基于MPC和PID的脚轮式全向移动平台轨迹跟踪  

Trajectory tracking of caster-type omnidirectional mobile platform based on MPC and PID

作　　者：李华夏 黄晓蓉 沈安林 蒋鹏 彭忆强 隋立起[4] LI Huaxia;HUANG Xiaorong;SHEN Anlin;JIANG Peng;PENG Yiqiang;SUI Liqi(School of Automobile and Transportation,Xihua University,Chengdu Sichuan 610039,China;Vehicle Measurement,Control and Safety Key Laboratory of Sichuan Province(Xihua University),Chengdu Sichuan 610039,China;Provincial Engineering Research Center for New Energy Vehicle Intelligent Control and Simulation Test Technology of Sichuan(Xihua University),Chengdu Sichuan 610039,China;Yibin Fengchuan Powertrain Technology Company Limited,Yibin Sichuan 644600,China)

机构地区：[1]西华大学汽车与交通学院,成都610039 [2]汽车测控与安全四川省重点实验室(西华大学),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(西华大学),成都610039 [4]宜宾丰川动力科技有限公司,四川宜宾644600

出　　处：《计算机应用》2024年第7期2285-2293,共9页journal of Computer Applications

基　　金：四川省科技厅重点研发项目(2020YFG0211);四川省科技厅国际合作项目(2023YFH0065);四川省科技创新基地建设项目(2022ZYD0125)。

摘　　要：针对现有运动控制策略无法保证独立驱动脚轮式全向移动平台位姿的高精度控制问题,提出一种基于模型预测控制(MPC)和PID控制相结合的双闭环轨迹跟踪控制策略。首先,利用运动学几何关系建立独立驱动脚轮式全向移动平台在世界坐标系下的三自由度运动学模型,基于正交分解法建立平台在机器人坐标系下的逆运动学模型,以反映平台中心点速度与各个脚轮转速间的关系;其次,采用MPC并基于三自由度运动学模型设计位姿控制器,使平台对期望轨迹进行位姿跟踪,并在考虑多目标约束条件的情况下通过位姿控制器求解出最优控制量;最后,采用PID设计速度控制器,用于跟踪位姿控制器输出的期望速度,通过平台逆运动学模型计算得到期望轮速,从而驱动平台实现全向运动。通过仿真验证了所提控制策略的有效性,平台能有效跟踪直线轨迹和圆形轨迹。仿真结果表明,与通过平台转角逆运动学模型解耦驱动轮速的位置单环轨迹跟踪控制策略相比,加入速度内环后系统超调量下降97.23%,响应时间缩短36.84%。Aiming at the problem that existing motion control strategies cannot guarantee high-precision control for independently driven caster-type omnidirectional mobile platform,a double closed-loop trajectory tracking control strategy was proposed by combining Model Predictive Control(MPC)and Proportion Integral Differential(PID)control.Firstly,kinematic geometric relationship was used to establish three-degree-of-freedom kinematic model of independently driven caster-type omnidirectional mobile platform in world coordinate system,and based on orthogonal decomposition method,inverse kinematic model of platform in robot coordinate system was established to reflect the relationship between center point speed of platform and rotation speed of each caster.Secondly,MPC was used to design position controller based on threedegree-of-freedom kinematic model,so that platform could track positions of desired trajectory,and the optimal control quantity was solved through the position controller while taking multi-objective constraints into account.Finally,PID was used to design speed controller to track desired speed output by position controller.Desired caster speed was calculated through the inverse kinematic model of platform,thereby driving platform to achieve omnidirectional motion.The effectiveness of the proposed control strategy was verified through simulation,and the platform could effectively track linear trajectories and circular trajectories.Simulation results show that compared with position single-loop trajectory tracking control strategy that decouples drive caster speed through angle inverse kinematic model of platform,the system overshoot is reduced by 97.23%and the response time is shortened by 36.84%after adding speed inner loop.

关 键 词：独立驱动脚轮式全向移动平台 模型预测控制 轨迹跟踪 PID控制 运动学模型 

分 类 号：TP273.4[自动化与计算机技术—检测技术与自动化装置]