dubins曲线的matlab代码

以下是一个简单的 Dubins 曲线的 Matlab 代码示例：

function [path] = dubins_curve(start, end, R)
% DUBINS_CURVE  Compute Dubins curve between two points with a given minimum turning radius
%   start: starting pose [x, y, theta]
%   end: ending pose [x, y, theta]
%   R: minimum turning radius
%   path: [length, curvature, segment_type] for each segment in the Dubins curve

q0 = start(1:2)';
theta0 = start(3);
q1 = end(1:2)';
theta1 = end(3);

c = [q0(1) - R*sin(theta0); q0(2) + R*cos(theta0)];
angle = atan2(q1(2)-c(2), q1(1)-c(1));
d = norm(q1-c);

if d < 2*R
    error('Dubins path not possible, distance between points is too small');
end

path = [];

% Compute LSL path
theta = mod(angle - theta0, 2*pi);
if theta < 0
    theta = theta + 2*pi;
end
L = d - 2*R*sin(theta/2);
if L >= 0
    path(end+1,:) = [L, 0, 'L'];
    path(end+1,:) = [R, theta, 'S'];
    path(end+1,:) = [L, 0, 'L'];
end

% Compute RSR path
theta = mod(angle - theta1, 2*pi);
if theta < 0
    theta = theta + 2*pi;
end
L = d - 2*R*sin(theta/2);
if L >= 0
    path(end+1,:) = [L, 0, 'R'];
    path(end+1,:) = [R, theta, 'S'];
    path(end+1,:) = [L, 0, 'R'];
end

% Compute LSR path
theta = mod(theta1 - angle, 2*pi);
if theta < 0
    theta = theta + 2*pi;
end
L = sqrt(d^2 - 4*R^2) + R*theta;
if L >= 0
    path(end+1,:) = [sqrt(d^2 - 4*R^2), 0, 'L'];
    path(end+1,:) = [R, mod(angle - atan2(q1(2)-c(2), q1(1)-c(1)), 2*pi), 'S'];
    path(end+1,:) = [R, mod(angle - theta1 + atan2(q1(2)-c(2), q1(1)-c(1)), 2*pi), 'S'];
    path(end+1,:) = [sqrt(d^2 - 4*R^2), 0, 'L'];
end

% Compute RSL path
theta = mod(theta0 - angle, 2*pi);
if theta < 0
    theta = theta + 2*pi;
end
L = sqrt(d^2 - 4*R^2) + R*theta;
if L >= 0
    path(end+1,:) = [sqrt(d^2 - 4*R^2), 0, 'R'];
    path(end+1,:) = [R, mod(theta0 - atan2(q1(2)-c(2), q1(1)-c(1)), 2*pi), 'S'];
    path(end+1,:) = [R, mod(theta0 - angle + atan2(q1(2)-c(2), q1(1)-c(1)), 2*pi), 'S'];
    path(end+1,:) = [sqrt(d^2 - 4*R^2), 0, 'R'];
end

end

这个函数将起始点、终点和最小转弯半径作为输入参数，并返回一个包含 Dubins 曲线的各个段的长度、曲率和类型的列表。