【路径规划】基于matlab GUI改进的DWA算法机器人动态避障路径规划【含Matlab源码 1271期】

本文介绍了基于MATLAB的动态窗口算法(DWA)在移动机器人避障路径规划中的应用。DWA通过在速度空间采样并评估不同轨迹，选择最优速度来实现避障。作者分享了部分源代码，包括轨迹模拟、速度采样和障碍物处理等关键部分，并展示了实时仿真的用户界面。此外，还提供了MATLAB版本和相关参考文献信息。

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⛄一、DWA算法简介

DWA算法全称为dynamic window approach，其原理主要是在速度空间（v,w）中采样多组速度，并模拟这些速度在一定时间内的运动轨迹，再通过一个评价函数对这些轨迹打分，最优的速度被选择出来发送给下位机。
1 原理分析
在这里插入图片描述

2 速度采样

机器人的轨迹运动模型有了，根据速度就可以推算出轨迹。
因此只需采样很多速度，推算轨迹，然后评价这些轨迹好不好就行了。
（一）移动机器人受自身最大速度最小速度的限制
（二）移动机器人受电机性能的影响:由于电机力矩有限,存在最大的加減速限制,因此移动机器人軌迹前向模拟的周期sim_period内,存在一个动态窗口,在该窗口内的速度是机器人能够实际达到的速度:
（三）基于移动机器人安全的考虑:为了能够在碰到障碍物前停下来, 因此在最大减速度条件下, 速度有一个范围。

⛄二、部分源代码

function varargout = Simulate(varargin)
clc
SamplingPeriod = 0.1;
time = 0;
timer1 = [];
txt_timer = [];
FuzzyLoaded = 0;
Z1 = [];
Z2 = [];
W_Zone = 20;
H_Zone = 20;

data = importdata (‘fuzzytabledata.mat’);
OUT1 = data.OUT1;
OUT2 = data.OUT2;
Z1 = reshape(OUT1(102:end,1)‘,101,[]);
Z2 = reshape(OUT2(102:end,1)’,101,[]);
FuzzyLoaded = 1;

scrsz = get(0,‘ScreenSize’);

% Create a figure that will have a uitable, axes and checkboxes
figure(‘Position’,[15scrsz(3)/100 70 scrsz(3)-2(15*scrsz(3)/100) scrsz(4)-100],…
‘WindowStyle’, ‘normal’,…
‘CloseRequestFcn’,{@CloseFcn},…
‘Name’, ‘具有动态障碍物的DWA仿真’,… % Title figure
‘NumberTitle’, ‘off’) % Do not show figure number

% figure(‘Position’,[15scrsz(3)/100 70 scrsz(3)-2(15*scrsz(3)/100) scrsz(4)-100],…
% ‘WindowStyle’, ‘normal’,…
% ‘CloseRequestFcn’,{@CloseFcn},…
% ‘Name’, ‘具有动态障碍物的DWA仿真’,… % Title figure
% ‘NumberTitle’, ‘off’,… % Do not show figure number
% ‘MenuBar’, ‘none’); % Hide standard menu bar menus

% Create an axes set x and y limits to the value extremes, and format labels
W_Zone = ceil(W_Zone/10)*10;
H_Zone = ceil(H_Zone/10)*10;
haxes = axes(‘Units’, ‘normalized’,…
‘Position’, [.25 .05 0.75 0.9],…
‘XLim’, [-W_Zone/2 W_Zone/2],…
‘YLim’, [-H_Zone/2 H_Zone/2],…
‘XLimMode’, ‘manual’,…
‘YLimMode’, ‘manual’,…
‘XTick’,-W_Zone/2:1:W_Zone/2,…
‘YTick’,-H_Zone/2:1:H_Zone/2);%,…
% ‘XTickLabel’,…
% {‘-10 m’,‘-5 m’,‘0’,‘5 m’,‘10 m’},…
% ‘YTickLabel’,…
% {‘-10 m’,‘-5 m’,‘0’,‘5 m’,‘10 m’});
set(haxes,‘DataAspectRatio’,[1 1 1]);
title(haxes, ‘移动机器人动态避障仿真’) % Describe data set
% Prevent axes from clearing when new lines or markers are plotted
hold(haxes, ‘all’)
grid on;

uicontrol(‘Style’, ‘pushbutton’,…
‘Units’, ‘normalized’,…
‘Position’, [.02 .86 .2 .05],…
‘String’, ‘开始仿真’,…
‘Value’, 0,…
‘Callback’, {@StartSimulation});

uicontrol(‘Style’, ‘pushbutton’,…
‘Units’, ‘normalized’,…
‘Position’, [.02 .81 .2 .05],…
‘String’, ‘重新仿真’,…
‘Value’, 0,…
‘Callback’, {@ResetSimulation});

% % Create a text to show timer;
txt_timer = uicontrol(‘Style’, ‘text’,…
‘Units’, ‘normalized’,…
‘Position’, [.02 .915 .2 .035],…
‘FontWeight’, ‘bold’,…
‘ForegroundColor’, [0 .2 .8],…
‘fontname’, ‘Helvetica’,…
‘fontsize’, 14,…
‘BackgroundColor’, ‘w’, ‘String’,‘00:00 00’);

% % Create some texts to monitor variables;
txt_inp1 = uicontrol(‘Style’, ‘text’, ‘Units’, ‘normalized’, ‘Position’, [.05 .54 .08 .035],…
‘FontWeight’, ‘bold’, ‘ForegroundColor’, [0 0 0], ‘fontname’, ‘Helvetica’, ‘fontsize’, 12, ‘BackgroundColor’, [0.9 0.9 0.9]);
txt_inp2 = uicontrol(‘Style’, ‘text’, ‘Units’, ‘normalized’, ‘Position’, [.14 .54 .08 .035],…
‘FontWeight’, ‘bold’, ‘ForegroundColor’, [0 0 0], ‘fontname’, ‘Helvetica’, ‘fontsize’, 12, ‘BackgroundColor’, [0.9 0.9 0.9]);
txt_out1 = uicontrol(‘Style’, ‘text’, ‘Units’, ‘normalized’, ‘Position’, [.05 .47 .08 .035],…
‘FontWeight’, ‘bold’, ‘ForegroundColor’, [0 0 0], ‘fontname’, ‘Helvetica’, ‘fontsize’, 12, ‘BackgroundColor’, [0.9 0.9 0.9]);
txt_out2 = uicontrol(‘Style’, ‘text’, ‘Units’, ‘normalized’, ‘Position’, [.14 .47 .08 .035],…
‘FontWeight’, ‘bold’, ‘ForegroundColor’, [0 0 0], ‘fontname’, ‘Helvetica’, ‘fontsize’, 12, ‘BackgroundColor’, [0.9 0.9 0.9]);

uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.05 .61 .15 .025],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 10,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘DWA权值调整’);

uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.00 .55 .05 .02],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 9,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘INPs :’);
uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.00 .48 .05 .02],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 9,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘误差值 :’);
uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.05 .58 .08 .02],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 9,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘目标航向角’);
uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.14 .58 .08 .02],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 9,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘障碍物’);
uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.05 .51 .08 .02],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 9,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘左偏离’);
uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.14 .51 .08 .02],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 9,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘右偏离’);

uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.09 .78 .12 .025],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 10,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘X Y’);
uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.02 .74 .06 .03],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 10,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ‘起始点坐标：’);
uicontrol(‘Style’, ‘text’,‘Units’, ‘normalized’, ‘Position’, [.02 .7 .06 .03],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 10,…
‘BackgroundColor’, [0.8 0.8 0.8], ‘String’, ’ 目标点坐标：');

% % Create a text get Robot X0 Pos;
edit_robot_x0 = uicontrol(‘Style’, ‘edit’,…
‘Units’, ‘normalized’,…
‘Position’, [.09 .74 .06 .035],… %‘String’,… %‘Use Plot check boxes to graph columns’,…
‘FontWeight’, ‘bold’,…
‘fontname’, ‘Helvetica’,…
‘fontsize’, 12);
% % Create a text get Robot Y0 Pos;
edit_robot_y0 = uicontrol(‘Style’, ‘edit’,…
‘Units’, ‘normalized’,…
‘Position’, [.16 .74 .06 .035],… %‘String’,… %‘Use Plot check boxes to graph columns’,…
‘FontWeight’, ‘bold’,…
‘fontname’, ‘Helvetica’,…
‘fontsize’, 12);

% % Create a text get Goal X Pos;
edit_goal_x = uicontrol(‘Style’, ‘edit’,…
‘Units’, ‘normalized’,…
‘Position’, [.09 .7 .06 .035],… %‘String’,… %‘Use Plot check boxes to graph columns’,…
‘FontWeight’, ‘bold’,…
‘fontname’, ‘Helvetica’,…
‘fontsize’, 12);
% % Create a text get Goal Y Pos;
edit_goal_y = uicontrol(‘Style’, ‘edit’,…
‘Units’, ‘normalized’,…
‘Position’, [.16 .7 .06 .035],… %‘String’,… %‘Use Plot check boxes to graph columns’,…
‘FontWeight’, ‘bold’,…
‘fontname’, ‘Helvetica’,…
‘fontsize’, 12);

uicontrol(‘Style’, ‘pushbutton’,…
‘Units’, ‘normalized’,…
‘Position’, [.09 .655 .13 .04],… %‘TooltipString’, ‘Update Values Independently’,…
‘String’, ‘更新’,…
‘Value’, 0,…
‘Callback’, {@UpdateParams});

slider_x = uicontrol(‘Style’, ‘slider’,‘Units’, ‘normalized’, ‘Position’, [.02 .41 .2 .025],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 10,…
‘BackgroundColor’, [0.8 0.8 0.8],‘Min’,0,‘Value’,1,‘Max’,2,‘SliderStep’,[0.01 0.1]);

slider_y = uicontrol(‘Style’, ‘slider’,‘Units’, ‘normalized’, ‘Position’, [.02 .37 .2 .025],…
‘FontWeight’, ‘bold’, ‘fontname’, ‘Helvetica’, ‘fontsize’, 10,…
‘BackgroundColor’, [0.8 0.8 0.8],‘Min’,0,‘Value’,1,‘Max’,2,‘SliderStep’,[0.01 0.1]);

% uicontrol(‘Style’, ‘pushbutton’,…
% ‘Units’, ‘normalized’,…
% ‘Position’, [0.35 .95 .25 .05],… %‘TooltipString’, ‘Update Values Independently’,…
% ‘String’, ‘Save Data’,…
% ‘Value’, 0,…
% ‘Callback’, {@SaveData});

% % Create an invisible marker plot of the data and save handles
% % to the lineseries objects; use this to simulate data brushing.
% % hmkrs = plot([1:10],[1:10].^2, ‘LineStyle’, ‘none’,…
% % ‘Marker’, ‘o’,…
% % ‘MarkerFaceColor’, ‘y’,…
% % ‘HandleVisibility’, ‘off’,…
% % ‘Visible’, ‘on’);

% Create three check boxes to toggle plots for columns
% uicontrol(‘Style’, ‘checkbox’,…
% ‘Units’, ‘normalized’,…
% ‘Position’, [.10 .96 .09 .035],…
% ‘TooltipString’, ‘Check to plot column 1’,…
% ‘String’, ‘Col 1’,…
% ‘Value’, 0,…
% ‘Callback’, {@plot_callback,1});
%
% % Create a text label to say what the checkboxes do
% uicontrol(‘Style’, ‘text’,…
% ‘Units’, ‘normalized’,…
% ‘Position’, [.025 .955 .06 .035],…
% ‘String’, ‘Plot’,…
% ‘FontWeight’, ‘bold’);

% Subfuntions implementing the two callbacks
% ------------------------------------------

% function plot_callback(hObject, eventdata, column)
% % hObject Handle to Plot menu
% % eventdata Not used
% % column Number of column to plot or clear
%
% colors = {‘b’,‘m’,‘r’}; % Use consistent color for lines
% colnames = get(htable, ‘ColumnName’);
% colname = colnames{column};
% if get(hObject, ‘Value’)
% % Turn off the advisory text; it never comes back
% set(hprompt, ‘Visible’, ‘off’)
% % Obtain the data for that column
% ydata = get(htable, ‘Data’);
% set(haxes, ‘NextPlot’, ‘Add’)
% % Draw the line plot for column
% plot(haxes, ydata(:,column),…
% ‘DisplayName’, colname,…
% ‘Color’, colors{column});
% else % Adding a line to the plot
% % Find the lineseries object and delete it
% delete(findobj(haxes, ‘DisplayName’, colname))
% end
% end

w = 0.5;
l = 0.6;
D = 0.4;

x0 = -8;
y0 = -8;
teta0 = 0;
Vr0 = 0;
Vl0 = 0;
x = x0;
y = y0;
teta = teta0;
Vr = Vr0;
Vl = Vl0;
V_MAX = 5;

x_Goal = 8.;
y_Goal = 8;

n_of_obs = 6;

x_obs0(1) = 3;
y_obs0(1) = 3;
x_obs(1) = x_obs0(1);
y_obs(1) = y_obs0(1);
w_obs(1) = 2.5;
h_obs(1) = 2.5;
n_obs(1) = 50;
%teta_obs(1) = pi/4; 

x_obs0(2) = -1;
y_obs0(2) = 0.5;
x_obs(2) = x_obs0(2);
y_obs(2) = y_obs0(2);
w_obs(2) = 0.5;
h_obs(2) = 3;
n_obs(2) = 50;
%teta_obs(2) = pi/4; 

x_obs0(3) = 5;
y_obs0(3) = -3;
x_obs(3) = x_obs0(3);
y_obs(3) = y_obs0(3);
w_obs(3) = 5;
h_obs(3) = 1;
n_obs(3) = 50;
%teta_obs(3) = pi/4; 

x_obs0(4) = -3;
y_obs0(4) = 5;
x_obs(4) = x_obs0(4);
y_obs(4) = y_obs0(4);
w_obs(4) = 2;
h_obs(4) = 1;
n_obs(4) = 50;
%teta_obs(4) = pi/4; 

x_obs0(5) = -3;
y_obs0(5) = -5;
x_obs(5) = x_obs0(5);
y_obs(5) = y_obs0(5);
w_obs(5) = 2;
h_obs(5) = 2;
n_obs(5) = 2;
%teta_obs(5) = pi/4; 

x_obs0(6) = -5;
y_obs0(6) = 1;
x_obs(6) = x_obs0(6);
y_obs(6) = y_obs0(6);
w_obs(6) = 1;
h_obs(6) = 1;
n_obs(6) = 2;
%teta_obs(6) = pi/4; 


counter = 0;
trace_x = [];
trace_y = [];

    
    if(abs(y_obs(jj)-y_obs0(jj)) < get(slider_y,'Value'))
        y_obs(jj) = y_obs(jj) + (cos(time*4+rand(1)*3)*rand(1)*3)*SamplingPeriod;
    else
        y_obs(jj) = y_obs(jj) + (y_obs0(jj)-y_obs(jj))*0.2*SamplingPeriod;
    end

    ss(jj)= max(ss);
    
    [ss_min,jj] = min(ss);
    if(abs(x_obs(jj)-x_obs0(jj)) < get(slider_x,'Value'))
        x_obs(jj) = x_obs(jj) + ((sin(time*3+rand(1)*2)+0.2*(x-x_obs(jj)))*rand(1)*3)*SamplingPeriod;
    else
        x_obs(jj) = x_obs(jj) + (x_obs0(jj)-x_obs(jj))*0.2*SamplingPeriod;
    end
    
    if(abs(y_obs(jj)-y_obs0(jj)) < get(slider_y,'Value'))
        y_obs(jj) = y_obs(jj) + (cos(time*4+rand(1)*3)*rand(1)*3)*SamplingPeriod;
    else
        y_obs(jj) = y_obs(jj) + (y_obs0(jj)-y_obs(jj))*0.2*SamplingPeriod;
    end
    
    
    %Check Obstacles
    ray_i = 1;
    ray_x = []; ray_y = []; ray_s = []; ray_teta = [];
    rayplot_x = []; rayplot_y = []; rayplot_i = 1;
    for dir = linspace(-pi/4,pi/4,16)
        Obstacle_Found = 0;
        s = 0;
        while(Obstacle_Found==0)
            s = s + 0.02;
            ray_pos = [x + s*sin(teta+dir), y + s*cos(teta+dir)];
            for i = 1:n_of_obs
                if( (2*(ray_pos(1)-x_obs(i))/w_obs(i))^n_obs(i)+(2*(ray_pos(2)-y_obs(i))/h_obs(i))^n_obs(i) < 1 )
                    Obstacle_Found = 1;
                end
            end
            if( (2*ray_pos(1)/W_Zone)^100+(2*ray_pos(2)/H_Zone)^100>1 || s>3)
                Obstacle_Found = 1;
            end
            if(Obstacle_Found==1)
                ray_x(ray_i) = ray_pos(1); 
                ray_y(ray_i) = ray_pos(2);
                ray_s(ray_i) = s;
                ray_teta(ray_i) = dir;
                rayplot_x(rayplot_i:rayplot_i+2) = [x ray_pos(1) x];
                rayplot_y(rayplot_i:rayplot_i+2) = [y ray_pos(2) y];
            end
        end
        ray_i = ray_i + 1;
        rayplot_i = rayplot_i + 3;
    end
    
    j=0;
    if(mod(counter,1)==0)
        cla(haxes);            
        robot_extents = [cos(teta) sin(teta) x; -sin(teta) cos(teta) y] * [-w/2,-l/2,1; w/2,-l/2,1; w/2,l/2,1; -w/2,l/2,1; -w/2,-l/2,1; w/2,-l/2,1]';        
        plot(haxes,robot_extents(1,:),robot_extents(2,:), 'LineWidth' ,3,'Color',[0 0 1]);
        robot_tyre = [cos(teta) sin(teta) x; -sin(teta) cos(teta) y] * [-w/2-0.1,-l/2-l/4,1; -w/2-0.1,-l/2+l/4,1; w/2+0.1,-l/2-l/4,1; w/2+0.1,-l/2+l/4,1; -w/2-0.1,l/2-l/4,1; -w/2-0.1,l/2+l/4,1; w/2+0.1,l/2-l/4,1; w/2+0.1,l/2+l/4,1; 0,l/2,1; 0,l/2+l/2,1]';
        plot(haxes,robot_tyre(1,1:2),robot_tyre(2,1:2), 'LineWidth' ,4,'Color',[0 0 0]); plot(haxes,robot_tyre(1,3:4),robot_tyre(2,3:4), 'LineWidth' ,4,'Color',[0 0 0]);
        plot(haxes,robot_tyre(1,5:6),robot_tyre(2,5:6), 'LineWidth' ,4,'Color',[0 0 0]); plot(haxes,robot_tyre(1,7:8),robot_tyre(2,7:8), 'LineWidth' ,4,'Color',[0 0 0]);
        plot(haxes,robot_tyre(1,9:10),robot_tyre(2,9:10), 'LineWidth' ,1,'Color',[0.4 0.4 0.4]);

        s = linspace(0,2*pi,360);
        for i = 1:n_of_obs
            x_o = (1./((sin(s)/(h_obs(i)/2)).^n_obs(i) + (cos(s)/(w_obs(i)/2)).^n_obs(i)).^(1/n_obs(i))).*cos(s) + x_obs(i);
            y_o = (1./((sin(s)/(h_obs(i)/2)).^n_obs(i) + (cos(s)/(w_obs(i)/2)).^n_obs(i)).^(1/n_obs(i))).*sin(s) + y_obs(i);
            plot(haxes,x_o,y_o, 'LineWidth' ,2,'Color',[0 0 0]);
            %if(gca == haxes), fill(x_o,y_o,[0.5 0.5 0.5],'LineWidth' ,2); end
        end
        plot(haxes,[-W_Zone/2 W_Zone/2 W_Zone/2 -W_Zone/2 -W_Zone/2],[-H_Zone/2 -H_Zone/2 H_Zone/2 H_Zone/2 -H_Zone/2], 'LineWidth' ,4,'Color',[0 0 0]);
        plot(haxes, rayplot_x, rayplot_y, 'LineWidth' ,1,'Color',[1 0.8 0]);
        plot(haxes, trace_x, trace_y, ':', 'LineWidth' ,2,'Color',[0.4 0.4 0.7]);
        plot(haxes, x_Goal, y_Goal,'*','MarkerSize',15,'MarkerEdgeColor','g','LineWidth',3);
        if(j>0)
            plot(haxes, ray_x(j), ray_y(j),'s','MarkerSize',8,'MarkerEdgeColor','r','LineWidth',3); 
        end
        %plot(haxes, [x x_Goal], [y y_Goal],'-.', 'LineWidth' ,1,'Color',[0.8 0.95 0.2]);
    end
end
%% create and start timer1 to execute the function Command sequentially.
timer1 = timer('TimerFcn', @Command, 'Period', SamplingPeriod, 'ExecutionMode', 'fixedRate');

⛄三、运行结果

在这里插入图片描述

⛄四、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
[1]卞永明,季鹏成,周怡和,杨濛.基于改进型DWA的移动机器人避障路径规划[J].中国工程机械学报. 2021,19(01)

3 备注
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生产调度、经济调度、装配线调度、充电优化、车间调度、发车优化、水库调度、三维装箱、物流选址、货位优化、公交排班优化、充电桩布局优化、车间布局优化、集装箱船配载优化、水泵组合优化、解医疗资源分配优化、设施布局优化、可视域基站和无人机选址优化

2 机器学习和深度学习方面
卷积神经网络（CNN）、LSTM、支持向量机（SVM）、最小二乘支持向量机（LSSVM）、极限学习机（ELM）、核极限学习机（KELM）、BP、RBF、宽度学习、DBN、RF、RBF、DELM、XGBOOST、TCN实现风电预测、光伏预测、电池寿命预测、辐射源识别、交通流预测、负荷预测、股价预测、PM2.5浓度预测、电池健康状态预测、水体光学参数反演、NLOS信号识别、地铁停车精准预测、变压器故障诊断

3 图像处理方面
图像识别、图像分割、图像检测、图像隐藏、图像配准、图像拼接、图像融合、图像增强、图像压缩感知

4 路径规划方面
旅行商问题（TSP）、车辆路径问题（VRP、MVRP、CVRP、VRPTW等）、无人机三维路径规划、无人机协同、无人机编队、机器人路径规划、栅格地图路径规划、多式联运运输问题、车辆协同无人机路径规划、天线线性阵列分布优化、车间布局优化

5 无人机应用方面
无人机路径规划、无人机控制、无人机编队、无人机协同、无人机任务分配

6 无线传感器定位及布局方面
传感器部署优化、通信协议优化、路由优化、目标定位优化、Dv-Hop定位优化、Leach协议优化、WSN覆盖优化、组播优化、RSSI定位优化

7 信号处理方面
信号识别、信号加密、信号去噪、信号增强、雷达信号处理、信号水印嵌入提取、肌电信号、脑电信号、信号配时优化

8 电力系统方面
微电网优化、无功优化、配电网重构、储能配置

9 元胞自动机方面
交通流人群疏散病毒扩散晶体生长

10 雷达方面
卡尔曼滤波跟踪、航迹关联、航迹融合