Adaptive tracking control for omnidirectional mobile robots with full-state constraints and input saturation
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摘要: 研究了全狀態約束與輸入飽和情況下的全向移動機器人軌跡跟蹤控制問題.首先，針對一類三輪驅動的全向移動機器人，考慮系統存在模型參數不確定與外部擾動，建立了運動學與動力學模型；其次，利用障礙Lyapunov函數，結合反步設計方法，有效處理全向移動機器人跟蹤過程中存在的狀態約束，保證所有狀態變量不會超出狀態約束的限制區域；然后，針對系統參數不確定和未知有界擾動，設計相應的自適應律進行處理；同時，提出一種抗飽和補償器保證機器人輸入力矩滿足飽和約束；并且利用Lyapunov理論分析證明了當選取合適的控制參數時閉環系統中的所有信號均能保證一致有界；最后，通過與未考慮狀態約束和輸入飽和的控制器以及經典比例-微分控制器進行仿真對比，驗證了該方法的有效性和魯棒性.Abstract: The omnidirectional mobile robot (OMR), which is different from the two-wheeled differential drive mobile robots, can achieve three-degree-of-freedom motion in a plane with no non-holonomic constraint. Therefore, this type of robot has been widely used in many fields owing to its superior maneuverability and controllability. In practical applications, the trajectory tracking problem of the OMRs is a key issue that requires an urgent solution. The challenges with respect to the tracking performance can be categorized into the following: first, the parameter uncertainty of the OMR model and external disturbances affect the accuracy of the control. Second, on account of the limited workspace and the security requirements, the positions, attitudes, and speeds of the OMRs are subject to state constraints during the tracking process. Finally, the limited capability of the actuators can lead to input saturation, which will further degrade the tracking performance or even result in failure to track the desired trajectory. Thus, this study investigates the trajectory-tracking control problem of the OMRs with full-state constraints and input saturation. The kinematics and dynamics for a class of three-wheeled omnidirectional mobile robots were presented with the model uncertainties and external disturbance. Moreover, the barrier Lyapunov method was applied to handle the state constraints using the backstepping technique so that none of the state variables violated the restrictions. Meanwhile, adaptive control laws were designed to deal with the parameter uncertainties and unknown bounded disturbance. Moreover, an anti-windup compensator was adopted to ensure the input torque of the robot met the input constraints. The Lyapunov theory was used to prove that all the signals in the closed-loop system were uniformly bounded when the control parameters were selected suitably. Finally, using numerical simulations, the proposed robust adaptive controller was compared with other controllers, and the results verify the effectiveness and robustness of the proposed method.
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圖 1 三輪全向移動機器人與受力分析. (a)機器人示意圖；(b)受力分析
Figure 1. Three-wheeled omnidirectional mobile robot and force analysis: (a) schematic of the robot; (b) force analysis
圖 2 在控制器(20)作用下的q1 (a)和q2(b)跟蹤性能
Figure 2. Tracking performance of q1 (a) and q2 (b) with the proposed controller (20)
圖 3 在控制器(20)作用下的z1 (a)和z2 (b)的收斂特性
Figure 3. Convergence of z1(a) and z2 (b) with the controller (20)
圖 4 控制器(20)作用下的自適應參數更新律(a)和輔助系統狀態(b)
Figure 4. Adaptive laws (a) and auxiliary system status (b) with the controller (20)
圖 6 控制器(30)作用下的q1 (a)和q2(b)跟蹤性能
Figure 6. Tracking performance of q1 (a) and q2 (b) with the proposed controller (30)
圖 7 在控制器(30)作用下的z1 (a)和z2 (b)的收斂特性
Figure 7. Convergence of z1 (a) and z2 (b) with the controller (30)
圖 9 在PD控制器(31)作用下q1 (a)和q2 (b)跟蹤性能
Figure 9. Tracking performance of q1 (a) and q2 (b) with the PD controller (31)
中文字幕在线观看表 1 全向移動機器人的物理參數
Table 1. Physical parameters of the omnidirectional mobile robot
數值 機器人質量，
m/kg質心到輪子中心垂線距離，L/m 輪子半徑，
r/m黏滯摩擦系數，
c/(kg·m2·s-1)機器人轉動慣量，IR/(kg·m2) 輪子轉動慣量，
Iw/(kg·m2)減速機倍數，n 實際值 10 0.50 0.100 0.01 20 0.10 1 標稱值 8 0.55 0.005 0.12 25 0.12 1 
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參考文獻
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