机器人鲁棒学习控制
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摘要
近二十多年来,以神经网络、模糊逻辑和进化算法为代表的人工智能理论与方法开始被运用到机器人系统的控制当中。神经网络具有通用的逼近能力、分布式的结构,控制过程中可以不需要系统的数学模型知识等优点,并且具有与其它控制理论如自适应控制,变结构控制等很强的融合能力,因此神经网络被广泛应用于含有未知动力学的机器人系统的控制。
稳定自适应控制是近年来基于神经网络的非线性系统自适应控制方法的研究主流,在保证稳定性方面有了越来越严格的理论证明。但是自适应神经网络控制中的一个不足或局限就是网络需要反复训练,不像人脑一样具有一次学习的能力,而且不能将学习到的知识重新利用。同样基于自适应神经网络的机器人控制虽然取得了很大的成绩,但是对于系统的未知动力学在控制任务完成后仍然是未知的。研究者对于神经网络有没有真正学习到系统的未知动力学未进行探索,每次即使重复相同的控制任务都要进行网络的重新训练,而这一训练过程是耗时耗能的,所以很有必要进一步探讨神经网络在稳定的自适应闭环控制过程中学习未知动力学知识的能力,并且期望能将学习到的动力学知识运用到相同或者相似的控制任务中,避免网络的重复训练,同时使得自适应神经网络控制器能根据经验累积知识,改善控制性能。
根据确定学习原理,对于一个合理设计的自适应神经网络控制器,在跟踪周期或者类周期的参考轨迹时,其径向基函数网络的回归向量满足部分持续激励条件,进一步分析可得到网络估计权值的部分收敛,根据径向基函数网络的局部特性,最终系统的未知非线性能够由一个常值神经网络逼近。
本文利用确定学习的最新成果,提出了含有未知动力学和干扰的机器人鲁棒学习控制策略。在稳定的闭环控制过程中,所设计的鲁棒自适应神经网络控制器在跟踪周期或者类周期的参考轨迹时,回归向量满足部分持续激励条件,通过分析由闭环系统推导而来的线性时变系统的指数稳定性,可得到网络估计权值的部分收敛,从而神经网络可以学习到机器人闭环系统未知的动力学,并将学到的动力学作为经验知识以常值网络权值的形式表示。通过学习,使我们了解系统未知动力学模型特性成为可能,并且在下次重复相同或者相似的控制任务时,控制器可以调用以往所学动力学知识用于控制并获得更好的控制性能。该策略避免了耗时耗能的神经网络重新训练过程,使得机器人具有真正意义上的从经历中获取知识,表达知识,并将学到的知识再利用的能力。
In the past decades, artificial intelligence theory and methods such as neural networks, fuzzy logics and evolution algorithms have been used to control robot system. Neural networks have lots of advantages including universal approximation abilities, distributed architecture, accurate system mathematic model is not needed in control process and powerful ability of working with other control theory such as adaptive control, variable structure control, so neural networks have been widely applied to the control of robot system with unknown dynamics.
In recent years, stable adaptive control has been the main trend of neural network based adaptive control of nonlinear system, and there is stricter theoretical proof on system stability. But one of the shortness of adaptive neural networks is that the network need to be trained repeatedly, do not have the ability of learning as human brains and reusing the learned knowledge. Great achievements have been made toward adaptive neural networks based robot control, however, the system unknown dynamics are still unknown when the control task is finished. The researchers have not explored whether the neural network have learned the unknown dynamics, even for the same control task the neural networks have to be trained repeatedly, which is time and energy wasted. So it is meaningful to further investigate the neural networks’ability of learning the unknown dynamics in the stable adaptive closed loop control process. The learned knowledge is expected to be reused in the same or similar control tasks so that the repeated training phase can be avoided. Moreover, the adaptive neural network controller is expected to accumulate knowledge by experiences so that better control performance can be achieved.
According to deterministic learning theory, for an appropriately designed adaptive neural network controller, the sub-vector of the radial basis function networks’regression vector satisfy the persistent exciting condition when tracking period or period-like desired trajectory, the estimate errors of neural network weights are proved to be convergent to a small neighborhood of zero, and ultimately the unknown the nonlinearity could be learned by a constant neural network due to the local property of radial basis function networks.
In this thesis, by using the achievements of deterministic learning theory, robust learning control scheme is presented for robots with unknown dynamics and disturbances. In the stable closed loop control process, the regression vector of the designed robust adaptive neural network controller satisfies partial persistent exciting condition. By analyzing the linear time varying system obtained from the closed loop system, partial neural network weights convergence can be achieved. The unknown dynamics of closed loop robot system can be learned by neural network, and saved as experience knowledge in the form of constant neural weights. The learning enables us to understand the underlying characteristic of the unknown system dynamics. When repeat the same or similar control task, the controller can also reuse the learned dynamic knowledge and better control performance can be achieved with little efforts. Time and energy wasting repeated training phase can be avoided through the proposed scheme, both of the true learning and the reusing of learned knowledge are realized.
稳定自适应控制是近年来基于神经网络的非线性系统自适应控制方法的研究主流,在保证稳定性方面有了越来越严格的理论证明。但是自适应神经网络控制中的一个不足或局限就是网络需要反复训练,不像人脑一样具有一次学习的能力,而且不能将学习到的知识重新利用。同样基于自适应神经网络的机器人控制虽然取得了很大的成绩,但是对于系统的未知动力学在控制任务完成后仍然是未知的。研究者对于神经网络有没有真正学习到系统的未知动力学未进行探索,每次即使重复相同的控制任务都要进行网络的重新训练,而这一训练过程是耗时耗能的,所以很有必要进一步探讨神经网络在稳定的自适应闭环控制过程中学习未知动力学知识的能力,并且期望能将学习到的动力学知识运用到相同或者相似的控制任务中,避免网络的重复训练,同时使得自适应神经网络控制器能根据经验累积知识,改善控制性能。
根据确定学习原理,对于一个合理设计的自适应神经网络控制器,在跟踪周期或者类周期的参考轨迹时,其径向基函数网络的回归向量满足部分持续激励条件,进一步分析可得到网络估计权值的部分收敛,根据径向基函数网络的局部特性,最终系统的未知非线性能够由一个常值神经网络逼近。
本文利用确定学习的最新成果,提出了含有未知动力学和干扰的机器人鲁棒学习控制策略。在稳定的闭环控制过程中,所设计的鲁棒自适应神经网络控制器在跟踪周期或者类周期的参考轨迹时,回归向量满足部分持续激励条件,通过分析由闭环系统推导而来的线性时变系统的指数稳定性,可得到网络估计权值的部分收敛,从而神经网络可以学习到机器人闭环系统未知的动力学,并将学到的动力学作为经验知识以常值网络权值的形式表示。通过学习,使我们了解系统未知动力学模型特性成为可能,并且在下次重复相同或者相似的控制任务时,控制器可以调用以往所学动力学知识用于控制并获得更好的控制性能。该策略避免了耗时耗能的神经网络重新训练过程,使得机器人具有真正意义上的从经历中获取知识,表达知识,并将学到的知识再利用的能力。
In the past decades, artificial intelligence theory and methods such as neural networks, fuzzy logics and evolution algorithms have been used to control robot system. Neural networks have lots of advantages including universal approximation abilities, distributed architecture, accurate system mathematic model is not needed in control process and powerful ability of working with other control theory such as adaptive control, variable structure control, so neural networks have been widely applied to the control of robot system with unknown dynamics.
In recent years, stable adaptive control has been the main trend of neural network based adaptive control of nonlinear system, and there is stricter theoretical proof on system stability. But one of the shortness of adaptive neural networks is that the network need to be trained repeatedly, do not have the ability of learning as human brains and reusing the learned knowledge. Great achievements have been made toward adaptive neural networks based robot control, however, the system unknown dynamics are still unknown when the control task is finished. The researchers have not explored whether the neural network have learned the unknown dynamics, even for the same control task the neural networks have to be trained repeatedly, which is time and energy wasted. So it is meaningful to further investigate the neural networks’ability of learning the unknown dynamics in the stable adaptive closed loop control process. The learned knowledge is expected to be reused in the same or similar control tasks so that the repeated training phase can be avoided. Moreover, the adaptive neural network controller is expected to accumulate knowledge by experiences so that better control performance can be achieved.
According to deterministic learning theory, for an appropriately designed adaptive neural network controller, the sub-vector of the radial basis function networks’regression vector satisfy the persistent exciting condition when tracking period or period-like desired trajectory, the estimate errors of neural network weights are proved to be convergent to a small neighborhood of zero, and ultimately the unknown the nonlinearity could be learned by a constant neural network due to the local property of radial basis function networks.
In this thesis, by using the achievements of deterministic learning theory, robust learning control scheme is presented for robots with unknown dynamics and disturbances. In the stable closed loop control process, the regression vector of the designed robust adaptive neural network controller satisfies partial persistent exciting condition. By analyzing the linear time varying system obtained from the closed loop system, partial neural network weights convergence can be achieved. The unknown dynamics of closed loop robot system can be learned by neural network, and saved as experience knowledge in the form of constant neural weights. The learning enables us to understand the underlying characteristic of the unknown system dynamics. When repeat the same or similar control task, the controller can also reuse the learned dynamic knowledge and better control performance can be achieved with little efforts. Time and energy wasting repeated training phase can be avoided through the proposed scheme, both of the true learning and the reusing of learned knowledge are realized.
引文
[1]陈昱昆,钟映春,杨玲玲.机械臂轨迹跟踪控制的仿真[J].计算机仿真, 2005,22(11).
[2] Paul R C. Modeling trajectory calculation and servoing of a computer controlled arm. A. I. Memo 177, Stanford Artificial Intellegence Laboratory, Stanford University, 1972.
[3] J. J. Slotine. The Robust Control of Robot Manipulators[J]. The Inter. Journ. of Robotics Research, 1985, 4(2):49-64.
[4]王朝立,霍伟.一类不确定非完整动力学系统的鲁棒镇定及其在移动机器人中的应用[J].机器人, 1998, 20(6)
[5] LI Qingxiang, HU Yueming, PEI Hailong, et al. Robust Output Tracking for Mobile Robot[J], Control Theory and Applications, 1998, 15(4)
[6] J.J.Slotine, Li. W. Adaptive Manipulator Control: Case Study[J]. IEEE Transactions on Automatic Control, 1988,33(11):995-1003.
[7]彭金柱,王耀南,余洪山.基于神经网络的非完整移动机器人鲁棒跟踪控制[J].中国机械工程,2008,19(7).
[8] Yildirim S. Adaptive Robust Neural Controller for Robots[J]. Robotics and Autonomous Systems ,2004 , 46 : 175-184.
[9] Fierro R, Lewis F L. Control of a Nonholonomic Mobile Robot Using Neural Networks[J]. IEEE Trans. on Neural Network , 1998 , 9 (4) : 589-600.
[10]孙富春,孙增圻,张钹.机械手神经网络稳定自适应控制的理论与方法[M].高等教育出版社, 2005.
[11]裴海龙,周其节,梁天培.机械臂神经网络变结构控制器[J].控制理论与应用,1996,13(2).
[12] Chiman Kwan, Frank L. Lewis and Darren M. Dawson, Robust Neural network Control of Rigid-link Electrically Driven Robots[J]. IEEE Transaction on Neural Networks. 1998, 9(4):581-588.
[13]Lewis F.L., Dawson D.M. and Abdallah C.T.. Robot manipulator control: theory and practice [M], 2nd ed. New York: Marcel Dekker,2004: 125-127,431-458
[14] S. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence, and Robustness.Englewood Cliffs, NJ: Prentice-Hall, 1989.
[15] Wang C. and Hill D.J.. Learning from neural control[J]. IEEE Transactions on Neural Networks 2006,17(1):130-145
[16] J. Park and I. W. Sandberg, "Universal approximation using radial-basis-function net-works", Neural Computation, vol. 3, pp. 246-257, 1991.
[17] P. A. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1995.
[18] Kurdila A.J., Narcowich F.J. and Ward J. D. Persistancy of excitation in identification using radial basis function approximants [J]. SIAM J. Control and Optimization, 1995, 33(2): 625-642.
[19] Tengfei Liu and Cong Wang, Learning From Neural Control of General Brunovsky Systems, IEEE International Symposium on Intelligent Control, pp. 2366-2371, Germany, Oct. 2006.
[20] Liu TF, Wang C. Learning from neural control of strict feedback systems. In: IEEE international conference on control and automation Guangzhou, China; 2007.p.636-641.
[21] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[22] P. A. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1995.
[23] T Zhang and M Nakamura, High-Precision Contour Control by Gaussian Neural Network Controller for Industrial Articulated Robot Arm with Uncertainties, Transactions on Control, Automation and Systems Engineering, vol. 3(4), pp. 272-281, Dec. 2001.
[24] M. Kawato, K. Furukawa, and R. Suzuki,”A hierarchical neural-network model for control and learning of voluntary movement,”Biological Cybernetics, vol. 57, pp. 169-185, 1987.
[25] Yamada, Y., Kermanshahi, B., Tagawa, N. and Moriya, T., Intelligent control of robot arm using artificial neural networks, Electrotechnical Conference, 8th Mediterranean, vol. 2, pp. 1164-1167, May 1996.
[26] T Tsuji and Y Tanaka, On-line learning of robot arm impedance using neural networks, Robotics and Autonomous Systems, vol. 52(4), pp. 257- 271, Sep. 2005.
[27] Tsuji, T., Ito, K. and Morasso, P.G., Neural network learning of robot arm impedance inoperational space, IEEE Transactions on Systems, Man and Cybernetics, Part B, vol. 26(2), pp. 290-298, Apr.1996.
[28]L.Behera, S.Chaudhury and M.Gopal, Neuro-adaptive hybrid controller for robot-manipulator tracking control, IEEE Proceedings on Control Theory and Applications, vol. 143(3), pp. 270-275, May,1996.
[29] Robert M. Sanner and Jean-Jacques E. Slotine, Stable adaptive control of robot manipulators using neural networks, Neural Comput, vol. 7, pp. 753-788, 1994.
[30] Robert M. Sanner and Jean-Jacques E. Slotine, Structurally dynamic wavelet networks for adaptive control of robotic systems, International Journal of Control, vol. 70(3), pp. 405-421, June 1998.
[31] Robert M. Sanner and Makio Kosha, A mathematical model of the adaptive control of human motions, Biological Cybernetics, vol. 80, pp. 369-382, 1999.
[32] Frank L. Lewis, Kai Liu and Aydin Yesildirek, Neural net robot controller with guaranteed tracking performance, IEEE Transaction on Neural Networks, vol. 6(3), pp. 703-715, May 1995.
[33] Chiman Kwan, Frank L. Lewis and Darren M. Dawson, Robust neuralnetwork control of rigid-link electrically driven robots, IEEE Transaction on Neural Networks, vol. 9(4), pp. 581-588, July 1998.
[34] Chiman Kwan and F. L. Lewis, Robust back-stepping control of nonlinear systems using neural networks, IEEE Transactions on Systems, Man and Cybernetics, Part A, vol. 30(6), pp. 753-766,Nov. 2000.
[35] C. Baroglio, A. Giordana, M. Kaiser, M. Nuttin, and R. Piola, Learning Controllers for Industrial Robots, Machine Learning, vol. 23(2-3), pp. 221-249, May 1996.
[36] V. N. Vapnik, The Nature of Statistical Learning Theory, 2nd ed. New York: Springer-Verlag, 2000.
[37] F. L. Lewis, C. Abdallah, and D. M. Dawson, Control of Robot Manipulators. New York: MacMillan, 1993.
[38] S. S. Ge and C.Wang, Diret adaptive NN control of a class of nonlinear systems, IEEE Trans. Neural Netw., vol. 13, no. 1, pp. 214-221, Jan. 2002.
[39] S. S. Ge and C.Wang, Uncertain chaotic system control via adaptive neural design,International Journal of Bifurcation and Chaos, Vol. 12, No. 5 (2002) 1097-1109
[40] Fierro R, Lewis F L. Control of a Nonholonomic Mobile Robot: Backstepping Kinematics into Dynamics[J]. Journal of Robotic Systems, 1997, 14(3): 149-163.
[41] Jiang Z P, Nijmeijer H. Tracking Control of Mobile Robots: a Case Study in Backstepping [J]. Automatica, 997 , 33 (7):1393-1399.
[42]祝晓才,董国华,蔡自兴,胡德文.不确定曲面上非完整移动机器人的鲁棒镇定[J].动力学与控制学报, 2006 4(04).
[43] Yang J M, Kim J H. Sliding Mode Control for Trajectory of Nonholonomic Wheeled Mobile Robots [J]. IEEE Trans. on Robotics and Automation, 1999, 15 (3): 578-587.
[44]晁红敏,胡跃明,吴忻生.高阶滑模控制在非完整移动机器人鲁棒输出跟踪中的应用[J].控制理论与应用, 2002, 19(02).
[2] Paul R C. Modeling trajectory calculation and servoing of a computer controlled arm. A. I. Memo 177, Stanford Artificial Intellegence Laboratory, Stanford University, 1972.
[3] J. J. Slotine. The Robust Control of Robot Manipulators[J]. The Inter. Journ. of Robotics Research, 1985, 4(2):49-64.
[4]王朝立,霍伟.一类不确定非完整动力学系统的鲁棒镇定及其在移动机器人中的应用[J].机器人, 1998, 20(6)
[5] LI Qingxiang, HU Yueming, PEI Hailong, et al. Robust Output Tracking for Mobile Robot[J], Control Theory and Applications, 1998, 15(4)
[6] J.J.Slotine, Li. W. Adaptive Manipulator Control: Case Study[J]. IEEE Transactions on Automatic Control, 1988,33(11):995-1003.
[7]彭金柱,王耀南,余洪山.基于神经网络的非完整移动机器人鲁棒跟踪控制[J].中国机械工程,2008,19(7).
[8] Yildirim S. Adaptive Robust Neural Controller for Robots[J]. Robotics and Autonomous Systems ,2004 , 46 : 175-184.
[9] Fierro R, Lewis F L. Control of a Nonholonomic Mobile Robot Using Neural Networks[J]. IEEE Trans. on Neural Network , 1998 , 9 (4) : 589-600.
[10]孙富春,孙增圻,张钹.机械手神经网络稳定自适应控制的理论与方法[M].高等教育出版社, 2005.
[11]裴海龙,周其节,梁天培.机械臂神经网络变结构控制器[J].控制理论与应用,1996,13(2).
[12] Chiman Kwan, Frank L. Lewis and Darren M. Dawson, Robust Neural network Control of Rigid-link Electrically Driven Robots[J]. IEEE Transaction on Neural Networks. 1998, 9(4):581-588.
[13]Lewis F.L., Dawson D.M. and Abdallah C.T.. Robot manipulator control: theory and practice [M], 2nd ed. New York: Marcel Dekker,2004: 125-127,431-458
[14] S. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence, and Robustness.Englewood Cliffs, NJ: Prentice-Hall, 1989.
[15] Wang C. and Hill D.J.. Learning from neural control[J]. IEEE Transactions on Neural Networks 2006,17(1):130-145
[16] J. Park and I. W. Sandberg, "Universal approximation using radial-basis-function net-works", Neural Computation, vol. 3, pp. 246-257, 1991.
[17] P. A. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1995.
[18] Kurdila A.J., Narcowich F.J. and Ward J. D. Persistancy of excitation in identification using radial basis function approximants [J]. SIAM J. Control and Optimization, 1995, 33(2): 625-642.
[19] Tengfei Liu and Cong Wang, Learning From Neural Control of General Brunovsky Systems, IEEE International Symposium on Intelligent Control, pp. 2366-2371, Germany, Oct. 2006.
[20] Liu TF, Wang C. Learning from neural control of strict feedback systems. In: IEEE international conference on control and automation Guangzhou, China; 2007.p.636-641.
[21] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[22] P. A. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1995.
[23] T Zhang and M Nakamura, High-Precision Contour Control by Gaussian Neural Network Controller for Industrial Articulated Robot Arm with Uncertainties, Transactions on Control, Automation and Systems Engineering, vol. 3(4), pp. 272-281, Dec. 2001.
[24] M. Kawato, K. Furukawa, and R. Suzuki,”A hierarchical neural-network model for control and learning of voluntary movement,”Biological Cybernetics, vol. 57, pp. 169-185, 1987.
[25] Yamada, Y., Kermanshahi, B., Tagawa, N. and Moriya, T., Intelligent control of robot arm using artificial neural networks, Electrotechnical Conference, 8th Mediterranean, vol. 2, pp. 1164-1167, May 1996.
[26] T Tsuji and Y Tanaka, On-line learning of robot arm impedance using neural networks, Robotics and Autonomous Systems, vol. 52(4), pp. 257- 271, Sep. 2005.
[27] Tsuji, T., Ito, K. and Morasso, P.G., Neural network learning of robot arm impedance inoperational space, IEEE Transactions on Systems, Man and Cybernetics, Part B, vol. 26(2), pp. 290-298, Apr.1996.
[28]L.Behera, S.Chaudhury and M.Gopal, Neuro-adaptive hybrid controller for robot-manipulator tracking control, IEEE Proceedings on Control Theory and Applications, vol. 143(3), pp. 270-275, May,1996.
[29] Robert M. Sanner and Jean-Jacques E. Slotine, Stable adaptive control of robot manipulators using neural networks, Neural Comput, vol. 7, pp. 753-788, 1994.
[30] Robert M. Sanner and Jean-Jacques E. Slotine, Structurally dynamic wavelet networks for adaptive control of robotic systems, International Journal of Control, vol. 70(3), pp. 405-421, June 1998.
[31] Robert M. Sanner and Makio Kosha, A mathematical model of the adaptive control of human motions, Biological Cybernetics, vol. 80, pp. 369-382, 1999.
[32] Frank L. Lewis, Kai Liu and Aydin Yesildirek, Neural net robot controller with guaranteed tracking performance, IEEE Transaction on Neural Networks, vol. 6(3), pp. 703-715, May 1995.
[33] Chiman Kwan, Frank L. Lewis and Darren M. Dawson, Robust neuralnetwork control of rigid-link electrically driven robots, IEEE Transaction on Neural Networks, vol. 9(4), pp. 581-588, July 1998.
[34] Chiman Kwan and F. L. Lewis, Robust back-stepping control of nonlinear systems using neural networks, IEEE Transactions on Systems, Man and Cybernetics, Part A, vol. 30(6), pp. 753-766,Nov. 2000.
[35] C. Baroglio, A. Giordana, M. Kaiser, M. Nuttin, and R. Piola, Learning Controllers for Industrial Robots, Machine Learning, vol. 23(2-3), pp. 221-249, May 1996.
[36] V. N. Vapnik, The Nature of Statistical Learning Theory, 2nd ed. New York: Springer-Verlag, 2000.
[37] F. L. Lewis, C. Abdallah, and D. M. Dawson, Control of Robot Manipulators. New York: MacMillan, 1993.
[38] S. S. Ge and C.Wang, Diret adaptive NN control of a class of nonlinear systems, IEEE Trans. Neural Netw., vol. 13, no. 1, pp. 214-221, Jan. 2002.
[39] S. S. Ge and C.Wang, Uncertain chaotic system control via adaptive neural design,International Journal of Bifurcation and Chaos, Vol. 12, No. 5 (2002) 1097-1109
[40] Fierro R, Lewis F L. Control of a Nonholonomic Mobile Robot: Backstepping Kinematics into Dynamics[J]. Journal of Robotic Systems, 1997, 14(3): 149-163.
[41] Jiang Z P, Nijmeijer H. Tracking Control of Mobile Robots: a Case Study in Backstepping [J]. Automatica, 997 , 33 (7):1393-1399.
[42]祝晓才,董国华,蔡自兴,胡德文.不确定曲面上非完整移动机器人的鲁棒镇定[J].动力学与控制学报, 2006 4(04).
[43] Yang J M, Kim J H. Sliding Mode Control for Trajectory of Nonholonomic Wheeled Mobile Robots [J]. IEEE Trans. on Robotics and Automation, 1999, 15 (3): 578-587.
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