forked from IITISoC-IVR/PathPlanning-IVR5
-
Notifications
You must be signed in to change notification settings - Fork 0
/
minimumCurvaturePathGeneration.m
166 lines (125 loc) · 4.29 KB
/
minimumCurvaturePathGeneration.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
function [trajMCP, trackData] = minimumCurvaturePathGeneration(track,name)
%% Processing track data
% track data - first point repeated
data = track;
% x,y and track width data
x = data(:,1);
y = data(:,2);
twr = data(:,3);
twl = data(:,4);
% interpolate data to get finer curve with equal distances between each segment
% higher no. of segments causes trajectory to follow the reference line
nseg = 1500;
pathXY = [x y];
stepLengths = sqrt(sum(diff(pathXY,[],1).^2,2));
stepLengths = [0; stepLengths]; % add the starting point
cumulativeLen = cumsum(stepLengths);
finalStepLocs = linspace(0,cumulativeLen(end), nseg);
finalPathXY = interp1(cumulativeLen, pathXY, finalStepLocs);
xt = finalPathXY(:,1);
yt = finalPathXY(:,2);
twrt = interp1(cumulativeLen, twr, finalStepLocs,'spline')';
twlt = interp1(cumulativeLen, twl, finalStepLocs,'spline')';
% normal direction for each vertex
dx = gradient(xt);
dy = gradient(yt);
dL = hypot(dx,dy);
% offset curve - anonymous function
xoff = @(a) -a*dy./dL + xt;
yoff = @(a) a*dx./dL + yt;
% plot reference line
plot(xt,yt,'g')
hold on
% offset data
offset = [-twrt twlt];
for i = 1:numel(xt)
xin = xoff(offset(i,1)); % get inner offset curve
yin = yoff(offset(i,1));
xout = xoff(offset(i,2)); % get outer offset curve
yout = yoff(offset(i,2));
end
% plot inner track
plot(xin,yin,'color','b','linew',2)
% plot outer track
plot(xout,yout,'color','r','linew',2)
hold off
axis equal
xlabel('x(m)','fontweight','bold','fontsize',14)
ylabel('y(m)','fontweight','bold','fontsize',14)
title(sprintf(name),'fontsize',16)
% % plot segments
% figure
% hold on
% for i=1:numel(xout)
% plot([xin(i) xout(i)], [yin(i) yout(i)])
% end
% form delta matrices
delx = xout - xin;
dely = yout - yin;
trackData = [xt yt xin yin xout yout];
%% Matrix Definition
% number of segments
n = numel(delx);
% preallocation
H = zeros(n);
B = zeros(size(delx)).';
% formation of H matrix (nxn)
for i=2:n-1
% first row
H(i-1,i-1) = H(i-1,i-1) + delx(i-1)^2 + dely(i-1)^2;
H(i-1,i) = H(i-1,i) - 2*delx(i-1)*delx(i) - 2*dely(i-1)*dely(i);
H(i-1,i+1) = H(i-1,i+1) + delx(i-1)*delx(i+1) + dely(i-1)*dely(i+1);
%second row
H(i,i-1) = H(i,i-1) - 2*delx(i-1)*delx(i) - 2*dely(i-1)*dely(i);
H(i,i) = H(i,i ) + 4*delx(i)^2 + 4*dely(i)^2;
H(i,i+1) = H(i,i+1) - 2*delx(i)*delx(i+1) - 2*dely(i)*dely(i+1);
% third row
H(i+1,i-1) = H(i+1,i-1) + delx(i-1)*delx(i+1) + dely(i-1)*dely(i+1);
H(i+1,i) = H(i+1,i) - 2*delx(i)*delx(i+1) - 2*dely(i)*dely(i+1);
H(i+1,i+1) = H(i+1,i+1) + delx(i+1)^2 + dely(i+1)^2;
end
% formation of B matrix (1xn)
for i=2:n-1
B(1,i-1) = B(1,i-1) + 2*(xin(i+1)+xin(i-1)-2*xin(i))*delx(i-1) + 2*(yin(i+1)+yin(i-1)-2*yin(i))*dely(i-1);
B(1,i) = B(1,i) - 4*(xin(i+1)+xin(i-1)-2*xin(i))*delx(i) - 4*(yin(i+1)+yin(i-1)-2*yin(i))*dely(i);
B(1,i+1) = B(1,i+1) + 2*(xin(i+1)+xin(i-1)-2*xin(i))*delx(i+1) + 2*(yin(i+1)+yin(i-1)-2*yin(i))*dely(i+1);
end
% define constraints
lb = zeros(n,1);
ub = ones(size(lb));
% if start and end points are the same
Aeq = zeros(1,n);
Aeq(1) = 1;
Aeq(end) = -1;
beq = 0;
%% Solver
options = optimoptions('quadprog','Display','iter');
[resMCP,fval,exitflag,output] = quadprog(2*H,B',[],[],Aeq,beq,lb,ub,[],options);
%% Plotting results
% co-ordinates for the resultant curve
xresMCP = zeros(size(xt));
yresMCP = zeros(size(xt));
for i = 1:numel(xt)
xresMCP(i) = xin(i)+resMCP(i)*delx(i);
yresMCP(i) = yin(i)+resMCP(i)*dely(i);
end
% plot minimum curvature trajectory
figure
plot(xresMCP,yresMCP,'color','r','linew',2)
hold on
% plot starting line
plot([xin(1) xout(1)], [yin(1) yout(1)],'color','b','linew',2)
% plot([xin(2) xout(2)], [yin(2) yout(2)],'color','k','linew',2)
% plot reference line
plot(xt,yt,'--')
hold on
% plot inner track
plot(xin,yin,'color','k')
%plot outer track
plot(xout,yout,'color','k')
hold off
axis equal
xlabel('x(m)','fontweight','bold','fontsize',14)
ylabel('y(m)','fontweight','bold','fontsize',14)
title(sprintf(name,'%s - Minimum Curvature Trajectory'),'fontsize',16)
trajMCP = [xresMCP yresMCP];