﻿ 基于智能优化算法的Pendubot轨迹规划与控制方法设计
 控制与决策  2020, Vol. 35 Issue (5): 1085-1090 0

### 引用本文 [复制中英文]

[复制中文]
WANG Le-jun, WANG Ya-wu, LAI Xu-zhi, WU Min. Trajectory planning and control method for Ppendubot based on intelligent optimization algorithm[J]. Control and Decision, 2020, 35(5): 1085-1090. DOI: 10.13195/j.kzyjc.2019.0899.
[复制英文]

### 文章历史

1. 中国地质大学(武汉) 自动化学院，武汉 430074;
2. 复杂系统先进控制与智能自动化湖北省重点实验室，武汉 430074

Trajectory planning and control method for Ppendubot based on intelligent optimization algorithm
WANG Le-jun , WANG Ya-wu , LAI Xu-zhi , WU Min
1. School of Automation, China University of Geosciences, Wuhan 430074, China;
2. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China
Abstract: Taking the Pendubot moving in vertical plane motion as the research object, a trajectory planning and control method based on the intelligent optimization algorithm is proposed to solve the problem that it is difficult to transit from swing-up area to balance area in the control process. Firstly, a forward trajectory from the initial angle to the middle angle and a reverse trajectory from the middle angle to the target angle are planned for the Pendubot. The unactuated link moves under the action of system coupling relation, and the corresponding end point of the Pendubot moves to the relevant position. The genetic algorithm is used to optimize the trajectory parameters, so that the forward and reverse trajectories are combined into a driving link trajectory from the initial angle to the target angle, and the corresponding Pendubot terminal trajectory moves from the vertical downward balance position to the vertical upward balance position. Then, a tracking controller is designed to make the driving link move to the target angle along the optimized trajectory of the driving link, the end point of Pendubot also moves to the vertical upward balance position in virtue of the existence of coupling relationship. Due to the influence of gravity, it is difficult for the Pendubot to stabilize the end point at the vertical upward position for a long time. Thus, the stabilization controller is designed to keep the end point stable at the vertical upward balance position. Finally, the effectiveness of the proposed method is proved by simulation experiments, the advantages of this method in singularity avoidance, controller design and control effect are illustrated by comparison.
Keywords: Pendubot    trajectory planning    genetic algorithm    tracking controller    stabilization controller
0 引言

1 Pendubot动力学模型

 图 1 Pendubot模型示意图

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g=9.8N/kg; a1a2a3a4a5为模型参数, 表达式见文献[20].

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2 轨迹规划

2.1 轨迹设计

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q1m确定后, Γ1Γ2拼合为一条由初始角度q10到目标角度q1d的完整轨迹, 记为Γ. 图 2为轨迹Γ的示意图.

 图 2 轨迹Γ示意图

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2.2 轨迹参数优化

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step 1:设定基本参数:种群数目N, 遗传代数gen, 最大遗传代数G, 变量数Nvar, 参数初始范围, 选择因子ns, 交叉因子nc, 变异因子nm.

step 2:初始化参数(q1m, k1, k2), 将(q1m, k1, k2)代入设计的轨迹(11)和(12)中, 结合系统动力学模型(1)和(2), 计算.

step 3:将代入式(14), 计算评价函数f.

step 4:如果f < δ(δ为正数), 则(q1m, k1, k2)=(q1m, k1, k2)|gen, 算法结束; 否则, 经过变异、交叉和选择操作, 更新(q1m, k1, k2), gen=gen+1, 转至step 2.

3 控制器设计

3.1 跟踪控制器设计

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V1求导, 可得

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, 则s1 ≡ 0.根据LaSalle不变集原理, 当t → ∞时, s1 →0, 驱动连杆跟踪轨迹Γ运动到q1d.由第2节分析可知, 当驱动连杆沿优化后的轨迹Γ由初始角度q10运动到目标角度q1d时, 对应的Pendubot末端点沿着轨迹Γy由垂直向下位置运动至垂直向上平衡位置.

3.2 镇定控制器设计

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V2求导, 可得

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, s2 ≡ 0, 即t → ∞时, s2 → 0.虽然在t → ∞时, 滑模跟踪控制器可以实现s2→ 0, 但却无法保证e1→ 0, , e2→ 0, .

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 图 3 Pendubot控制过程
4 仿真实验及分析

4.1 仿真1

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 图 4 第1组仿真结果
4.2 仿真2

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 图 5 第2组仿真结果
5 结论

1) 将轨迹规划方法应用于垂直Pendubot, 利用遗传算法优化轨迹参数, 从而间接得到由垂直向下位置直接运动至垂直向上位置的末端点轨迹.控制过程中无需限定摇起区和平衡区的范围, 解决了分区控制中难以从摇起区过渡至平衡区的问题.

2) 控制器设计简单.当跟踪优化后的驱动连杆轨迹运动至目标角度时, 各连杆角度、角速度均收敛到目标值, 控制力矩收敛到零, 在控制器切换时力矩不会出现较大的突变, 切换更加平滑.

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