具有狀態約束與輸入飽和的全向移動機器人自適應跟蹤控制

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.
- 全向移動機器人 /
- 跟蹤控制 /
- 自適應控制 /
- 狀態約束 /
- 輸入飽和
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.
- omnidirectional mobile robot /
- tracking control /
- adaptive control /
- state constraints /
- input saturation

HTML全文

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

下載: 全尺寸圖片幻燈片

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)

下載: 全尺寸圖片幻燈片

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)

下載: 全尺寸圖片幻燈片

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)

下載: 全尺寸圖片幻燈片

圖 5 控制器(20)作用下的輸出力矩

Figure 5. Input torque with the proposed controller (20)

下載: 全尺寸圖片幻燈片

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)

下載: 全尺寸圖片幻燈片

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)

下載: 全尺寸圖片幻燈片

圖 8 控制器(30)下的輸入力矩

Figure 8. Input torque with the controller (30)

下載: 全尺寸圖片幻燈片

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)

下載: 全尺寸圖片幻燈片

圖 10 PD控制器(31)下的輸入力矩

Figure 10. Input torque with the PD controller (31)

下載: 全尺寸圖片幻燈片

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，I_R/(kg·m²)	輪子轉動慣量， I_w/(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

下載: 導出CSV

www.77susu.com

參考文獻(25)

[1]	Kramer J, Scheutz M. Development environments for autonomous mobile robots: a survey. Auton Robot, 2007, 22(2): 101 doi: 10.1007/s10514-006-9013-8
[2]	Watanabe K, Shiraishi Y, Tzafestas S G, et al. Feedback control of an omnidirectional autonomous platform for mobile service robots. J Intell Rob Syst, 1998, 22(3-4): 315 http://www.springerlink.com/content/t517772768520pn8/
[3]	Al Mamun M A, Nasir M T, Khayyat A. Embedded system for motion control of an omnidirectional mobile robot. IEEE Access, 2018, 6: 6722 doi: 10.1109/ACCESS.2018.2794441
[4]	Kalmár-Nagy T, D'Andrea R, Ganguly P. Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle. Robot Auton Syst, 2004, 46(1): 47 doi: 10.1016/j.robot.2003.10.003
[5]	Purwin O, D'Andrea R. Trajectory generation and control for four wheeled omnidirectional vehicles. Robot Auton Syst, 2006, 54(1): 13 doi: 10.1016/j.robot.2005.10.002
[6]	Liu Y, Zhu J J, Williams Ⅱ R L, et al. Omni-directional mobile robot controller based on trajectory linearization. Robot Auton Syst, 2008, 56(5): 461 doi: 10.1016/j.robot.2007.08.007
[7]	Indiveri G. Swedish wheeled omnidirectional mobile robots: kinematics analysis and control. IEEE Trans Rob, 2009, 25(1): 164 doi: 10.1109/TRO.2008.2010360
[8]	Hashemi E, Jadidi M G, Jadidi N G. Model-based PI-fuzzy control of four-wheeled omni-directional mobile robots. Robot Auton Syst, 2011, 59(11): 930 doi: 10.1016/j.robot.2011.07.002
[9]	Huang H C, Tsai C C. Adaptive trajectory tracking and stabilization for omnidirectional mobile robot with dynamic effect and uncertainties. IFAC Proc Vol, 2008, 41(2): 5383 doi: 10.3182/20080706-5-KR-1001.00907
[10]	Wang M M, Zhu Y Y, Zhang L, et al. An adaptive robust controller for a mobile robot driven by Mecanum wheels. J Northwest Polytech Univ, 2018, 36(4): 627 doi: 10.3969/j.issn.1000-2758.2018.04.004 王明明, 朱瑩瑩, 張磊, 等. 麥克納姆輪驅動的移動機器人自適應滑模控制器設計. 西北工業大學學報, 2018, 36(4): 627 doi: 10.3969/j.issn.1000-2758.2018.04.004
[11]	Alakshendra V, Chiddarwar S S. Adaptive robust control of Mecanum-wheeled mobile robot with uncertainties. Nonlinear Dyn, 2017, 87(4): 2147 doi: 10.1007/s11071-016-3179-1
[12]	Xu D, Zhao D B, Yi J Q, et al. Trajectory tracking control of omnidirectional wheeled mobile manipulators: robust neural network-based sliding mode approach. IEEE Trans Syst Man Cybern Part B Cybern, 2009, 39(3): 788 doi: 10.1109/TSMCB.2008.2009464
[13]	Kang S Z, Wu H T. Research on fuzzy adaptive sliding mode control of omni-directional mobile robot. Mach Des Manuf Eng, 2017, 46(3): 70 doi: 10.3969/j.issn.2095-509X.2017.03.014 康升征, 吳洪濤. 全向移動機器人模糊自適應滑模控制方法研究. 機械設計與制造工程, 2017, 46(3): 70 doi: 10.3969/j.issn.2095-509X.2017.03.014
[14]	Tee K P, Ge S S, Tay E H. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 2009, 45(4): 918 doi: 10.1016/j.automatica.2008.11.017
[15]	Liu Y J, Li D J, Tong S C. Adaptive output feedback control for a class of nonlinear systems with full-state constraints. Int J Control, 2014, 87(2): 281 doi: 10.1080/00207179.2013.828854
[16]	Liu Y J, Tong S C. Barrier Lyapunov Functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica, 2016, 64: 70 doi: 10.1016/j.automatica.2015.10.034
[17]	Bai R. Neural network control-based adaptive design for a class of DC motor systems with the full state constraints. Neurocomputing, 2015, 168: 65 doi: 10.1016/j.neucom.2015.04.090
[18]	Meng W C, Yang Q M, Sun Y X. Adaptive neural control of nonlinear MIMO systems with time-varying output constraints. IEEE Trans Neural Networks Learn Syst, 2015, 26(5): 1074 doi: 10.1109/TNNLS.2014.2333878
[19]	Ding L, Li S, Liu Y J, et al. Adaptive neural network-based tracking control for full-state constrained wheeled mobile robotic system. IEEE Trans Syst Man Cybern Syst, 2017, 47(8): 2410 doi: 10.1109/TSMC.2017.2677472
[20]	Wang C X, Wu Y Q. Finite-time tracking control for strict-feedback nonlinear systems with full state constraints. Int J Control, 2017, 46(7): 1
[21]	Chen X H, Jia Y M, Matsuno F. Tracking control for differential-drive mobile robots with diamond-shaped input constraints. IEEE Trans Control Syst Technol, 2014, 22(5): 1999 doi: 10.1109/TCST.2013.2296900
[22]	Liu C X, Gao J, Xu D M. Lyapunov-based model predictive control for tracking of nonholonomic mobile robots under input constraints. Int J Control Autom Syst, 2017, 15(5): 2313 doi: 10.1007/s12555-016-0350-x
[23]	Chen M, Ge S S, Ren B B. Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica, 2011, 47(3): 452 doi: 10.1016/j.automatica.2011.01.025
[24]	Wen C Y, Zhou J, Liu Z T, et al. Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Trans Autom Control, 2011, 56(7): 1672 doi: 10.1109/TAC.2011.2122730
[25]	Khalil H K. Nonlinear Systems. 3rd Ed. London: Prentice Hall Inc, 2002