forked from symao/minimum_snap_trajectory_generation
-
Notifications
You must be signed in to change notification settings - Fork 0
/
demo4_minimum_snap_guiding.m
148 lines (129 loc) · 3.64 KB
/
demo4_minimum_snap_guiding.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
function demo4_minimum_snap_guiding()
clear,clc;
%% condition
waypts = [0,0;
1,2;
2,0;
4,5;
5,2]';
v0 = [0,0];
a0 = [0,0];
v1 = [0,0];
a1 = [0,0];
T = 5;
n_order = 5;
lambda = 10; %guiding weight
%% sample mid points
r = 0.5; %% corridor r
step = r;
new_waypts = waypts(:,1);
for i=2:size(waypts,2)
x1 = waypts(1,i-1);
y1 = waypts(2,i-1);
x2 = waypts(1,i);
y2 = waypts(2,i);
n = ceil(hypot(x1-x2,y1-y2)/step)+1;
sample_pts = [linspace(x1,x2,n);linspace(y1,y2,n)];
new_waypts = [new_waypts sample_pts(:,2:end)];
end
ts = arrangeT(new_waypts,T);
figure(1)
plot_idx = 221;
for lambda = [0,10,100,10000]
subplot(plot_idx);
%% trajectory plan
polys_x = minimum_snap_single_axis_guiding_path(new_waypts(1,:),ts,n_order,v0(1),a0(1),v1(1),a1(1),r,lambda);
polys_y = minimum_snap_single_axis_guiding_path(new_waypts(2,:),ts,n_order,v0(2),a0(2),v1(2),a1(2),r,lambda);
%% result show
plot(new_waypts(1,:),new_waypts(2,:),'.g');hold on;
plot(waypts(1,:),waypts(2,:),'*r');hold on;
for i=1:size(new_waypts,2)
plot_rect(new_waypts(:,i),r);
end
title(['\lambda = ' num2str(lambda)]);
tt = 0:0.01:T;
xx = polys_vals(polys_x,ts,tt,0);
yy = polys_vals(polys_y,ts,tt,0);
plot(xx,yy,'r');
plot_idx = plot_idx+1;
end
end
function plot_rect(center,r)
p1 = center+[-r;-r];
p2 = center+[-r;r];
p3 = center+[r;r];
p4 = center+[r;-r];
plot_line(p1,p2);
plot_line(p2,p3);
plot_line(p3,p4);
plot_line(p4,p1);
end
function plot_line(p1,p2)
a = [p1(:),p2(:)];
plot(a(1,:),a(2,:),'b');
end
function polys = minimum_snap_single_axis_guiding_path(waypts,ts,n_order,v0,a0,ve,ae,corridor_r,lambda)
p0 = waypts(1);
pe = waypts(end);
n_poly = length(waypts)-1;
n_coef = n_order+1;
% compute Q
Q_all = [];
for i=1:n_poly
Q_all = blkdiag(Q_all,computeQ(n_order,3,ts(i),ts(i+1)));
end
b_all = zeros(size(Q_all,1),1);
% add guiding pos
H_guide = [];
b_guide = [];
for i = 1:n_poly
t1 = ts(i);
t2 = ts(i+1);
p1 = waypts(i);
p2 = waypts(i+1);
a1 = (p2-p1)/(t2-t1);
a0 = p1-a1*t1;
ci = zeros(n_coef,1);
ci(1:2,1) = [a0;a1]; %guiding polynormial with linear curve
Qi = computeQ(n_order,0,t1,t2);
bi = -Qi'*ci;
H_guide = blkdiag(H_guide,Qi);
b_guide = [b_guide;bi];
end
Q_all = Q_all+lambda*H_guide;
b_all = b_all+lambda*b_guide;
Aeq = zeros(3*n_poly+3,n_coef*n_poly);
beq = zeros(3*n_poly+3,1);
% start/terminal pva constraints (6 equations)
Aeq(1:3,1:n_coef) = [calc_tvec(ts(1),n_order,0);
calc_tvec(ts(1),n_order,1);
calc_tvec(ts(1),n_order,2)];
Aeq(4:6,n_coef*(n_poly-1)+1:n_coef*n_poly) = ...
[calc_tvec(ts(end),n_order,0);
calc_tvec(ts(end),n_order,1);
calc_tvec(ts(end),n_order,2)];
beq(1:6,1) = [p0,v0,a0,pe,ve,ae]';
neq = 6;
% continuous constraints ((n_poly-1)*3 equations)
for i=1:n_poly-1
tvec_p = calc_tvec(ts(i+1),n_order,0);
tvec_v = calc_tvec(ts(i+1),n_order,1);
tvec_a = calc_tvec(ts(i+1),n_order,2);
neq=neq+1;
Aeq(neq,n_coef*(i-1)+1:n_coef*(i+1))=[tvec_p,-tvec_p];
neq=neq+1;
Aeq(neq,n_coef*(i-1)+1:n_coef*(i+1))=[tvec_v,-tvec_v];
neq=neq+1;
Aeq(neq,n_coef*(i-1)+1:n_coef*(i+1))=[tvec_a,-tvec_a];
end
% corridor constraints (n_ploy-1 iequations)
Aieq = zeros(2*(n_poly-1),n_coef*n_poly);
bieq = zeros(2*(n_poly-1),1);
for i=1:n_poly-1
tvec_p = calc_tvec(ts(i+1),n_order,0);
Aieq(2*i-1:2*i,n_coef*i+1:n_coef*(i+1)) = [tvec_p;-tvec_p];
bieq(2*i-1:2*i) = [waypts(i+1)+corridor_r corridor_r-waypts(i+1)];
end
p = quadprog(Q_all,b_all,Aieq,bieq,Aeq,beq);
polys = reshape(p,n_coef,n_poly);
end