作者：张天宇1, 彭忆强1,2,3, 黄晓蓉1,3, 孙树磊1,2,3, 何灼馀1,3
作者单位：1. 西华大学汽车与交通学院，四川 成都 610039;
2. 汽车测控与安全四川省重点实验室，四川 成都 610039;
3. 四川省新能源汽车智能控制与仿真测试技术工程研究中心，四川 成都 610039
关键词：全向移动平台;奇异位形;动力学模型简化;双闭环模糊PID
摘要：
针对装配有3个单电机脚轮的全驱动全向移动平台（以下简称平台）运动控制问题，首先，采用正交分解法，根据纯滚动约束条件建立平台运动学模型；对于速度雅可比矩阵不可逆时平台处于奇异位形，失去全向移动能力的问题，通过耦合转角运动学和转向角运动学，设计耦合因子识别平台当前位形和奇异位形靠近程度，动态调节平台摆脱奇异位形。其次，采用拉格朗日法建立平台动力学模型，分析动力学Matlab仿真结果，消除转向角对平台的影响，合理简化动力学模型。最后，设计基于逆动力学的双闭环模糊PID控制策略使平台跟踪期望速度。仿真结果表明，耦合运动学模型可驱动平台产生特定运动方式摆脱奇异位形；动态耦合因子可减小转速超调量，降低驱动轮响应时间；在基于逆动力学的双闭环模糊PID控制策略作用下，平台实际速度能够快速稳定的收敛于期望速度。
Motion control and simulation of caster wheeled omnidirectional mobile platform
ZHANG Tianyu1, PENG Yiqiang1,2,3, HUANG Xiaorong1,3, SUN Shulei1,2,3, HE Zhuoyu1,3
1. School of Automobile and Transportation, Xihua University, Chengdu 610039, China;
2. Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Chengdu 610039, China;
3. Provincial Engineering Research Center for New Energy Vehicle Intelligent Control and Simulation Test Technology of Sichuan, Chengdu 610039, China
Abstract: For the motion control problem of a fully driven omnidirectional moving platform (hereinafter referred to as the platform) equipped with three single motor casters, the kinematics model of the platform was firstly established according to the pure rolling constraints by adopting the orthogonal decomposition method. When the platform is in singular position, it will lose omni-directional mobility and the velocity Jacobian is irreversible. Through coupling angle kinematics and steering angle kinematics, coupling factors are designed to identify the proximity between the platform's current position and singular position and the platform is dynamically adjusted to get rid of singular position. Secondly, the Lagrangian method is adopted to establish the platform dynamics model, and the platform's dynamics is analyzed with Matlab software. The simulation is used to eliminate the influence of steering angle on the platform, and reasonably simplify the dynamics model. Then, a double closed loop fuzzy PID control strategy based on inverse dynamics is designed to track the expected speed of the platform. The simulation results show that the coupled kinematics model can drive the platform to generate a specific motion mode to get rid of the singular configuration. Dynamic coupling factor can reduce speed overshoot and drive wheel response time. Under the action of the double closed loop fuzzy PID control strategy based on inverse dynamics, the actual velocity of the platform can converge to the expected velocity rapidly and stably.
Keywords: omnidirectional mobile platform;singular configuration;dynamics model simplification;double closed loop fuzzy PID
2021, 47(7):109-118,124 收稿日期: 2020-09-29;收到修改稿日期: 2020-11-08
基金项目: 国家重点研发计划项目（2018YFB1201603）；四川省科技厅重点研发项目（2020YFG0211，2018GZ0110，2020YFG0023）；四川省青年科技创新研究团队资助项目(2015TD0021)；四川省教育厅科研创新团队资助项目(17TD0035)；“西华杯”大学生创新创业项目(2020144)
作者简介: 张天宇(1994-),男,四川成都市人,硕士研究生,专业方向为汽车电控技术
参考文献
[1] 李阳, 刘子明, 陈庆盈. 考虑打滑干扰的解耦式主动脚轮全向移动机器人跟踪控制[J]. 中国机械工程学报, 2020, 31(18): 2247-2253
[2] 曾志雄, 余桥东, 吕恩利. 巡检机器人底盘设计与实验[J]. 中国农业机械化学报, 2020, 41(7): 55-61
[3] 叶长龙, 李怀勇, 马书根. 具有MY轮的全方位移动机器人运动学研究[J]. 机器人, 2012, 34(2): 144-151
[4] BRUNO S, OUSSAMA K. Springer handbook of robotics[M]. Springer, 2016: 391-393.
[5] AHMED K E. Motion control of holonomics wheeled mobile robot with modular actuation[D]. Mannheim: The University of Mannheim, 2010.
[6] 李宪华, 盛蕊, 张雷刚. 六自由度模块化机器人手臂奇异构形分析[J]. 农业机械学报, 2017, 48(7): 376-382
[7] JAE H C, BYUNG J Y, WHEE K K, et al. The dynamic modeling and analysis for an omnidirectional mobile robot with three caster wheels[C]// International Conference on Robotics and Automation. IEEE, 2003: 521-527.
[8] KIM D, KWON W H, PARK H S. Geometric kinematics and applications of mobile robot[C]//2003 International Conference on Robotics and Automation. IEEE, 1(2003): 376-384.
[9] SHI C S. Speed control of wheeled mobile robots using pid with dynamic and kinematic modelling[C]//2017 International Conference on Innovations in Information Embedded and Communication Systems (ICⅡECS). IEEE, 2017: 1523-1529.
[10] SOUDBAKHSH D, ESKANDARIAN A. Comparison of linear and non-linear controllers for active steering of vehicles in evasive maneuvers[J]. Journal of Systems and Control Engineering, 2012, 226(12): 215-232
[11] 倪洪杰, 王宏霞, 俞立. 轮式移动机器人快速轨迹跟踪[J]. 哈尔滨工业大学学报, 2020, 52(10): 167-174
[12] 孙棣华, 崔明月, 李永福. 具有参数不确定性的轮式移动机器人自适应控制[J]. 控制理论与应用, 2012, 29(9): 1198-1204
[13] 庄园, 张宁宁, 马龙博, 等. 液体流量标准装置流量控制系统设计[J]. 中国测试, 2020, 46(11): 126-131
[14] MUIR P F. Modeling and control of wheeled mobile robot[D]. Pittsburgh: Carnegie Mellon University, 1987.
[15] 王立新. 模糊系统与模糊控制教程[M]. 北京: 清华大学出版社, 2003: 198-200.
