四旋翼飞行器的动力学、控制和路径规划matlab仿真

✅作者简介：热爱科研的Matlab仿真开发者，修心和技术同步精进，matlab项目合作可私信。

🍎个人主页：Matlab科研工作室

🍊个人信条：格物致知。

⛄ 内容介绍

四旋翼飞行器的动力学、控制和路径规划是飞行器设计和操作中的重要领域。下面我将简要介绍一下这些方面的内容：

1. 动力学：四旋翼飞行器的动力学研究主要涉及到飞行器的运动学和动力学特性。运动学描述了飞行器的位置、速度和加速度等运动状态，而动力学描述了飞行器的受力和力矩等物理特性。了解四旋翼飞行器的动力学特性有助于优化飞行控制系统，提高飞行性能。
2. 控制：四旋翼飞行器的控制是指通过调节电机转速或改变电机输出力矩来控制飞行器的姿态和位置。常用的控制方法包括PID控制器、模型预测控制（MPC）和自适应控制等。控制系统需要根据传感器获取的数据实时调整飞行器的姿态和位置，以实现期望的飞行任务。
3. 路径规划：路径规划是指在给定环境中找到一条合适的路径，使得飞行器能够顺利地从起点到达目标点。在四旋翼飞行器中，路径规划可以通过全局路径规划和局部路径规划两种方式实现。全局路径规划通常使用遗传算法、A*算法等搜索算法来找到最优路径，而局部路径规划则根据当前飞行状态和环境信息来调整飞行器的姿态和速度，以避免障碍物和保持航迹稳定。

⛄ 部分代码

clear;
close all;
%% Simulation Parameters
dt = 0.001; % simulation time step

controllerRate = 0.01; % interval at which the controller activates
plan_rate = 0.5;
gps_rate = 0.1; % 10Hz gps update
vicon_rate = 0.0025; %400hz update for the vicon system
motor_control_period = 1/500;
using_vicon = true;

lab_z = 12.2;
lab_y = 9.1;
lab_x = 9.1;

% for repeatability:
rng('default');

%% Target Craft Parameters
target_velocity = [0; 0; 0];  % velocity of the target

obs_pos = [1 1 8]';        % position of the target

% Capturing Parameters
obs_radi = [0.5 0.5 0.25];
buffer = 0.75;
start_pos = [3,3,0];
tilt_angle = pi/10;
claw_length = 0.4;
ds = 0.001;
%% State Machine Parameters
state = 0;
generated_trajectory = 0;
in_hover = 0;
position_for_hover = [0;0;0];
%% Quadrotor Parameters
I = [0.1 0 0;
   0 0.1 0;
   0 0 0.1];  % moment of inertia matrix
m = 4;      % mass - smaller mass helps performance
g = -9.8;    % gravity

L = 0.25;    % length of quad arm

c_T = 0.00000545;
c_Q = 0.0000002284; 
gamma = [c_T, c_T, c_T, c_T;
     0, L*c_T, 0, -L*c_T;
     -L*c_T, 0, L*c_T, 0;
     -c_Q, c_Q, -c_Q, c_Q];  
gammainv = inv(gamma);

A1c = 1;
A1s = 1; 
dx = 0.058; % this should be roughly correct. Note that we drag I believe I have a speed cap
dy = 0.058; % drag in y
D = diag([dx, dy, 0]);
%% Motor Parameters
V_batt = 12; % volts 
% max rotor speed ~2000.0 rad/s (at 12v) (which translates to about 87N of thrust at max)
%% Sensor Parameters
gps_sigma = 0.02;      % 2cm standard deviation
vicon_sigma = 0.0001;    % 0.1mm standard deviation

imu_rate = controllerRate;
R_dot_hat = [0 0 0; 0 0 0; 0 0 0];  % Initial rotation matrix derivative estimate
R_hat = [1 0 0; 0 1 0; 0 0 1];    % Initial rotation matrix estimate

b_dot_hat = [0; 0; 0];
b_hat = [0; 0; 0];

bias_a = [0.000; 0.000; 0.000];   % bias of the accelerometer in newtons - can revise this number/make it different between runs
mu_a = 0;             % mean of the accelerometer noise
sigma_a = 0.0006;         % standard deviation of the accelerometer noise

bias_b = 0;             % bias of the gyro. Can also be changed/made random between runs
mu_b = 0;             % mean of the gyro noise
sigma_b = 0.000015;         % standard deviation of the rate measurements in rad/s

ka = 1;
kb = 1;

k_w = 1;
%% Initial Conditions
eulerAngles = zeros(3,1); % ZYX: yaw, roll, pitch
omega = zeros(3,1);
omegadot = zeros(3,1);

q_position = start_pos';    % this is position of the center of mass of the quad in the world frame
q_velocity = [0; 0; 0];      % in the world frame
q_acceleration = [0; 0; 0];    % in the world frame
q_jerk = [0;0;0];

r_hat = [0; 0; 0];        % initial estimate of the position

omega_motor_act = zeros(4,1);

rotMat = eul2rotm(eulerAngles', 'XYZ');

xw = [1; 0; 0]; % world coordinate x axis
yw = [0; 1; 0]; % world coordinate y axis
zw = [0; 0; 1]; % world coordinate z axis

a_hat = [0; 0; 0];
thrust = 0;

% "History" of the given variables
anglesHist = zeros(3,1);
positionHist = zeros(3,1);
rotMatHist = zeros(3, 3, 1);
velHist = zeros(3, 1);
omega_motor_hist = zeros(4,1);
moment_des_hist = zeros(3,1);
b1_hist = zeros(3, 1);
b2_hist = zeros(3, 1);
b3_hist = zeros(3, 1);
e_R_hist = zeros(3, 1);
R_com_hist = zeros(3, 3, 1);
b1_com_hist = zeros(3,1);
b2_com_hist = zeros(3,1);
b3_com_hist = zeros(3,1);
in_bounds_hist = [true; true; true];
target_position_hist = obs_pos;

r_effort = zeros(3, 1);
v_effort = zeros(3, 1);

%% Gains
k_motor = 0.00001;
k_motor_ff = 0.006;

kp_attitude = 19.5;
kd_attitude = 6;

kp_thrust = [35.5 0 0;
       0 35.5 0;
       0 0 35.5];
kd_thrust = 75.5;

%% Trajectory Planning
j_max = 11; % max jerk
a_max = 15; % max acceleration
v_max = 20; % max velocity

%% Path Planning
[pathCoefs, path, arc_len, T, N, B, curvature, torsion, lookup_table] = makeGeoPath(obs_pos', obs_radi, buffer, start_pos, tilt_angle, claw_length);
T = T';
N = N';
B = B';
[len, vel, acc, jerk] = optimizeSplineTrajectory(controllerRate, arc_len(1)+arc_len(2));

psi_s = zeros(length(acc),1); % Right now, I don't use yaw
psi_dot_s = zeros(length(acc),1);
endtime = length(acc)*controllerRate - controllerRate + 1;
%% Simulation Params %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
simCounter = 1;
controllerCounter = 1;
endtime_mod = endtime+1;

geo_path_index = 2;
profile_index = 2;

%% Simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for t = 0:dt:endtime
  tspan = [t, t+dt];

  %% Sensors %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % Position estimate will come from a "GPS" that will report at 10Hz
  % with a 2cm standard deviation
  % if using VICON, the update rate will be faster and sigma will be ~2
  % orders of magnitude smaller
  if(~using_vicon)
    if(mod(t, gps_rate) == 0)
      r_hat = normrnd(q_position, gps_sigma);
    end
  else
    if(mod(t, vicon_rate) == 0)
      r_hat = normrnd(q_position, vicon_sigma);
    end
  end
  
  % IMU complementary observer with gyro and accelerometer. magnetometer
  % is not used because in most practical cases it yields to much noise
  % to be effective
  % future improvements could involve using the vicon data to improve the
  % attitude estimate
  if(mod(t, imu_rate) == 0)
    eta_a = normrnd(mu_a, sigma_a);
    a_imu = rotMat' * (q_acceleration - g*zw) + bias_a + eta_a; % the reading of the imu
    a_hat = rotMat * a_imu;
    
    eta_b = normrnd(mu_b, sigma_b);
    omega_imu = omega + bias_b + eta_b;

    % this filter assumes minimal up and down accelerations I believe
    alpha = (ka/g^2)*cross(rotMat'*zw, a_imu); % can add in vicon terms here

    b_dot_hat_prev = b_dot_hat;
    b_dot_hat = kb*alpha;
    b_hat = b_hat + ((b_dot_hat + b_dot_hat_prev)/2) * imu_rate; % this is a simple trapezoidal intregration routine

    R_dot_hat_prev = R_dot_hat;
    R_dot_hat = (R_hat * hatmap(omega_imu - b_hat))- alpha;
    R_hat = R_hat + ((R_dot_hat + R_dot_hat_prev)/2) * imu_rate; % this is a simple trapezoidal intregration routine
  end
  

  %% Controller %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  if(mod(t, controllerRate) == 0)
  if t <= 1
    u1_com = norm(-g*m);
    M = [0;0;0];
  else
  %% Path Following
  index = controllerCounter - 1/controllerRate;

  % Step 1: Get the location on the path that is closests to the current
  % location
  geo_path_index = getClosestLocation(geo_path_index, path, q_position);
  
  % Step 2: Get the corresponding arc length of the path
  profile_index = getClosestLocationProfile(profile_index, len, lookup_table(geo_path_index));
  
  % Step 3: Get the velocity, acceleration and jerk that correspond to
  % that arc length
  v_des = T(:, geo_path_index)*vel(profile_index);
  a_des = acc(profile_index)*T(:, geo_path_index) + vel(profile_index)^2*curvature(geo_path_index)*N(:, geo_path_index);
  if controllerCounter > 1
    kappa_prime = (curvature(geo_path_index)-curvature(geo_path_index-1))/0.0001;
    j_des = (jerk(profile_index) - curvature(geo_path_index)^2*vel(profile_index)^3)*T(:, geo_path_index) +(3*curvature(geo_path_index)*vel(profile_index)*acc(profile_index)+kappa_prime*vel(profile_index)^2)*N(:, geo_path_index) + curvature(geo_path_index)*torsion(geo_path_index)*vel(profile_index)^3*B(:, geo_path_index);
  else
    j_des = [0;0;0];
  end
  
  e_r = dot((path(geo_path_index,:)'-r_hat),N(:, geo_path_index))*(N(:, geo_path_index)) + dot((path(geo_path_index,:)'-r_hat),B(:, geo_path_index))*(B(geo_path_index));
  e_v = v_des - q_velocity;
  
  e_r_hist(:, controllerCounter) = e_r;
  e_v_hist(:, controllerCounter) = e_v;
  
  a_com = 6.25*e_r + 4.5*e_v + m*a_des -g*m*zw; 
  u1_com = norm(a_com);
  e1 = [cos(psi_s(profile_index)); sin(psi_s(profile_index)); 0];
  
  b3 = (a_com)/norm(a_com); 
  b2 = cross(b3, e1)/norm(cross(b3, e1));
  b1 = cross(b2, b3);
  
  Rd = [b1 b2 b3];
    
  h_omega = (m/norm(m*a_com)) * (j_des - (dot(b3, j_des) * b3));
  omega_des = [dot(-h_omega, b2); dot(h_omega, b1); dot(psi_dot_s(profile_index) * zw, b3)];
  
  e_R = veeMap(0.5*(Rd'*R_hat - R_hat'*Rd))';
  e_w = omega - R_hat' * Rd * omega_des;
  M = -2.0*e_R - 2.75*e_w; 
  
  omega_des_hist(:, controllerCounter) = omega_des;
  j_des_hist(:, controllerCounter) = j_des;
  e_R_hist(:, controllerCounter) = e_R;
  e_w_hist(:, controllerCounter) = e_w;
  a_des_hist(:, controllerCounter) = a_des;
  v_des_hist(:, controllerCounter) = v_des;
  a_com_hist(:, controllerCounter) = a_com;
  b3_com_hist(:, controllerCounter) = b3;
  u1_com_hist(:, controllerCounter) = u1_com;
  M_hist(:, controllerCounter) = M;
  geo_path_index_hist(controllerCounter) = geo_path_index;
   profile_index_hist(controllerCounter) = profile_index;
  lookup_hist(controllerCounter) = lookup_table(geo_path_index);
  
  end
  u_des = [u1_com; M]; % Thrust mag, moment around X, moment around Y, moment around Z

  omega_motor_des = gammainv * (u_des);
  omega_motor_des = sign(omega_motor_des) .* sqrt(abs(omega_motor_des));

   omega_motor_des(1) = 1*(omega_motor_des(1));
   omega_motor_des(2) = -1*(omega_motor_des(2));
   omega_motor_des(3) = 1*(omega_motor_des(3));
   omega_motor_des(4) = -1*(omega_motor_des(4));

  omega_motor_des_hist(:, controllerCounter) = omega_motor_des;
  controllerCounter = controllerCounter + 1;

  end
  if (mod(t, motor_control_period) == 0)
    Vin = k_motor*(omega_motor_des - omega_motor_act) + k_motor_ff*omega_motor_des; % motor controller
    
    % saturate Vin to the motor battery
    for n = 1:4
      Vin(n) = min([Vin(n), V_batt]);
      Vin(n) = max([Vin(n), -V_batt]);
    end
    Vin_hist(:, simCounter) = Vin;
  end
  
  
  %% Model %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %% Motor Dynamics
   [~, y] = ode45(@(t_s, omega_motor_act) motorDynamics(Vin, omega_motor_act), tspan, omega_motor_act);
   omega_motor_act = y(size(y, 1), :)';
   omega_motor_hist(:, simCounter) = omega_motor_act;

  u = gamma * omega_motor_act.^2;
  moments = u(2:4);
  thrust = u(1) * rotMat*zw;
  thrust_hist(simCounter) = u(1);
  moments_hist(:,simCounter) = u(2:4);
  %% Attitude Dynamics
  [~, y] = ode45(@(t_s, y) attitudeChange(omega, moments, I), tspan,  [eulerAngles; omega]); % is omega or omegadot the initial condition? should be omega
  omega = (y(size(y, 1), [4 5 6]))';
  eulerAngles = (y(size(y, 1), [1 2 3]))';
  
  anglesHist(:, simCounter) = eulerAngles;

  rotMat = eul2rotm(eulerAngles', 'XYZ');

  rotMatHist(:, :, simCounter) = rotMat;
  
  %% Rotor Flapping and Drag Dynamics
  % this will need to be factored into the position dynamics
  % this flapping model is assuming: 
  % - the vehicle's velocity is small compared to the tip velocity
  % - the wind speed is negligble 
  % - the vertical distance from the rotor to the CoM is very small 
  % - the induced drag acts as a torsional spring
  
  A_flap = 1/(omega_motor_des(1)) * [A1c, -A1s, 0; A1s, A1c, 0; 0, 0, 0];
  D_ind = diag([dx, dy, 0]);
  D = A_flap + D_ind;
  F_ext = u(1) * ((D_ind + A_flap) * (rotMat' * q_velocity));
  F_ext_hist(:, simCounter) = F_ext;

  %% Position Dynamics
  [~, y] = ode45(@(t_s, y) sumOfForces(rotMat, g, m, thrust, F_ext), tspan, q_velocity);
  q_velocity = (y(size(y, 1), :))';

  [~, y] = ode45(@(t_s, y) simpleIntegral(q_velocity, 1), tspan, q_position);
  q_position = (y(size(y, 1), :))';
  
  q_acceleration = sumOfForces(rotMat, g, m, thrust, F_ext);
  
  if q_position(3) <= 0 % effect of the ground
    q_position(3) = 0;
    q_velocity(3) = 0;
    q_acceleration(3) = 0;
  end
  
  if(t ~= 0)
    in_bounds_hist(:, simCounter) = check_bounds(q_position, lab_x, lab_y, lab_z, t, in_bounds_hist(:, simCounter - 1));
  end
  
  if simCounter > 1
    q_jerk = (q_acceleration - acc_hist(:, simCounter-1))/dt;
  else
    q_jerk = [0;0;0];
  end
  
  positionHist(:, simCounter) = q_position; 
  acc_hist(:, simCounter) = q_acceleration;
  velHist(:, simCounter) = q_velocity;
  j_hist(:, simCounter) = q_jerk;  
  %% Update the target craft
  obs_pos = obs_pos + target_velocity * dt;
  target_position_hist(:, simCounter) = obs_pos;
  
  simCounter = simCounter + 1;
  endtime_mod = t;
  
end
%% Visualization
n_sim = 0:dt:endtime_mod;
n_controller = 0:controllerRate:endtime_mod;
n_sensors = 0:imu_rate:endtime_mod;
n_motor = 0:motor_control_period:endtime_mod;
n_plan = 0:plan_rate:endtime_mod;
k_simCounter = 1:simCounter-1;
k_plan = 1:(plan_rate/dt):simCounter-1;

figure;
subplot(3, 1, 1);
plot(n_sim, anglesHist(1, k_simCounter));
title('Yaw of Craft vs. Time');

subplot(3,1,2);
plot(n_sim, anglesHist(2, k_simCounter));
title('Pitch of Craft vs Time');

subplot(3,1,3);
plot(n_sim, anglesHist(3, k_simCounter));
title('Roll of Craft vs Time');

figure;
subplot(3, 1, 1);
plot(n_sim, positionHist(1, k_simCounter));
hold on
plot(n_sim, target_position_hist(1, k_simCounter));
hold off
legend('q pos', 't pos');
title('x of Craft vs. Time');
grid on;

subplot(3,1,2);
plot(n_sim, positionHist(2, k_simCounter));
hold on
plot(n_sim, target_position_hist(2, k_simCounter));
hold off
legend('q pos', 't pos');
title('y of Craft vs Time');
grid on;

subplot(3,1,3);
plot(n_sim, positionHist(3, k_simCounter));
hold on
plot(n_sim, target_position_hist(3, k_simCounter));
hold off
legend('q pos', 't pos');
title('z of Craft vs Time');
grid on;

figure;
plot3(positionHist(1, :), positionHist(2, :), positionHist(3, :), '-o','Color', 'm', 'MarkerSize', 3);
hold on;
plot3(path(:,1), path(:,2), path(:,3), '--');
k = 1:20:controllerCounter-1;
h = 1:200:simCounter-1;
% for w = 1:length(h)
%   v1 = [positionHist(1,h(w)), positionHist(2,h(w)), positionHist(3,h(w))];
%   v2 = [positionHist(1,h(w))+b3_com_hist(1,k(w)), positionHist(2,h(w))+b3_com_hist(2,k(w)), positionHist(3,h(w))+b3_com_hist(3,k(w))];
%   v = [v1; v2];
%   plot3(v(:,1), v(:,2), v(:,3), 'Color', 'r', 'MarkerSize', 3);
%   
%   v1 = [positionHist(1,h(w)), positionHist(2,h(w)), positionHist(3,h(w))];
%   v2 = [positionHist(1,h(w))+rotMatHist(1,3,h(w)), positionHist(2,h(w))+rotMatHist(2,3,h(w)), positionHist(3,h(w))+rotMatHist(3,3,h(w))];
%   v = [v1; v2];
%   plot3(v(:,1), v(:,2), v(:,3), 'Color', 'b', 'MarkerSize', 3);
%   
%   %   v1 = [positionHist(1,h(w)), positionHist(2,h(w)), positionHist(3,h(w))];
%   %   v2 = [positionHist(1,h(w))+b3_d_hist(1,k(w)), positionHist(2,h(w))+b3_d_hist(2,k(w)), positionHist(3,h(w))+b3_d_hist(3,k(w))];
%   %   v = [v1; v2];
%   %   plot3(v(:,1), v(:,2), v(:,3), 'Color', 'k', 'MarkerSize', 3);
%   %
% end
grid on;
%title('position in 3d space');
[x_ell, y_ell, z_ell] = ellipsoid(obs_pos(1), obs_pos(2), obs_pos(3), obs_radi(1), obs_radi(2), obs_radi(3));
surf(x_ell, y_ell, z_ell);

axis equal;
xlabel('Position in X');
ylabel('Position in Y');
zlabel('Position in Z');
hold off;
nC = 1:controllerCounter -1;

figure; 
plot(n_controller, u1_com_hist, 'lineWidth', 2.0)
%title('Commanded Thrust and Actual Thrust');
hold on;
plot(0:dt:endtime_mod, thrust_hist, 'lineWidth', 2.0)
hold off
axis([0 endtime 0 70]);
legend('Commanded Thrust', 'Actual Thrust');
xlabel('Time (s)');
ylabel('Force (N)');

figure; plot(1:controllerCounter-1, M_hist(2,:));
legend('y');
title('Moments Commanded');

figure; plot(1:controllerCounter-1, omega_des_hist)
title('Omega_des');

figure; plot(1:controllerCounter-1, e_R_hist)
title('Rotation error');

figure; plot(1:controllerCounter-1, e_w_hist)
title('Omega error')

figure;
for k = 1:simCounter-1
  magV(k) = norm(velHist(:,k));
  magA(k) = norm(acc_hist(:,k));
end
plot(1:k, magV);
title('Mag of Linear Vel');

figure;
plot(1:k, magA);
title('Mag of Linear Acc');


figure; plot(((1:controllerCounter-1)-1)/100, e_v_hist, 'lineWidth', 2.0)
xlabel('Time (s)');
ylabel('Distance (m)');
legend('Error in X', 'Error in Y', 'Error in Z');
title('Velocity Error');

figure; plot(1:controllerCounter-1, e_r_hist)
title('Position Error');

figure; plot(1:controllerCounter-1, e_R_hist)
title('Rotation Error');

figure; plot(1:controllerCounter-1, e_w_hist)
title('Angular Velocity Error');

figure; plot(1:controllerCounter-1, M_hist)
title('Applied Moments');

figure;
subplot(2,1,1);
plot((1:controllerCounter-1)/100, a_des_hist, 'lineWidth', 2.0);
legend('X Acceleration', 'Y Acceleration', 'Z Acceleration');
xlabel('Time (s)');
ylabel('Acceleration (m/s^2)');
title('Desired Acceelration');

subplot(2,1,2);
plot((1:simCounter-1)/1000, acc_hist, 'lineWidth', 2.0);
legend('X Acceleration', 'Y Acceleration', 'Z Acceleration');
xlabel('Time (s)');
ylabel('Acceleration (m/s^2)');
title('Actual Acceleration');

%% Helper Functions %%%%%%%
function M = hatmap(vector)
  M = [0 -vector(3) vector(2);
     vector(3) 0 -vector(1);
     -vector(2) vector(1) 0];
end

function s = veeMap(R)
s = [R(3,2), R(1,3), R(2,1)];
end

function k = getClosestLocation(k_prev, path, r)
k = k_prev;
if k+1 < length(path)
  if norm(path(k,:)-r) > norm(path(k+1,:)-r)
    minNotFound = true;
    k = k+1;
    while minNotFound && k+1 < length(path)
      if norm(path(k,:)-r) < norm(path(k+1,:)-r)
        minNotFound = false;
      else
        k = k+1;
      end
    end
  end
else
  k = length(path);
end
end

function k = getClosestLocationProfile(k_prev, path, r)
k = k_prev;
if k+1 < length(path)
  if norm(path(k)-r) > norm(path(k+1)-r)
    minNotFound = true;
    k = k+1;
    while minNotFound && k+1 < length(path)
      if norm(path(k)-r) < norm(path(k+1)-r)
        minNotFound = false;
      else
        k = k+1;
      end
    end
  end
else
  k = length(path);
end
end

⛄ 运行结果

⛄ 参考文献

[1] 赵帅.四旋翼飞行器几种姿态控制算法的研究[D].广西师范大学,2017.

[2] 万斌.四旋翼无人机协同作业研究[D].青岛理工大学[2023-07-30].DOI:CNKI:CDMD:2.1018.072052.

⛳️ 代码获取关注我

❤️部分理论引用网络文献，若有侵权联系博主删除

❤️ 关注我领取海量matlab电子书和数学建模资料

🍅 仿真咨询

1 各类智能优化算法改进及应用

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

2.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

3 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

4 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

5 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

6 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

7 电力系统方面

微电网优化、无功优化、配电网重构、储能配置

8 元胞自动机方面

交通流 人群疏散 病毒扩散 晶体生长

9 雷达方面

卡尔曼滤波跟踪、航迹关联、航迹融合