-
Notifications
You must be signed in to change notification settings - Fork 2
/
quaternionTest.m
141 lines (96 loc) · 3.77 KB
/
quaternionTest.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
clc;
%% Rotating 90° around X
clear all; disp('Rotating 90° around X');
disp('----------------------------------------');
A = affine_rotation_x(degtorad(90));
Rin = A(1:3, 1:3);
q = quaternionFromRotation(Rin);
R = quaternionToRotation(q)
expect = Rin;
maximumError = max(max(expect - R))
X = R*[1; 0; 0]; Y = R*[0; 1; 0]; Z = R*[0; 0; 1];
fprintf('X: %10.2f %10.2f %10.2f\n', X(1), X(2), X(3));
fprintf('Y: %10.2f %10.2f %10.2f\n', Y(1), Y(2), Y(3));
fprintf('Z: %10.2f %10.2f %10.2f\n\n', Z(1), Z(2), Z(3));
%% Rotating 45° around X twice
clear all; disp('Rotating 45° around X twice');
disp('----------------------------------------');
A = affine_rotation_x(degtorad(45));
Rin = A(1:3, 1:3);
q = quaternionFromRotation(Rin);
q = quaternionMul(q, q);
R = quaternionToRotation(q)
expect = Rin * Rin;
maximumError = max(max(expect - R))
X = R*[1; 0; 0]; Y = R*[0; 1; 0]; Z = R*[0; 0; 1];
fprintf('X: %10.2f %10.2f %10.2f\n', X(1), X(2), X(3));
fprintf('Y: %10.2f %10.2f %10.2f\n', Y(1), Y(2), Y(3));
fprintf('Z: %10.2f %10.2f %10.2f\n\n', Z(1), Z(2), Z(3));
%% Rotating 45° around X, then 45° around Y
clear all; disp('Rotating 90° around X, then 90° around Y');
disp('----------------------------------------');
Ax = affine_rotation_x(degtorad(90));
Ay = affine_rotation_y(degtorad(90));
qx = quaternionFromRotation(Ax);
qy = quaternionFromRotation(Ay);
q = quaternionMul(qy, qx);
R = quaternionToRotation(q)
expect = Ay*Ax;
maximumError = max(max(expect(1:3, 1:3) - R))
X = R*[1; 0; 0]; Y = R*[0; 1; 0]; Z = R*[0; 0; 1];
fprintf('X: %10.2f %10.2f %10.2f\n', X(1), X(2), X(3));
fprintf('Y: %10.2f %10.2f %10.2f\n', Y(1), Y(2), Y(3));
fprintf('Z: %10.2f %10.2f %10.2f\n\n', Z(1), Z(2), Z(3));
Xq = quaternionRotateVector(q, [1; 0; 0]);
Yq = quaternionRotateVector(q, [0; 1; 0]);
Zq = quaternionRotateVector(q, [0; 0; 1]);
fprintf('Xq: %10.2f %10.2f %10.2f\n', Xq(1), Xq(2), Xq(3));
fprintf('Yq: %10.2f %10.2f %10.2f\n', Yq(1), Yq(2), Yq(3));
fprintf('Zq: %10.2f %10.2f %10.2f\n\n', Zq(1), Zq(2), Zq(3));
%% Angular velocity: Rotating with 90°/sec
clear all; disp('Angular velocity: Rotating with 90°/sec');
disp('----------------------------------------');
T = 0.1;
omega = degtorad([90 0 0]);
qomega = quaternionFromAngularVelocity(omega, T);
q = [1 0 0 0];
N = 1/T;
for i = 1:N
q = quaternionMul(qomega, q);
end
Xq = quaternionRotateVector(q, [1; 0; 0]);
Yq = quaternionRotateVector(q, [0; 1; 0]);
Zq = quaternionRotateVector(q, [0; 0; 1]);
fprintf('Xq: %10.2f %10.2f %10.2f\n', Xq(1), Xq(2), Xq(3));
fprintf('Yq: %10.2f %10.2f %10.2f\n', Yq(1), Yq(2), Yq(3));
fprintf('Zq: %10.2f %10.2f %10.2f\n\n', Zq(1), Zq(2), Zq(3));
%% Angular velocity: Determine angular velocity from two quaternions
clear all; disp('Angular velocity: Determine angular velocity from two quaternions');
disp('----------------------------------------');
T = 0.1;
omega = degtorad([90 45 22.5]);
qomega = quaternionFromAngularVelocity(omega, T);
q = [1 0 0 0];
N = 1/T;
for i = 1:N
q_previous = q;
q = quaternionMul(qomega, q);
derived_omega = quaternionToAngularVelocity(q, q_previous, T);
end
expect = omega;
maximumError = max(max(expect - derived_omega))
%% Angular velocity: Determine angular velocity from two quaternions using SLERP differentiation
clear all; disp('Angular velocity: Determine angular velocity from two quaternions (hypersphere)');
disp('----------------------------------------');
T = 0.1;
omega = degtorad([90 45 22.5]);
qomega = quaternionFromAngularVelocity(omega, T);
q = [1 0 0 0];
N = 1/T;
for i = 1:N
q_previous = q;
q = quaternionMul(qomega, q);
derived_omega = quaternionToAngularVelocity2(q, q_previous, T);
end
expect = omega;
maximumError = max(max(expect - derived_omega))