自动驾驶——【规划】记忆泊车特殊学习路径拟合

1.Back ground

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如上图，SLAM学习路线Start到End路径，其中曲线SDAB为D档位学习路径，曲线BC为R学习路径，曲线AE为前进档D档学习路径。
为了使其使用记忆泊车时，其驾驶员体验感好，需去除R档倒车部分轨迹，并拟合一条可用的曲线

2.Algorithm Introduction

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D点作为起点，D（XD,YD,theta_D）,C点作为终点（XC,YC,theta_C），使用y = a0 + a1 * x + a2 * x^2 + a3 * x^3拟合曲线DC，有：
YC = a0 + a1 * XC+ a2 * XC ^2 + a3 * XC^3
YD = a0 + a1 * XD + a2 * XD ^2 + a3 * XD ^3
tan(theta_C) = a1 + 2 * a2 * XC + 3 * a3 * XC^2
tan(theta_D) = a1 + 2 * a2 * XD + 3 * a3 * XD^2
即可求解a0 a1 a2 a3，进而得出曲线DC。
最后优化的曲线为SDCE。

3.Coding using MATLAB

%Function：记忆泊车学习路径拟合
%Create by：Juchunyu
%Date：2023-09-01 17:00:42%设计轨迹x，y
% y = 2 (10>=x>=0)
% y = -1.2/50 *x^2 - 4.4/10 *x   (10>=x>=5)
% y = 1.6 (20>=x>=5)
slam_x     = [];
slam_y     = [];
slam_theta = [];
GearInfo   = [];%D:4 R:2
D  = 4;
R  = 2;
%Generate trajpoint
for i = 0 : 0.2 :10slam_x   = [slam_x i];slam_y   = [slam_y 2];GearInfo = [GearInfo D];slam_theta = [slam_theta 0];
end
for i =10:-0.2:5slam_x   = [slam_x i];y_temp   = -1.2*i*i/50 + 4.4 * i/10;slam_y   = [slam_y y_temp];GearInfo = [GearInfo R];slam_theta_temp = -2.4*i/50 - 4.4/10;slam_theta = [slam_theta slam_theta_temp];
endfor i = 5:0.2:20slam_x   = [slam_x i];slam_y   = [slam_y 1.6];GearInfo = [GearInfo D];slam_theta = [slam_theta 0];
endfigure(1)
plot(slam_x,slam_y);
title('SLAM学习曲线')
hold on 
%%处理算法%检测倒车 只检测一次倒车
Index_start = 0;
Index_end   = 0;
Index_startArr = [];
Index_endArr   = [];[m_ size_] = size(slam_x);while i < size_Index_start = 0;Index_end   = 0;finish_Flag = 0;if(GearInfo(1,i) == R)Index_start = i;j = Index_start;while j < size_if GearInfo(1,j) == DIndex_end   = j;finish_Flag = 1;break;endj = j + 1;  endif(finish_Flag == 1)Index_startArr = [Index_startArr Index_start];Index_endArr   = [Index_endArr Index_end];endi = j;endi = i + 1;
endPointCIndx = Index_endArr(1,1);
PointBIndx = Index_startArr(1,1); 
PointAIndx = 0;
%处理算法
% find near Point
min_ = 1000000;
for i = 1:1:Index_startArr(1,1)dist = ((slam_x(1,PointCIndx) - slam_x(1,i))^2 + (slam_y(1,PointCIndx) - slam_y(1,i))^2)^(0.5);if(dist < min_)min_       =  dist;PointAIndx = i;end
end%计算DAdistDA = ((slam_x(1,PointAIndx) - slam_x(1,1))^2 + (slam_y(1,PointAIndx) - slam_y(1,1))^2)^(0.5);%往前推算1m
PointDIndx = PointAIndx;
if(distDA > 1.0)for i = PointAIndx:-1:1dist_  = ((slam_x(1,PointAIndx) - slam_x(1,i))^2 + (slam_y(1,PointAIndx) - slam_y(1,i))^2)^(0.5);if(dist_ > 1.0)PointDIndx = i;break; endend
end%处理D点到C点曲线平滑
PointDx = slam_x(1,PointDIndx);
PointDy = slam_y(1,PointDIndx);PointCx = slam_x(1,PointCIndx);
PointCy = slam_y(1,PointCIndx);
%A*X = BA(1,1) = 1;
A(1,2) = PointCx;
A(1,3) = PointCx * PointCx;
A(1,4) = PointCx * PointCx * PointCx;A(2,1) = 1;
A(2,2) = PointDx;
A(2,3) = PointDx * PointDx;
A(2,4) = PointDx * PointDx * PointDx;A(3,1) = 0;
A(3,2) = 1;
A(3,3) = 2 * PointCx;
A(3,4) = 3 * PointCx * PointCx;A(4,1) = 0;
A(4,2) = 1;
A(4,3) = 2 * PointDx;
A(4,4) = 3 * PointDx * PointDx;B(1,1) = PointCy;
B(2,1) = PointDy;
B(3,1) = tan(slam_theta(1,PointCIndx));
B(4,1) = tan(slam_theta(1,PointDIndx));X = A^-1 * B;%%拟合曲线系数
a0 = X(1,1);
a1 = X(2,1);
a2 = X(3,1);
a3 = X(4,1);%重组轨迹曲线
slam_Xfinal = [];
slam_Yfinal = [];
slam_thetaFinal = [];
for i = 1:1:PointDIndxslam_Xfinal = [slam_Xfinal slam_x(1,i)];slam_Yfinal = [slam_Yfinal slam_y(1,i)];slam_thetaFinal = [slam_thetaFinal slam_theta(1,i)];
end%拟合曲线DC
for x = PointDx:0.2:PointCxslam_Xfinal = [slam_Xfinal x];y_temp      = a0 + a1 * x + a2 * x^2 + a3 * x^3;theta_temp  = a1 + 2 * a2 * x + 3 * a3 *x^2;slam_Yfinal = [slam_Yfinal y_temp];slam_thetaFinal = [slam_thetaFinal theta_temp]; 
end%组合后部分曲线
for i = PointCIndx:1:size_slam_Xfinal = [slam_Xfinal slam_x(1,i)];slam_Yfinal = [slam_Yfinal slam_y(1,i)];slam_thetaFinal = [slam_thetaFinal slam_theta(1,i)];
endhold on figure(2)
plot(slam_Xfinal,slam_Yfinal,'r');
title('处理后的SLAM学习曲线')