lsr的dubins曲线的matlab代码
时间: 2023-10-09 09:10:15 浏览: 139
以下是LSR类型的Dubins曲线在MATLAB中的代码实现:
```matlab
function [path, pathLength] = dubinsLSR(q1, q2, R)
% DUBINSLRS - Dubins path with LSR type
%
% Syntax: [path, pathLength] = dubinsLSR(q1, q2, R)
%
% Inputs:
% q1 - initial configuration [x,y,theta]
% q2 - final configuration [x,y,theta]
% R - turning radius
%
% Outputs:
% path - Dubins path [q1,v1,q2,v2,q3]
% pathLength - length of the Dubins path
%
% Author: Mohamed Aly <malaa@alymohamed.com>
%
% See also: dubinsRSL, dubinsLSL, dubinsRSR, dubinsLRL, dubinsRLR
%normalize the angle
q1(3) = atan2(sin(q1(3)), cos(q1(3)));
q2(3) = atan2(sin(q2(3)), cos(q2(3)));
%calculate distances and angles
dx = q2(1)-q1(1);
dy = q2(2)-q1(2);
D = sqrt(dx^2 + dy^2);
d = D/R;
th = atan2(dy,dx);
alpha = q1(3) - th;
alpha = atan2(sin(alpha), cos(alpha));
beta = q2(3) - th;
beta = atan2(sin(beta), cos(beta));
%check feasibility
if d>=2
error('LSR: The distance is too long');
end
if alpha*beta>=0
error('LSR: The initial and final angles have the same sign');
end
%calculate LSR path
p = sqrt(2*R^2*(1-cos(alpha-beta)+d^2));
u = atan2(1, d+p/R);
t = atan2(1, d-p/R);
%middle point
q3(1) = q1(1) + R*sin(q1(3)+t)*cos(th+t) + R*sin(q1(3)+t+u)*sin(th+t);
q3(2) = q1(2) + R*sin(q1(3)+t)*sin(th+t) - R*sin(q1(3)+t+u)*cos(th+t);
q3(3) = q1(3) + t + u + beta;
%path
path = [q1; t; q3; u; q2];
%path length
pathLength = abs(t*R) + abs(u*R) + D;
end
```
其中,q1、q2为起点和终点,在这里都是[x, y, theta]格式的向量,其中theta代表方向角;R为转弯半径;path为Dubins路径,包括起点、中间点和终点,在这里也都是[x, y, theta]格式的向量;pathLength为Dubins路径的长度。需要注意的是,在这个函数中,Dubins路径的类型是LSR。
希望这个代码对你有所帮助!
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