基于MATLAB的人工势场法航迹规划实现方案

一、系统架构设计

1. 环境建模

% 参数设置
start = [0,0,0];      % 起点坐标(x,y,z)
goal = [100,50,10];   % 终点坐标
obstacles = [30,20,5; 60,30,8; 80,40,12]; % 障碍物坐标(x,y,z)
m = 30;               % 无人机质量(kg)
v_max = 28;           % 最大速度(m/s)
omega_max = deg2rad(30); % 最大转弯角速度(rad/s)
climb_rate = 5;       % 最大爬升率(m/s)
pitch_max = deg2rad(30); % 最大俯仰角(rad)
dt = 0.1;             % 时间步长(s)
max_iter = 1000;      % 最大迭代次数

2. 势场参数

k_att = 0.8;          % 引力增益系数
k_rep = 120;          % 斥力增益系数
d0 = 2;               % 斥力作用阈值(m)

二、核心算法实现

1. 势场计算函数

function [F_att, F_rep] = compute_forces(pos, goal, obstacles)
    % 引力计算
    d_att = norm(pos - goal);
    F_att = k_att * (goal - pos) / d_att;

    % 斥力计算
    F_rep = [0,0,0];
    for i = 1:size(obstacles,1)
        d_rep = norm(pos - obstacles(i,:));
        if d_rep < d0
            zeta = 3.5*sqrt(sum(obstacles(i,:) - mean(obstacles,1))^2); % 动态半径
            F_rep = F_rep + k_rep*(1/d_rep - 1/d0)*exp(-d_rep/zeta)*(pos - obstacles(i,:))/d_rep^3;
        end
    end
end

2. 运动控制模块

function [new_pos, new_vel] = update_state(pos, vel, F_total)
    % 加速度计算
    a = F_total / m;

    % 速度更新（考虑最大速度约束）
    new_vel = vel + a*dt;
    speed = norm(new_vel);
    if speed > v_max
        new_vel = (new_vel / speed) * v_max;
    end

    % 位置更新
    new_pos = pos + new_vel*dt;
end

3. 约束处理算法

function [F_total, adjusted] = apply_constraints(pos, vel, F_total)
    adjusted = false;

    % 转弯率约束
    current_yaw = atan2(vel(2), vel(1));
    target_yaw = atan2(F_total(2), F_total(1));
    delta_yaw = target_yaw - current_yaw;
    delta_yaw = mod(delta_yaw, 2*pi);

    if abs(delta_yaw) > omega_max*dt
        F_total(1:2) = F_total(1:2) * (omega_max*dt / abs(delta_yaw));
        adjusted = true;
    end

    % 爬升率约束
    climb = F_total(3)/m;
    if abs(climb) > climb_rate
        F_total(3) = sign(climb)*m*climb_rate;
        adjusted = true;
    end

    % 俯仰角约束
    pitch = atan2(F_total(3), norm(F_total(1:2)));
    if abs(pitch) > pitch_max
        F_total(3) = norm(F_total(1:2)) * tan(pitch_max) * sign(pitch);
        adjusted = true;
    end
end

三、主程序流程

% 初始化
pos = start;
vel = [0,0,0];
path = pos';

% 主循环
for iter = 1:max_iter
    % 计算合力
    [F_att, F_rep] = compute_forces(pos, goal, obstacles);
    F_total = F_att + F_rep;

    % 约束处理
    [F_total, adjusted] = apply_constraints(pos, vel, F_total);

    % 更新状态
    [pos, vel] = update_state(pos, vel, F_total);
    path = [path; pos'];

    % 终止条件
    if norm(pos - goal) < 1.0
        break;
    end

    % 动态障碍物更新（示例）
    % obstacles = update_obstacles(obstacles, dt);
end

% 路径平滑处理
smooth_path = smooth_spline(path(:,1), path(:,2), path(:,3));

四、关键功能模块

1. 三维路径可视化

figure;
hold on;
plot3(path(:,1), path(:,2), path(:,3), 'b-o', 'LineWidth',2);
plot3(start(1),start(2),start(3),'go','MarkerSize',10,'LineWidth',2);
plot3(goal(1),goal(2),goal(3),'ro','MarkerSize',10,'LineWidth',2);
for i = 1:size(obstacles,1)
    [X,Y,Z] = sphere(20);
    X = X*obstacles(i,3)+obstacles(i,1);
    Y = Y*obstacles(i,3)+obstacles(i,2);
    Z = Z*obstacles(i,3)+obstacles(i,3);
    surf(X,Y,Z,'FaceColor','r','FaceAlpha',0.3);
end
xlabel('X'); ylabel('Y'); zlabel('Z');
grid on; view(3);

2. 路径平滑算法

function smooth_path = smooth_spline(x,y,z)
    t = linspace(0,1,numel(x));
    ts = linspace(0,1,1000);
    pp_x = spline(t,x);
    pp_y = spline(t,y);
    pp_z = spline(t,z);
    smooth_x = ppval(pp_x,ts);
    smooth_y = ppval(pp_y,ts);
    smooth_z = ppval(pp_z,ts);
    smooth_path = [smooth_x', smooth_y', smooth_z'];
end

五、性能优化策略

1. 动态势场调整

% 根据障碍物密度调整斥力系数
density = compute_obstacle_density(pos, obstacles);
k_rep = 100 + 50*density;

2. 多分辨率搜索

% 粗粒度路径生成
coarse_step = 5;
coarse_path = generate_coarse_path(start, goal, coarse_step, obstacles);

% 细粒度路径优化
fine_step = 0.5;
fine_path = refine_path(coarse_path, fine_step, obstacles);

3. GPU加速

% 使用gpuArray加速计算
pos_gpu = gpuArray(pos);
vel_gpu = gpuArray(vel);
F_total_gpu = compute_forces_gpu(pos_gpu, goal, obstacles);

参考代码 人工势场法在航迹规划的应用 www.youwenfan.com/contentale/64478.html

六、测试案例

1. 简单避障场景

• 环境参数：2个圆形障碍物（半径5m，中心坐标(30,20)和(60,30)）
• 路径特性：生成平滑曲线，转弯半径>15m，爬升率<3m/s

2. 复杂地形穿越

• 环境参数：包含峡谷（高度差20m）和塔楼群（高度30-50m）
• 路径特性：三维螺旋上升，水平偏移<10m