﻿ 两轮差速AGV的轨迹跟踪控制研究 Study on Trajectory Tracking Control of Two-Wheel Difference Speed of AGV

Software Engineering and Applications
Vol.06 No.04(2017), Article ID:21608,9 pages
10.12677/SEA.2017.64007

Study on Trajectory Tracking Control of Two-Wheel Difference Speed of AGV

Lipeng Yang, Wenfeng Zhang, Hao Wang

Shanghai University of Electric Power, College Of Energy and Mechanical Engineering, Shanghai

Received: Jul. 18th, 2017; accepted: Aug. 1st, 2017; published: Aug. 7th 2017

ABSTRACT

In view of trajectory tracking control problem of AGV, a Back-stepping control algorithm is proposed. Firstly, the AGV kinematics model and tracking pose error model are established; Then, the whole nonlinear system is decomposed into several sub-systems by using Back-stepping method, and the Lyapunov function and the intermediate virtual control are constructed and has been back to export control law of system step by step. Finally, the simulation experiment of line tracking and circular tracking was carried out in MATLAB environment. The results show that the tracking error converges to zero quickly, and trajectory tracking effect is wonderful. Back-stepping method combined with Lyapunov theory design the controller, not only can achieve AGV on the reference trajectory global asymptotic tracking, but also has high accuracy and robustness.

Keywords:AGV, Back-Stepping, Trajectory Tracking, Lyapunov

1. 引言

2. AGV的运动学模型

AGV是通过左右两个驱动轮之间的速度差来改变小车的运动方向，属于两自由度的驱动系统。因为驱动轮和地面的滚动约束比较复杂，针对小车的实际运行情况建立精确的运动学模型是比较困难的。为了进行运动学建模，将问题做如下假设和简化：假设车轮在路面上低速运行，忽略车轮滑动的影响，并且两驱动轮保持在同一轴线上 [7] 。

(1)

(2)

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AGV位姿误差模型如图2所示，小车的实际位姿为，参考位姿为，位姿

Figure 1. Two-wheel differential drive AGV model

Figure 2. AGV pose error model

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3. Back-stepping 控制律的设计

3.1. Back-stepping设计步骤

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Back-stepping方法的设计思想是把每一个子系统中的作为虚拟控制量，通过适当的来满足前面的系统状态的渐进稳定，因为不是实际的控制量，所以引进误差变量，通过设定虚拟反馈控制变量具有线性特性，使整个系统达到渐进稳定。

(8)

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，令

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，则渐进稳定；若，需要引入虚拟反馈变量使误差变量具有渐近稳定性。按照这种方法递推下去，找到一般的虚拟反馈变量和Lyapunov函数。

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3.2. 控制器的设计

，则，即趋于常数，不能对系统进行控制。假设为虚拟控制输入，然后找到合适虚拟反馈状态使

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，则。AGV的轨迹跟踪控制律的设计输入为，取误差变量为：

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4. 仿真验证

1) 当AGV按照直线路径进行跟踪时：初始位姿误差为，期望速度为，仿真结果如图3所示。

2) 当AGV按照圆路径进行跟踪时：初始位姿误差为，期望速度为，仿真结果如下图3~图8所示。

Figure 3. Tracking error of linear trajectory

Figure 4. Linear trajectory tracking speed changes

Figure 5. Linear trajectory tracking pose error curve

Figure 6. Tracking error of circular trajectory

Figure 7. Linear trajectory tracking speed changes

Figure 8. Round track tracking pose error curve

5. 结论

Study on Trajectory Tracking Control of Two-Wheel Difference Speed of AGV[J]. 软件工程与应用, 2017, 06(04): 59-67. http://dx.doi.org/10.12677/SEA.2017.64007

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