﻿ 基于改进人工势场法的水下滑翔机路径规划
 舰船科学技术  2019, Vol. 41 Issue (4): 89-93 PDF

1. 上海交通大学 高新船舶与海洋开发装备协同创新中心，海洋工程国家重点实验室，上海 200240;
2. 上海交通大学海洋水下工程科学研究院有限公司，上海 200231

Path planning for underwater glider based on improved artificial potential field method
LI Pei-lun1, YANG Qi1,2
1. Collaborative Innovation Center for Advanced Ship and Deep-sea Exploration, State Key laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China;
2. Shanghai Jiaotong University Underwater Engineering Institute Co., Ltd., Shanghai 200231, China
Abstract: The problem of path planning for underwater glider avoiding obstacles in a single cycle is studied. An improved artificial potential field method is applied to generate an obstacle-avoiding path according to the motion characteristics of underwater glider. Firstly, to overcome the local minimum problem and destination unreachable problem, the traditional artificial potential field method is improved, and the velocity potential field function is introduced to transform the static potential field into dynamic potential field. Secondly, in terms of the motion characteristics and constraints of underwater glider, the method of determining the obstacle’s influence radius is proposed. Subsequently, the constant force of current is added and its influence on path planning is analyzed. Finally, taking the underwater glider named HUST-2 as an example, simulation tests of path planning for underwater glider are conducted. The simulation results indicate that the underwater glider can avoid the static and dynamic obstacles by using the proposed method.
Key words: underwater glider     path planning     artificial potential field     current influence
0 引　言

1 改进的人工势场法

1.1 改进斥力势场函数

 {U_{reps}}(X) = \left\{ \begin{aligned} & {\frac{1}{2}{\eta _r}{{\left( {\frac{1}{{\rho (X,{X_o})}} - \frac{1}{{{\rho _0}}}} \right)}^2}{\rho ^2}(X,{X_g})} {,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \rho (X,{X_o}) \leqslant {\rho _0}} {\text{；}}\\ & 0,\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad {\rho (X,{X_o}) > {\rho _0}} {\text{。}} \end{aligned} \right. (1)

 {\overrightarrow F _{reps}}(X) = \left\{ \begin{aligned} &{{\overrightarrow F }_{reps1}}(X) \cdot \nabla \rho (X,{X_o}) - {{\overrightarrow F }_{reps2}}(X) \times \\ & \nabla \rho (X,{X_g}),\quad {\rho (X,{X_o})\leqslant {\rho _0}}{\text{；}}\\ &0, \quad\quad\quad\quad\ {\rho (X,{X_o}) > {\rho _0}}{\text{。}} \end{aligned} \right. (2)

1.2 改进引力势场函数

 ${U_{local}}(X) = \left\{ {\begin{array}{*{20}{c}} {\dfrac{\varepsilon }{{{\rho ^2}(X,{X_g})}}}&{,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \rho (X,{X_g}) > {\rho _g}} {\text{；}}\\ 0&{,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \rho (X,{X_g}) \leqslant {\rho _g}} {\text{。}} \end{array}} \right.$ (3)

 {U_{att}}(X) = \left\{ \begin{aligned} &{\dfrac{1}{2}{\xi _a}{\rho ^2}(X,{X_g})} , \quad\quad\quad\quad\quad\rho (X,{X_g}) > {\rho _g}\\ &{\text{且}}{F_{total}}\left( X \right) \ne 0{\text{；}}\\ &{\dfrac{1}{2}{\xi _a}{\rho ^2}(X,{X_g}) + \frac{\varepsilon }{{{\rho ^2}(X,{X_g})}}} , \ \rho (X,{X_g}) > {\rho _g}\\ &{\text{且}}{F_{total}}\left( X \right) = 0{\text{；}}\\ &0{, \quad\quad\quad\quad\quad\quad\quad\quad\quad\ \ \rho (X,{X_g}) \leqslant {\rho _g}}{\text{。}} \end{aligned} \right. (4)

1.3 引入速度势场

 {U_{repv}}(X) = \left\{ \begin{aligned} & {{\eta _v}\left| {\left\| {\overrightarrow V - {{\overrightarrow V }_o}} \right\|\sin \phi } \right| = {\eta _v}{V_{or}}\left| {\sin \phi } \right|} ,\\ &\quad\quad\quad{\rho (X,{X_o}) \leqslant {\rho _0}}{\text{；}}\\ & 0, \quad\quad {\rho (X,{X_o}) > {\rho _0}} {\text{。}} \end{aligned} \right. (5)

$\cos \phi > 0$ 表示水下滑翔机在朝向障碍物运动，此时需要相对速度斥力； $\cos \phi \leqslant 0$ 表示水下滑翔机在远离障碍物运动，此时就算没有速度斥力也不会与障碍物发生碰撞，因此 $\cos \phi \leqslant 0$ ${U_{repv}} = 0$ 。于是距离和速度产生的总斥力势场函数 ${U_{rep}}$ 为：

 {U_{rep}}(X) = \left\{ \begin{aligned} &{{U_{reps}}(X) \!+\! {U_{repv}}(X)}, {\rho (X,\!{X_o}) \leqslant{\rho _0} {\text{且}} \cos \phi > 0}{\text{，}}\!\\ &{{U_{reps}}(X)},{\rho (X,{X_o}) \leqslant {\rho _0} {\text{且}} \cos \phi \leqslant 0}{\text{，}}\!\\ &0, {\rho (X,{X_o}) > {\rho _0}}{\text{。}} \end{aligned} \right. (6)
2 考虑水下滑翔机的运动特点及约束 2.1 水下滑翔机的运动特点及约束

 图 1 水下滑翔机一个周期内的运动情况 Fig. 1 Movement of underwater glider in one cycle

2.2 确定障碍物的影响半径

 图 2 临界情况示意图 Fig. 2 Diagram of the critical situation

 $\begin{split} &(4{R_{\min }}^2 + 4{\rho _0}^2){x^2} + [8{R_{\min }}r({\rho _0} - r) + 4{R_{\min }}{\left( {{\rho _0} - r} \right)^2}- \\ &8{R_{\min }}{\rho _0}^2]x + {[2r({\rho _0} - r) + {({\rho _0} - r)^2}]^2} = 0{\text{。}} \end{split}$ (7)

 ${\rho _{\min }} = \sqrt {{r^2} + 2Rr}{\text{，}}$ (8)

 ${\rho _{\min }} = {R_{\min }} + r{\text{，}}$ (9)

3 海流影响

 图 3 水下滑翔机总受力示意图 Fig. 3 Diagram of the whole forces of underwater glider

 $\varphi \! =\! \arctan \frac{{{F_{att,x}} \!\!+\!\! \displaystyle\sum\limits_{i \!=\! 1}^n {(F_{reps1,x}^i \!\!+\!\! F_{reps2,x}^i \!\!+\! F_{repv,x}^i)} \!\!+\!\! {F_c}}}{{{F_{att,y}} \!\!+\!\! \displaystyle\sum\limits_{i \!=\! 1}^n {(F_{reps1,y}^i \!\!+\! F_{reps2,y}^i \!\!+\!\! F_{repv,y}^i)} }}{\text{。}}$ (10)

4 仿真试验 4.1 无海流环境的路径规划

 图 4 躲避动态障碍物过程 Fig. 4 Process of avoiding dynamic obstacle

 图 5 动态环境下的最终路径规划结果 Fig. 5 Path planning result in dynamic environment

4.2 定常海流对路径规划的影响

 图 6 常值海流作用下的动态路径规划 Fig. 6 Dynamic path planning with constant current

 图 7 不同海流作用下的静态路径规划 Fig. 7 Static path planning with different currents
5 结　语

 [1] 赵宝强. 基于粒子群改进算法的水下滑翔机路径优化[J]. 舰船科学技术, 2015, 37(8): 140-145. ZHAO Bao-qiang. Underwater glider path optimization based on improved particle swarm algorithm[J]. Ship Science and Technology, 2015, 37(8): 140-145. DOI:10.3404/j.issn.1672-7649.2015.08.029 [2] ALVAREZ A, GARAU B, CAITI A. Combining networks of drifting profiling floats and gliders for adaptive sampling of the Ocean[C]// IEEE International Conference on Robotics and Automation. IEEE, 2007:157–162. [3] FERNÁNDEZ-PERDOMO E, CABRERA-GÁMEZ J, HERNÁNDEZ-SOSA D, et al. Path planning for gliders using regional ocean models: application of pinzón path planner with the ESEOAT model and the RU27 trans-Atlantic flight data[C]// Oceans. IEEE, 2010:1–10. [4] RAO D, WILLIAMS S B. Large-scale path planning for Underwater Gliders in ocean currents[J]. 2009. [5] PEREIRA A A, BINNEY J, HOLLINGER G A, et al. Risk-aware path planning for autonomous underwater vehicles using predictive ocean models[J]. Journal of Field Robotics, 2013, 30(5): 741-762. DOI:10.1002/rob.2013.30.issue-5 [6] 朱心科, 俞建成, 王晓辉. 能耗最优的水下滑翔机采样路径规划[J]. 机器人, 2011, 33(3): 360-365. ZHU Xin-ke, YU Jian-cheng, WANG Xiao-hui. Sampling path planning of underwater glider for optimal energy consumption[J]. Robot, 2011, 33(3): 360-365. [7] 张殿富, 刘福. 基于人工势场法的路径规划方法研究及展望[J]. 计算机工程与科学, 2013, 35(6): 88-95. DOI:10.3969/j.issn.1007-130X.2013.06.015 [8] 王奎民, 赵玉飞, 侯恕萍, 等. 一种改进人工势场的UUV动碍航物规避方法[J]. 智能系统学报, 2014(1): 47-52. [9] KIM Y, GU D W, POSTLETHWAITE I. Real-time path planning with limited information for autonomous unmanned air vehicles[M]. Pergamon Press, Inc. 2008. [10] 李惠光, 李旭锋, 邹立颖, 等. 动态环境下基于人工势场的足球机器人路径规划[J]. 国外电子测量技术, 2008, 27(5): 27-30. DOI:10.3969/j.issn.1002-8978.2008.05.010 [11] WU Z, ZHAO M, WANG Y, et al. Path Planning for Underwater Gliders with Motion Constraints[M]// Mechanism and Machine Science. Springer Singapore, 2017. [12] 曹璟. 复杂环境下AUV路径规划方法研究[D]. 青岛: 中国海洋大学, 2011. [13] 顾建农, 张志宏, 王冲, 等. 水下滑翔机定常螺旋回转运动特性分析[J]. 中国造船, 2017(3): 68-79. GU Jian-nong, ZHANG Zhi-hong, WANG Chong, et al. Analysis of steady spiral gyration motion characteristics of underwater glider[J]. Shipbuilding of China, 2017(3): 68-79. DOI:10.3969/j.issn.1000-4882.2017.03.022