-
Notifications
You must be signed in to change notification settings - Fork 1
/
newtonEuler.m
197 lines (163 loc) · 5.01 KB
/
newtonEuler.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
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
% newtonEuler computes the inverse dynamics of a serial link manipulator
% and provides the velocity jacobian and its rate of change.
%
% Output
%
% Jv - the velocity jacobian
% JvDot - the time derivative of the velocity jacobian
% jointTorques- returns the joint torques from the newton euler
%
% Input
%
%
% linkList – a list of the joint parameters created by
% createLink
% paramList – the current joint angles/distances. (anNx1 array)
% paramListDot – the current joint angle/distance speeds. (an Nx1 array)
% paramListDDot – the current joint angle/distanceaccelerations. (an Nx1 array)
%
% boundry_conditions – a structure containing:
% base_angular_velocity
% base_angular_acceleration
% base_linear_acceleration (add gravity in here)
% distal_force
% distal_torque
% Mohammed Aun Siddiqui
% 10834112
% 544
% 11/19/2017
function [jointTorques, Jv, JvDot] = newtonEuler( linkList, paramList, paramListDot, paramListDDot, boundary_conditions )
a = zeros(6,1);
d = zeros(6,1);
alpha = zeros(6,1);
theta = zeros(6,1);
isRotary = zeros(6,1);
J_Inertia = zeros(3,3,6);
theta_dot = zeros(6,1);
theta_ddot = zeros(6,1);
d_dot = zeros(6,1);
d_ddot = zeros(6,1);
J = zeros(3,3,6);
rcom = zeros(3,6);
rcom_base = zeros(3,6);
m = zeros(6,1);
jointTorques = zeros(6,1);
for i = 1:6
a(i) = linkList(i).a;
alpha(i) = linkList(i).alpha;
isRotary(i) = linkList(i).isRotary;
if isRotary(i) == 0
theta(i) = linkList(i).theta;
d(i) = paramList(i);
d_dot(i) = paramListDot(i);
d_ddot(i) = paramListDDot(i);
else
d(i) = linkList(i).d;
theta(i) = paramList(i);
theta_dot(i) = paramListDot(i);
theta_ddot(i) = paramListDDot(i);
end
J_Inertia(:,:,i) = linkList(i).inertia;
rcom(:,i) = linkList(i).com;
m(i) = linkList(i).mass;
end
[Jv,JvDot] = velocityJacobian(linkList,paramList,paramListDot);
T = zeros(4,4,6);
dd = zeros(3,7);
Z = zeros(3,6);
for i = 1:6
T(:,:,i) = zeros(4,4)
end
Z = zeros(3,6);
w = zeros(3,7);
dd = zeros(3,7);
dd_dot = zeros(3,7);
dd(:,1:1) = [0; 0; 0];
Z(:,1) = [0 0 1];
H = eye(4);
for i = 1:6
T(:,:,i)=H*dhTransform(a(i),d(i),alpha(i),theta(i));
H = T(:,:,i);
end
for i = 2:7
dd(:,i:i) = T(1:3,4:4,i-1);
Z(:,i) = T(1:3,3:3,i-1);
R(:,:,i-1) = T(1:3,1:3,i-1)
end
for i = 1:6
J(:,:,i) = R(:,:,i)*J_Inertia(:,:,i)*R(:,:,i).';
end
w = zeros(3,7);
w(:,1) = boundary_conditions(1).base_angular_velocity;
for i = 2:7
if isRotary(i-1) == 1
w(:,i) = w(:,i-1) + theta_dot(i-1)*Z(:,i-1);
elseif isRotary(i-1) == 0
w(:,i) = w(:,i-1);
end
end
w_dot = zeros(3,7);
w_dot(:,1:1) = boundary_conditions(1).base_angular_acceleration;
if isRotary(1) == 1
w_dot(:,2) = w_dot(:,1) + theta_ddot(1)*Z(:,1) + cross(w(:,1),Z(:,1));
else
w_dot(:,2) = w_dot(:,1);
end
for i = 3:7
if isRotary(i-1) == 1
w_dot(:,i) = w_dot(:,i-1) + theta_ddot(i-1)*Z(:,i-1) + cross(w(:,i-1),w(:,i));
else
w_dot(:,i) = w_dot(:,i-1);
end
end
dd_dot(:,1:1) = [0; 0; 0];
for i = 2:7
if isRotary(i-1) == 1
dd_dot(:,i) = dd_dot(:,i-1) + cross(w(:,i),(dd(:,i)-dd(:,i-1)));
elseif isRotary(i-1) == 0
dd_dot(:,i) = dd_dot(:,i-1) + cross(w(:,i),(dd(:,i)-dd(:,i-1))) + d_dot(i-1)*Z(:,i-1);
end
end
dd_ddot = zeros(3,7);
dd_ddot(:,1:1) = boundary_conditions(1).base_linear_acceleration;
for i = 2:7
if isRotary(i-1) == 1
dd_ddot(:,i:i) = dd_ddot(:,i-1) + cross(w_dot(:,i),(dd(:,i)-dd(:,i-1))) + cross(w(:,i),cross(w(:,i),(dd(:,i)-dd(:,i-1))));
elseif isRotary(i-1) == 0
dd_ddot(:,i:i) = dd_ddot(:,i-1) + cross(w_dot(:,i),(dd(:,i)-dd(:,i-1))) + cross(w(:,i),cross(w(:,i),(dd(:,i)-dd(:,i-1)))) + d_ddot(i-1)*Z(:,i-1) + cross(2*d_dot(i-1)*w(:,i-1),Z(:,i-1));
end
end
rcom_base = zeros(3,6);
for i = 1:6
rcom_base(:,i:i) = R(:,:,i)*rcom(:,i:i);
end
rcom_base_dot = zeros(3,6);
for i = 1:6
if isRotary(i) == 1
rcom_base_dot(:,i) = dd_dot(:,i) + cross(w(:,i+1),rcom(:,i));
else
rcom_base_dot(:,i) = dd_dot(:,i) + cross(w(:,i+1),rcom(:,i)) + d_dot(i)*Z(:,i);
end
end
rcom_base_ddot = zeros(3,6);
for i = 1:6
if isRotary(i) == 1
rcom_base_ddot(:,i) = dd_ddot(:,i) + cross(w_dot(:,i+1),(dd(:,i+1)-dd(:,i)+rcom_base(:,i))) + cross(w(:,i+1),cross(w(:,i+1),(dd(:,i+1)-dd(:,i)+rcom_base(:,i))));
else
rcom_base_ddot(:,i) = dd_ddot(:,i) + cross(w_dot(:,i+1),(dd(:,i+1)-dd(:,i)+rcom_base(:,i))) + cross(w(:,i+1),cross(w(:,i+1),(dd(:,i+1)-dd(:,i)+rcom_base(:,i)))) + cross(2*w(:,i),d_dot(i)*Z(:,i)) + d_ddot(i)*Z(:,i);
end
end
f = zeros(3,7);
f(:,7) = boundary_conditions(1).distal_force;
n = zeros(3,7);
n(:,7) = boundary_conditions(1).distal_torque;
for i = 6:-1:1
f(:,i:i) = f(:,i+1) + m(i)*rcom_base_ddot(:,i);
n(:,i:i) = n(:,i+1) + cross(dd(:,i+1)-dd(:,i)+rcom_base(:,i),f(:,i)) + J(:,:,i)*w_dot(:,i+1) + cross(w(:,i+1),J(:,:,i)*w(:,i+1)) - cross(rcom_base(:,i),f(:,i+1));
if isRotary(i) == 1
jointTorques(i,1) = Z(:,i).'*n(:,i);
else
jointTorques(i,1) = Z(:,i).'*f(:,i);
end
end
end