基于模型预测控制的双轮平衡轮椅轨迹跟踪

常宏，王赜^*

内蒙古工业大学机械工程学院，内蒙古 呼和浩特  010051

摘要：为实现双轮平衡轮椅的自主循迹出行，根据欧拉-拉格朗日方程建立双轮平衡轮椅的动力学模型，通过差动几何模型建立运动关系，采用Pure Pursuit算法规划系统的目标运动状态，分别采用模型预测控制（model predictive control，MPC）及线性二次型最优控制（linear quadratic regulator，LQR）对双轮平衡轮椅进行平衡控制及运动状态追踪。通过软件Simulink搭建双轮平衡轮椅控制仿真系统，验证双轮平衡轮椅系统分别采用LQR和MPC控制器时的轨迹跟踪效果及跟踪平稳性。仿真结果表明：MPC控制器的动态响应速度较LQR控制器快，MPC控制器作用下车体能快速恢复稳定状态；轨迹跟踪时，MPC控制器在启动转向及终点位置对车体倾角及速度的稳定控制优于LQR控制器。

关键词：双轮平衡轮椅；LQR控制器；MPC控制器；轨迹追踪

Trajectory tracking of two-wheel balanced wheelchair based on model predictive control

CHANG Hong, WANG Ze^*

School of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot 010051, China

Abstract: In order to achieve the autonomous tracking travel of the two-wheel balanced wheelchair, a dynamic model of the two-wheel balanced wheelchair is established based on the Euler-Lagrange equation, and the motion relationship is established through the differential geometric model. The Pure Pursuit algorithm is used to plan the target motion state of the system, and model predictive control（MPC）and linear quadratic optimal control（LQR）are used to balance and track the motion state of the two-wheel balanced wheelchair. The simulation system for the control of the two-wheel balanced wheelchair is built through software Simulink to verify the trajectory tracking effect and tracking stability of the two-wheel balanced wheelchair system when LQR and MPC controllers are used. The simulation results show that the dynamic response speed of the MPC controller is faster than that of the LQR controller, and the MPC controller can quickly restore the stable state of the vehicle body when acting on the vehicle body; when tracking the trajectory, the MPC controller has better stable control of the vehicle body inclination angle and speed at the starting and ending positions than the LQR controller.

Keywords: two-wheel balanced wheelchair; LQR controller; MPC controller; trajectory tracking