1. Institute of Robotics and Information Automatic System (IRIAS), Nankai University, Tianjin 300071, China;
2. Tianjin Key Laboratory of Intelligent Robotics (tjKLIR), Tianjin 300071, China
For an omnidirectional mobile robot with active caster wheels, a redundant encoders based dead reckoning method is proposed, and a trajectory tracking controller is further presented in the presence of velocity saturation constraints. Specifically, the reasons for wheel slipping are analyzed firstly, and then a passive caster wheel with redundant encoders are designed and equipped on the robot, inspired by the fact that the passive caster wheels present less slipping than the active casters. Subsequently, the dead reckoning problem is transformed into an equality-constrained linear least square problem. Experimental results show that, compared with the traditional dead reckoning method without redundant encoders, the proposed dead reckoning method alleviates the effects of the slipping on localization and improves the localization precision. Considering that the practical velocities are bounded for motors, a trajectory tracking controller is designed in the presence of such input saturation constraints, and the stability is proven by Lyapunov-based techniques while ensuring the velocity saturation constraints to be satisfied. Both simulation and experimental results demonstrate that the proposed controller presents superior performance, while satisfying the control saturation constraints.
[1] 曹其新,张蕾.轮式自主移动机器人[M].上海:上海交 通大学出版社,2012. Cao Q X, Zhang L. Wheeled autonomous mobile robot[M]. Shanghai: Shanghai Jiaotong University Press, 2012.[2] 赵冬斌,易建强.全方位移动机器人导论[M].北京:科 学出版社,2010. Zhao D B, Yi J Q. Introduction to the omnidirectional mobile robot[M]. Beijing: Science Press, 2010.[3] Zhang X B, Fang Y C, Liu X. Motion-estimation-based visual servoing of nonholonomic mobile robots[J]. IEEE Transactions on Robotics, 2011, 27(6): 1167-1175.[4] Siegwart R, Nourbakhsh I R, Scaramuzza D. Introduction to autonomous mobile robots[M]. Cambridge, USA: MIT Press, 2006.[5] 赵祥敏.全方位移动机器人的研制[D].哈尔滨:哈尔滨 工业大学,2008. Zhao X M. The development of the omni-directional mobile robot. A master’s degree thesis, Harbin: Harbin Institute of Technology, 2008.[6] 赵冬斌,易建强,邓旭玥.全方位移动机器人结构和运动 分析[J].机器人,2003,25(5):394-398. Zhao D B, Yi J Q, Deng X Y. Structure and kinematic analysis of omni-directional mobile robots[J]. Robot, 2003, 25(5): 394- 398.[7] Yi B J, Kim W K. The kinematics for redundantly actuated omnidirectional mobile robots[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2000: 2485-2492.[8] Chung J H, Yi B J, Kim W K, et al. The dynamic modeling and analysis for an omnidirectional mobile robot with three caster wheels[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2003: 521-527.[9] Deng X Y, Zhao D B, Yi J Q. Motion and squeeze force control for omnidirectional wheeled mobile robots[C]//Proceedings of the American Control Conference. Piscataway, USA: IEEE, 2006: 5608-5613.[10] Zhao D B, Deng X Y, Yi J Q. Motion and internal force control for omnidirectional wheeled mobile robots[J]. IEEE/ASME Transactions on Mechatronics, 2009, 14(3): 382-387.[11] 邓旭玥,易建强,赵冬斌.一种全方位移动机器人的控制 方法[J].电机与控制学报,2005,9(2):139-144. Deng X Y, Yi J Q, Zhao D B. A control approach to an omnidirectional mobile robot[J]. Electric Machines and Control, 2005, 9(2): 139-144.[12] 邓旭玥,易建强,赵冬斌.一种全方位移动机器人的运动 学分析[J].机器人,2004,26(1):49-53. Deng X Y, Yi J Q, Zhao D B. Kinematic analysis of an omnidirectional mobile robot[J]. Robot, 2004, 26(1): 49-53.[13] Park T B, Lee J H, Yi B J. Optimal design and actuator sizing of redundantly actuated omni-directional mobile robots[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2002: 732-737.[14] Kim H G, Huan D N, Park J C, et al. Design of the active split offset casters based omni-directional vehicle in high acceleration condition[C]//IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Piscataway, USA: IEEE, 2012: 714-718.[15] Jung E J, Lee H Y, Lee J H, et al. Navigation of an omnidirectional mobile robot with active caster wheels[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2008: 1659-1665.[16] Jung E J, Kim S M, Yi B J. Two-leveled obstacle avoidance scheme using a kinematically redundant omni-directional mobile robot[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA: IEEE, 2010: 3949- 3954.[17] Campion G, Bastin G, d’Andrea-Novel B. Structural properties and classification of kinematic and dynamic models of wheeled mobile robots[J]. IEEE Transactions on Robotics and Automation, 1996, 12(1): 47-62.[18] 周连第.关于用拉格朗日乘子法求解线性等式约束最小二 乘问题[J].计算数学,1979,1(3):264-271. Zhou L D. On the process of solving the linear equality constrained least squares problem by Lagrangian multiplier method[J]. Mathematica Numerica Sinica, 1979, 1(3): 264-271.[19] 方勇纯,卢桂章.非线性系统理论[M]. 北京:清华大学出 版社,2009. Fang Y C, Lu G Z. Nonlinear systems theory[M]. Beijing: Tsinghua University Press, 2009.[20] 张雪波,路晗,方勇纯,等.室外环境下PTZ 摄像机全自 动标定技术及其应用[J].机器人,2013,35(4):385-393. Zhang X B, Lu H, Fang Y C, et al. An automatic calibration method for outdoor PTZ cameras and its applications[J]. Robot, 2013, 35(4): 385-393.