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

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.