\theta }_{\max } $ 0.0104 0.0106 表 3 双扭线轨迹评价指标
控制器 ADRC SADRC 0 ~ 10 s $ T({e_{xy}}) $ 0.1281 0.1033 $ T({e_\theta }) $ 0.0132 0.0154 $ {e_{xy}}_{\max } $ 0.0104 0.0089 $ {e_\theta }_{\max } $ 0.0019 0.0015 10 ~ 25 s $ T({e_{xy}}) $ 0.8353 0.6165 $ T({e_\theta }) $ 0.0322 0.0459 $ {e_{xy}}_{\max } $ 0.0579 0.0235 $ {e_\theta }_{\max } $ 0.0176 0.0182 -
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