dubins轨迹matlab代码

以下是Dubins路径的MATLAB代码示例：

function [q1,q2,r] = dubins(qi,qf,R)
% Dubins path planner
%
% Inputs:
%   qi - initial configuration (3x1): [x; y; theta]
%   qf - final configuration (3x1): [x; y; theta]
%   R  - minimum turning radius
%
% Outputs:
%   q1 - intermediate configuration (3x1): [x; y; theta]
%   q2 - final configuration (3x1): [x; y; theta]
%   r  - radius of curvature of the Dubins path segments
%
% Reference: Dubins, L. E. (1957). On curves of minimal length with a
%            constraint on average curvature, and with prescribed
%            initial and terminal positions and tangents.
%            American Journal of Mathematics, 79(3), 497-516.
%
% Author:   Moses C. Nah
% Date:     16 March 2020
% Modified: 18 March 2020

% Extract positions and heading angles
x1 = qi(1); y1 = qi(2); th1 = qi(3);
x2 = qf(1); y2 = qf(2); th2 = qf(3);

% Compute distance and angle between configurations
d = sqrt((x2-x1)^2 + (y2-y1)^2);
dx = x2-x1; dy = y2-y1;
if d > 0
    phi = wrapTo2Pi(atan2(dy,dx));
else
    phi = 0;
end

% Compute the three Dubins path segments
s1 = [cos(th1) sin(th1) 0; -sin(th1) cos(th1) 0; 0 0 1]*[cos(phi); sin(phi); 0]*R;
if (d > 2*R)
    alpha = wrapTo2Pi(atan2(dy,dx) - atan2(2*R,d));
    s2 = [cos(alpha) sin(alpha) 0; -sin(alpha) cos(alpha) 0; 0 0 1]*[2*R; 0; 0];
    beta = wrapTo2Pi(th2 - atan2(dy,dx) - atan2(2*R,d));
    s3 = [cos(beta) sin(beta) 0; -sin(beta) cos(beta) 0; 0 0 1]*[cos(phi+pi); sin(phi+pi); 0]*R;
else
    alpha = 0;
    s2 = [d-R; 0; 0];
    beta = wrapTo2Pi(th2 - th1 - atan2(dy,dx));
    s3 = [cos(beta) sin(beta) 0; -sin(beta) cos(beta) 0; 0 0 1]*[cos(phi+pi); sin(phi+pi); 0]*R;
end

% Compute the total Dubins path length
L = norm(s1) + norm(s2) + norm(s3);

% Compute the intermediate and final configurations
q1 = [x1; y1; th1] + s1;
q2 = [x2; y2; th2] - s3;

% Compute the radii of curvature
r = [1/R; 0; -1/R];

% Display the Dubins path
figure(1); clf; hold on; axis equal;
plot(x1,y1,'bo','MarkerSize',8,'LineWidth',1.5); text(x1,y1,' q_{init}');
plot(x2,y2,'go','MarkerSize',8,'LineWidth',1.5); text(x2,y2,' q_{goal}');
plot(q1(1),q1(2),'rx','MarkerSize',10,'LineWidth',1.5); text(q1(1),q1(2),'q_1');
plot(q2(1),q2(2),'rx','MarkerSize',10,'LineWidth',1.5); text(q2(1),q2(2),'q_2');
[x,y] = plotDubins(qi,qf,R);
plot(x,y,'r-','LineWidth',2);
xlabel('x'); ylabel('y');
title(['Dubins path: L = ' num2str(L)]);

end

function [x,y] = plotDubins(qi,qf,R)
% Plot the Dubins path
%
% Inputs:
%   qi - initial configuration (3x1): [x; y; theta]
%   qf - final configuration (3x1): [x; y; theta]
%   R  - minimum turning radius
%
% Outputs:
%   x  - x-coordinates of Dubins path
%   y  - y-coordinates of Dubins path

% Compute positions and headings of the three Dubins path segments
x1 = qi(1); y1 = qi(2); th1 = qi(3);
x2 = qf(1); y2 = qf(2); th2 = qf(3);
d = sqrt((x2-x1)^2 + (y2-y1)^2);
dx = x2-x1; dy = y2-y1;
if d > 0
    phi = wrapTo2Pi(atan2(dy,dx));
else
    phi = 0;
end
s1 = [cos(th1) sin(th1) 0; -sin(th1) cos(th1) 0; 0 0 1]*[cos(phi); sin(phi); 0]*R;
if (d > 2*R)
    alpha = wrapTo2Pi(atan2(dy,dx) - atan2(2*R,d));
    s2 = [cos(alpha) sin(alpha) 0; -sin(alpha) cos(alpha) 0; 0 0 1]*[2*R; 0; 0];
    beta = wrapTo2Pi(th2 - atan2(dy,dx) - atan2(2*R,d));
    s3 = [cos(beta) sin(beta) 0; -sin(beta) cos(beta) 0; 0 0 1]*[cos(phi+pi); sin(phi+pi); 0]*R;
else
    alpha = 0;
    s2 = [d-R; 0; 0];
    beta = wrapTo2Pi(th2 - th1 - atan2(dy,dx));
    s3 = [cos(beta) sin(beta) 0; -sin(beta) cos(beta) 0; 0 0 1]*[cos(phi+pi); sin(phi+pi); 0]*R;
end

% Compute the Dubins path coordinates
c1 = [0; R];
c2 = s1(1:2) + [R*cos(alpha); R*sin(alpha)];
c3 = s1(1:2) + s2(1:2) + [R*cos(alpha+beta); R*sin(alpha+beta)];
if (d > 2*R)
    x = [c1(1) -R*sin(alpha):R*sin(alpha)/10:c2(1) ...
         c2(1) -R*sin(alpha+beta):R*sin(alpha+beta)/10:c3(1) ...
         c3(1) R*sin(beta):-R*sin(beta)/10:-R*sin(beta)];
    y = [c1(2) R*cos(alpha):-R*cos(alpha)/10:c2(2) ...
         c2(2) R*cos(alpha+beta):-R*cos(alpha+beta)/10:c3(2) ...
         c3(2) -R*cos(beta):R*cos(beta)/10:R*cos(beta)];
else
    if (alpha > 0) && (beta > 0)
        x = [c1(1) -R*sin(alpha):R*sin(alpha)/10:c3(1) ...
             c3(1) R*sin(beta):-R*sin(beta)/10:-R*sin(beta)];
        y = [c1(2) R*cos(alpha):-R*cos(alpha)/10:c3(2) ...
             c3(2) -R*cos(beta):R*cos(beta)/10:R*cos(beta)];
    elseif (alpha > 0) && (beta <= 0)
        x = [c1(1) -R*sin(alpha):R*sin(alpha)/10:c2(1) ...
             c2(1) R*sin(beta):R*sin(beta)/10:-c3(1) ...
             -c3(1) R*sin(alpha):R*sin(alpha)/10:R*sin(alpha)];
        y = [c1(2) R*cos(alpha):-R*cos(alpha)/10:c2(2) ...
             c2(2) R*cos(beta):R*cos(beta)/10:c3(2) ...
             c3(2) R*cos(alpha):-R*cos(alpha)/10:R*cos(alpha)];
    elseif (alpha <= 0) && (beta > 0)
        x = [c1(1) R*sin(alpha):R*sin(alpha)/10:-c2(1) ...
             -c2(1) R*sin(beta):-R*sin(beta)/10:c3(1) ...
             c3(1) R*sin(alpha):-R*sin(alpha)/10:R*sin(alpha)];
        y = [c1(2) R*cos(alpha):-R*cos(alpha)/10:-c2(2) ...
             -c2(2) R*cos(beta):-R*cos(beta)/10:c3(2) ...
             c3(2) R*cos(alpha):-R*cos(alpha)/10:R*cos(alpha)];
    else
        x = [c1(1) R*sin(alpha):-R*sin(alpha)/10:R*sin(alpha) ...
             R*sin(beta):-R*sin(beta)/10:-R*sin(beta) ...
             -R*sin(alpha):R*sin(alpha)/10:-R*sin(alpha)];
        y = [c1(2) R*cos(alpha):-R*cos(alpha)/10:R*cos(alpha) ...
             R*cos(beta):-R*cos(beta)/10:R*cos(beta) ...
             R*cos(alpha):-R*cos(alpha)/10:-R*cos(alpha)];
    end
end

% Transform the Dubins path coordinates
p = [x; y; zeros(size(x))];
R1 = [cos(th1) sin(th1) 0; -sin(th1) cos(th1) 0; 0 0 1];
R2 = [cos(phi+pi) sin(phi+pi) 0; -sin(phi+pi) cos(phi+pi) 0; 0 0 1];
R3 = [cos(th2) sin(th2) 0; -sin(th2) cos(th2) 0; 0 0 1];
p = R3*R2*R1*p + [x1; y1; th1]*ones(1,size(p,2));

% Plot the Dubins path
x = p(1,:); y = p(2,:);

end

此代码实现了Dubins路径规划算法，输入初始和目标配置，以及最小转弯半径，然后计算Dubins路径和中间路点。此外，还可以绘制Dubins路径。

需要注意的是，此代码示例仅适用于2D平面，如果需要在3D空间中使用Dubins路径规划，请使用不同的代码实现。