﻿ 基于优化人工势场法的无人艇局部路径规划
 舰船科学技术  2022, Vol. 44 Issue (16): 69-73    DOI: 10.3404/j.issn.1672-7649.2022.16.013 PDF

Local path planning of unmanned boat based on optimized artificial potential field method
LI Jia-lin, ZHANG Jian-qiang, LI Chun-lai
College of Weaponry Engineering , Naval University of Engineering, Wuhan 430033, china
Abstract: In order to solve the problems of the traditional artificial potential field method in the local path planning of the unmanned boat, it is easy to fall into the local minimum, the target is not reachable, and the safety of the unmanned boat during the navigation process, the traditional artificial potential field method is optimized. The introduction of a threshold solves the problem of collision with obstacles due to excessive gravity during the path planning process of the UAV. Proposes the concept of fuzzy far and near boundary points to solve the problem of unreachable targets; combines the simulated annealing algorithm to solve the local minimum value problem. When the UAV falls into the local minimum point, the Metropolis criterion is used to jump out of the local minimum point with a certain probability. The Matlab simulation results show that the improved artificial potential field method can help the UAV reach the target point safely in a multi-obstacle environment.
Key words: USV     local path planning     artificial potential field method     simulated annealing method
0 引　言

1 人工势场法

1.1 引力场

 $\mathop U\nolimits_{{{att}}} \left( q \right) = \frac{1}{2}\varepsilon \mathop \rho \nolimits^2 \left( {q,\mathop q\nolimits_{goal} } \right)。$ (1)

 $\mathop F\nolimits_{{{att}}} \left( q \right) = - \nabla \mathop U\nolimits_{att} \left( q \right) = \varepsilon \left( {\mathop q\nolimits_{goal} - q} \right)。$ (2)
1.2 斥力场

 $\mathop U\nolimits_{{{rep}}} \left( q \right) = \left\{ {\begin{array}{*{20}{l}} \dfrac{1}{2}\eta \left( {\dfrac{1}{{\rho \left( {q,\mathop q\nolimits_{obs} } \right)}} - \dfrac{1}{{\mathop \rho \nolimits_0 }}} \right)，{\rm{i}}{\rm{f}}\;\rho \left( {q,\mathop q\nolimits_{obs} } \right) \leqslant \mathop \rho \nolimits_0 ，\\ 0，{\rm{i}}{\rm{f}}\rho \left( {q,\mathop q\nolimits_{obs} } \right) > \mathop \rho \nolimits_0 。\end{array}} \right.$ (3)

 $\begin{gathered} \mathop F\nolimits_{{\text{rep}}} \left( q \right) = - \nabla \mathop U\nolimits_{rep} \left( q \right) = \\ \left\{ {\begin{array}{*{20}{l}} \eta \left( {\dfrac{1}{{\rho \left( {q,\mathop q\nolimits_{obs} } \right)}} - \dfrac{1}{{\mathop \rho \nolimits_0 }}} \right)\dfrac{1}{{\mathop \rho \nolimits^2 \left( {q,\mathop q\nolimits_{obs} } \right)}}\dfrac{{\partial \rho \left( {q - \mathop q\nolimits_{obs} } \right)}}{{\partial q}},\\ {\rm{i}}{\rm{f}}\;\rho \left( {q,\mathop q\nolimits_{obs} } \right) \leqslant \mathop \rho \nolimits_0 ，\\ {0,{\rm{i}}{\rm{f}}\;\rho \left( {q,\mathop q\nolimits_{obs} } \right) > \mathop \rho \nolimits_0 } 。\end{array}} \right. \\ \end{gathered}$ (4)

 $F\left( {{q}} \right) = \mathop F\nolimits_{att} \left( q \right) + \sum\limits_{i = 1}^m {\mathop F\nolimits_{rep} } \left( q \right)。$ (5)
2 模拟退火法

 $\begin{gathered} P= \left\{ {\begin{array}{*{20}{l}} 1\text{，}E\left(\text{n}+1\right) < E\left(n\right)，\\ {{\displaystyle e}}{-\dfrac{E\left(n+1\right)-E\left(n\right)}{T}},E\left(\text{n}+1\right)\geqslant E\left(n\right)。\end{array}} \right. \\ \end{gathered}$ (6)

3 人工势场法存在的问题

1）当目标点与障碍物的距离较远时，无人艇与目标点的引力较大，与障碍物的斥力较小。此时，障碍物产生的引力远大于目标点产生的引力，则无人艇易与障碍物产生碰撞，如图1所示。

 图 1 无人艇与障碍物的距离较远 Fig. 1 The distance between the target point and the obstacle is far

2）当障碍物距离目标点较近时，无人艇因受到的斥力作用较大但引力作用较小而导致无人艇在障碍物周围震荡，无法到达目标点，如图2所示。

 图 2 无人艇与障碍物的距离较近 Fig. 2 The target point is closer to the obstacle

3）由于无人艇在运动空间中是受到斥力和引力的共同作用而向前推进的，当在某一位置斥力和引力的合力为0时，无人艇会误以为已经到达目标点而停止运动，如图3所示。

 图 3 无人艇受到的合力为0 Fig. 3 The unmanned boat receives a combined force of 0
4 改进方法 4.1 改进引力场

 图 4 势场强度与无人艇和目标点距离的关系曲线 Fig. 4 Relationship curve between potential field strength and distance
 $\mathop U\nolimits_{{\text{att}}} = \left\{ {\begin{array}{*{20}{l}} \dfrac{1}{2}\varepsilon \mathop \rho \nolimits^2 \left( {q,\mathop q\nolimits_{goal} } \right),&{\rm{i}}{\rm{f}}\;\rho \left( {q,\mathop q\nolimits_{goal} } \right) \leqslant d ，\\ \mathop d\nolimits^{} \varepsilon \rho \left( {q,\mathop q\nolimits_{goal} } \right),&{\rm{i}}{\rm{f}}\;\rho \left( {q,\mathop q\nolimits_{goal} } \right) > d。\end{array}} \right.$ (7)
4.2 设置模糊远近界点

 图 5 模糊远近界点的判断关系图 Fig. 5 Judgment relationship diagram of fuzzy far and near boundary points
4.3 结合模拟退火算法

 图 6 局部路径规划流程图 Fig. 6 Partial path planning flowchart

5 仿真实验及分析

 图 7 传统人工势场法仿真情形 Fig. 7 Simulation of traditional artificial potential field method

 图 8 改进后的仿真结果 Fig. 8 Improved simulation results

 图 9 局部极小点情形改进前后的仿真情况 Fig. 9 The simulation situation before and after the improvement of the local minimum situation

 图 10 复杂环境下的仿真结果 Fig. 10 Simulation results under complex environment
6 结　语

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