力矩输入有界的柔性关节机器人轨迹跟踪控制
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摘要
为解决柔性关节机器人在关节驱动力矩输出受限情况下的轨迹跟踪控制问题,提出一种基于奇异摄动理论的有界控制器.首先,利用奇异摄动理论将柔性关节机器人动力学模型解耦成快、慢两个子系统.然后,引入一类平滑饱和函数和径向基函数神经网络非线性逼近手段,依据反步策略设计了针对慢子系统的有界控制器.在快子系统的有界控制器设计中,通过关节弹性力矩跟踪误差的滤波处理加速系统的收敛.同时,在快、慢子系统控制器中均采用模糊逻辑实现控制参数的在线动态自调整.此外,结合李雅普诺夫稳定理论给出了严格的系统稳定性证明.最后,通过仿真对比实验验证了所提出控制方法的有效性和优越性.
In order to solve the problem of trajectory tracking control for flexible-joint robot manipulators with limited output torque, a bounded controller based on singular perturbation theory is proposed. Firstly, the dynamics model of the flexible-joint robot manipulator is transformed into a fast subsystem and a slow subsystem by singularly perturbed decoupling method. Then, invoking a class of smooth saturation function and radial basis function neural network for nonlinear approximation, a bounded controller for the slow subsystem is designed by the back-stepping method. On the other side, in the bounded controller design for the fast subsystem, the convergence of the system is accelerated by filtering the tracking error of the joint elastic torque. At the same time, the fuzzy logic is used in the controllers for the fast and slow subsystems to realize the online dynamic self-tuning of control gains. In addition, the strict stability of system is proved with the Lyapunov stability theory. Finally, simulation results verify the effectiveness and superiority of the proposed approach.
In order to solve the problem of trajectory tracking control for flexible-joint robot manipulators with limited output torque, a bounded controller based on singular perturbation theory is proposed. Firstly, the dynamics model of the flexible-joint robot manipulator is transformed into a fast subsystem and a slow subsystem by singularly perturbed decoupling method. Then, invoking a class of smooth saturation function and radial basis function neural network for nonlinear approximation, a bounded controller for the slow subsystem is designed by the back-stepping method. On the other side, in the bounded controller design for the fast subsystem, the convergence of the system is accelerated by filtering the tracking error of the joint elastic torque. At the same time, the fuzzy logic is used in the controllers for the fast and slow subsystems to realize the online dynamic self-tuning of control gains. In addition, the strict stability of system is proved with the Lyapunov stability theory. Finally, simulation results verify the effectiveness and superiority of the proposed approach.
引文
[1]KIM J,CROFT E A.Full-state tracking control for flexible joint robots with singular perturbation techniques.IEEE Transactions on Control Systems Technology,2019,27(1):63-73.
[2] LIU Huashan, ZHU Shiqiang, WU Jianbo, et al. Trajectory tracking control for robot manipulators with bounded inputs based on the singular perturbation theory. Control Theory&Applications, 2009,26(12):1371–1377.(刘华山,朱世强,吴剑波,等.基于奇异摄动理论的输入有界机器人轨迹跟踪控制.控制理论与应用, 2009, 26(12):1371–1377.)
[3] SPONG M W. Modeling and control of elastic joint robots. Journal of Dynamic Systems, Measurement, and Control, 1987, 109(4):310–319.
[4] LIU Fucai, GAO Jingfang, LI Qian, et al. Adaptive robust control of flexible-joint space manipulators under different gravity environments. Chinese High Technology Letters, 2015, 25(1):61–69.(刘福才,高静方,李倩,等.不同重力环境下的柔性关节空间机械臂自适应鲁棒控制.高技术通讯, 2015, 25(1):61–69.)
[5] LESSARD J, BIGRAS P, LIU Z, et al. Characterization, modeling and vibration control of a flexible joint for a robotic system. Journal of Vibration and Control, 2014, 20(6):943–960.
[6] SALMASI H, FOTOUHI R, NIKIFORUK P N. A manoeuvre control strategy for flexible-joint manipulators with joint dry friction. Robotica, 2010, 28(4):621–635.
[7] LIGHTCAP C A, BANKS S A. An extended Kalman filter for realtime estimation and control of a rigid-link flexible-joint manipulator.IEEE Transactions on Control Systems Technology, 2010, 18(1):91–103.
[8] LIU Yechao, LIU Yiwei, LIU Hong. Singular perturbation control for flexible-joint manipulator. Electric Machines and Control, 2009,13(3):436–441.(刘业超,刘伊威,刘宏.柔性关节机器人奇异摄动控制.电机与控制学报, 2009, 13(3):436–441.)
[9] YU X, CHEN L. Modeling and observer-based augmented adaptive control of flexible-joint free-floating space manipulators. Acta Astronautica, 2015, 108:146–155.
[10] XIE Limin, CHEN Li. Modeling, saturation robust fuzzy sliding control and vibration suppression of free-floating flexible-joint flexiblelink space robot. Journal of Mechanical Engineering, 2015, 51(1):76–82.(谢立敏,陈力.漂浮基柔性关节、柔性臂空间机器人动力学建模、饱和鲁棒模糊滑模控制及双重柔性振动主动抑制.机械工程学报,2015, 51(1):76–82.)
[11] VAKIL M, FOTOUHI R, NIKIFORUK P N. Trajectory tracking for the end-effector of a class of flexible link manipulators. Journal of Vibration and Control, 2011, 17(1):55–68.
[12] MEHREZ M W, EL-BADAWY A A. Effect of the joint inertia on selection of under-actuated control algorithm for flexible-link manipulators. Mechanism and Machine Theory, 2010, 45(7):967–980.
[13] EL-BADAWY A A, MEHREZ M W, ALI A R. Nonlinear modeling and control of flexible-link manipulators subjected to parametric excitation. Nonlinear Dynamics, 2010, 62(4):769–779.
[14] LOPEZ-ARAUJO D J, ZAVALA-RIO A, SANTIBA′N?EZ V, et al. A generalized global adaptive tracking control scheme for robot manipulators with bounded inputs. International Journal of Adaptive Control and Signal Processing, 2015, 29(2):180–200.
[15] HE W, DONG Y, SUN C. Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2016, 46(3):334–344.
[16] LORIA A, NIJMEIJER H. Bounded output feedback tracking control of fully actuated Euler-Lagrange systems. Systems&Control Letters,1998, 33(3):151–161.
[17] MORENO-VALENZUELA J, SANTIBA′N?EZ V, CAMPA R. A class of OFT controllers for torque-saturated robot manipulators:Lyapunov stability and experimental evaluation. Journal of Intelligent and Robotic Systems, 2008, 51(1):65–88.
[18] MORENO-VALENZUELA J, SANTIBA′N?EZ V V, CAMPA R. On output feedback tracking control of robot manipulators with bounded torque input. International Journal of Control, Automation, and Systems, 2008, 6(1):76–85.
[19] LIU H, HAO K, LAI X. Fuzzy saturated output feedback tracking control for robot manipulators:a singular perturbation theory based approach. International Journal of Advanced Robotic Systems, 2011,8(4):43–53.
[20] YANG H, YU Y, YUAN Y, et al. Back-stepping control of two-link flexible manipulator based on an extended state observer. Advances in Space Research, 2015, 56(10):2312–2322.
[21] MIAO Z, WANG Y. Robust dynamic surface control of flexible joint robots using recurrent neural networks. Journal of Control Theory and Applications, 2013, 11(2):222–229.
[22] TAO Y, ZHENG J, LIN Y. A sliding mode control-based on a RBF neural network for deburring industry robotic systems. International Journal of Advanced Robotic Systems, 2016, 13(1):8.
[23] HONG Y, YAO B. A globally stable saturated desired compensation adaptive robust control for linear motor systems with comparative experiments. Automatica, 2007, 43(10):1840–1848.
[24] LI Y, TONG S. Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems. IEEE Transactions on Cybernetics, 2017, 47(4):1007–1016.
[25] LIU Jinkun. Intelligent Control. Third Edition. Beijing:Publishing House of Electronics Industry, 2014.(刘金琨.智能控制.第3版.北京:电子工业出版社, 2014.)
[26] KHOSRAVI M A, TAGHIRAD H D. Dynamic modeling and control of parallel robots with elastic cables:singular perturbation approach.IEEE Transactions on Robotics, 2014, 30(3):694–704.
[27] LIU Huashan, LI Sheng, WANG Baoxiang. Virtual decomposition control for flexible-joint robot manipulators with extended Kalman filtering. Control Theory&Applications, 2018, 35(6):850–858.(刘华山,李生,王保相.带扩展卡尔曼滤波的柔性关节机器人虚拟分解控制.控制理论与应用, 2018, 35(6):850–858.)
[2] LIU Huashan, ZHU Shiqiang, WU Jianbo, et al. Trajectory tracking control for robot manipulators with bounded inputs based on the singular perturbation theory. Control Theory&Applications, 2009,26(12):1371–1377.(刘华山,朱世强,吴剑波,等.基于奇异摄动理论的输入有界机器人轨迹跟踪控制.控制理论与应用, 2009, 26(12):1371–1377.)
[3] SPONG M W. Modeling and control of elastic joint robots. Journal of Dynamic Systems, Measurement, and Control, 1987, 109(4):310–319.
[4] LIU Fucai, GAO Jingfang, LI Qian, et al. Adaptive robust control of flexible-joint space manipulators under different gravity environments. Chinese High Technology Letters, 2015, 25(1):61–69.(刘福才,高静方,李倩,等.不同重力环境下的柔性关节空间机械臂自适应鲁棒控制.高技术通讯, 2015, 25(1):61–69.)
[5] LESSARD J, BIGRAS P, LIU Z, et al. Characterization, modeling and vibration control of a flexible joint for a robotic system. Journal of Vibration and Control, 2014, 20(6):943–960.
[6] SALMASI H, FOTOUHI R, NIKIFORUK P N. A manoeuvre control strategy for flexible-joint manipulators with joint dry friction. Robotica, 2010, 28(4):621–635.
[7] LIGHTCAP C A, BANKS S A. An extended Kalman filter for realtime estimation and control of a rigid-link flexible-joint manipulator.IEEE Transactions on Control Systems Technology, 2010, 18(1):91–103.
[8] LIU Yechao, LIU Yiwei, LIU Hong. Singular perturbation control for flexible-joint manipulator. Electric Machines and Control, 2009,13(3):436–441.(刘业超,刘伊威,刘宏.柔性关节机器人奇异摄动控制.电机与控制学报, 2009, 13(3):436–441.)
[9] YU X, CHEN L. Modeling and observer-based augmented adaptive control of flexible-joint free-floating space manipulators. Acta Astronautica, 2015, 108:146–155.
[10] XIE Limin, CHEN Li. Modeling, saturation robust fuzzy sliding control and vibration suppression of free-floating flexible-joint flexiblelink space robot. Journal of Mechanical Engineering, 2015, 51(1):76–82.(谢立敏,陈力.漂浮基柔性关节、柔性臂空间机器人动力学建模、饱和鲁棒模糊滑模控制及双重柔性振动主动抑制.机械工程学报,2015, 51(1):76–82.)
[11] VAKIL M, FOTOUHI R, NIKIFORUK P N. Trajectory tracking for the end-effector of a class of flexible link manipulators. Journal of Vibration and Control, 2011, 17(1):55–68.
[12] MEHREZ M W, EL-BADAWY A A. Effect of the joint inertia on selection of under-actuated control algorithm for flexible-link manipulators. Mechanism and Machine Theory, 2010, 45(7):967–980.
[13] EL-BADAWY A A, MEHREZ M W, ALI A R. Nonlinear modeling and control of flexible-link manipulators subjected to parametric excitation. Nonlinear Dynamics, 2010, 62(4):769–779.
[14] LOPEZ-ARAUJO D J, ZAVALA-RIO A, SANTIBA′N?EZ V, et al. A generalized global adaptive tracking control scheme for robot manipulators with bounded inputs. International Journal of Adaptive Control and Signal Processing, 2015, 29(2):180–200.
[15] HE W, DONG Y, SUN C. Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2016, 46(3):334–344.
[16] LORIA A, NIJMEIJER H. Bounded output feedback tracking control of fully actuated Euler-Lagrange systems. Systems&Control Letters,1998, 33(3):151–161.
[17] MORENO-VALENZUELA J, SANTIBA′N?EZ V, CAMPA R. A class of OFT controllers for torque-saturated robot manipulators:Lyapunov stability and experimental evaluation. Journal of Intelligent and Robotic Systems, 2008, 51(1):65–88.
[18] MORENO-VALENZUELA J, SANTIBA′N?EZ V V, CAMPA R. On output feedback tracking control of robot manipulators with bounded torque input. International Journal of Control, Automation, and Systems, 2008, 6(1):76–85.
[19] LIU H, HAO K, LAI X. Fuzzy saturated output feedback tracking control for robot manipulators:a singular perturbation theory based approach. International Journal of Advanced Robotic Systems, 2011,8(4):43–53.
[20] YANG H, YU Y, YUAN Y, et al. Back-stepping control of two-link flexible manipulator based on an extended state observer. Advances in Space Research, 2015, 56(10):2312–2322.
[21] MIAO Z, WANG Y. Robust dynamic surface control of flexible joint robots using recurrent neural networks. Journal of Control Theory and Applications, 2013, 11(2):222–229.
[22] TAO Y, ZHENG J, LIN Y. A sliding mode control-based on a RBF neural network for deburring industry robotic systems. International Journal of Advanced Robotic Systems, 2016, 13(1):8.
[23] HONG Y, YAO B. A globally stable saturated desired compensation adaptive robust control for linear motor systems with comparative experiments. Automatica, 2007, 43(10):1840–1848.
[24] LI Y, TONG S. Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems. IEEE Transactions on Cybernetics, 2017, 47(4):1007–1016.
[25] LIU Jinkun. Intelligent Control. Third Edition. Beijing:Publishing House of Electronics Industry, 2014.(刘金琨.智能控制.第3版.北京:电子工业出版社, 2014.)
[26] KHOSRAVI M A, TAGHIRAD H D. Dynamic modeling and control of parallel robots with elastic cables:singular perturbation approach.IEEE Transactions on Robotics, 2014, 30(3):694–704.
[27] LIU Huashan, LI Sheng, WANG Baoxiang. Virtual decomposition control for flexible-joint robot manipulators with extended Kalman filtering. Control Theory&Applications, 2018, 35(6):850–858.(刘华山,李生,王保相.带扩展卡尔曼滤波的柔性关节机器人虚拟分解控制.控制理论与应用, 2018, 35(6):850–858.)
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