The Newton（机器人最小惯性参数辨识 牛顿欧拉方法）.docx
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1.1. The Newton – Euler Method (NE)
The dynamic model of EFFORT is based the Newton – Euler formulation. It contains two
sets of recursions: the forward and backward recursions, which forward recursions transfer
the arms’ velocities and accelerations from the base to the end-e#ector, and backward
recursions transfer the forces of joints from end-e#ector to the base. The full formulations
are (Introduction to Robotics Mechanics and Control 3rd, Chapter 6, Page 173):
The forward recursions, from 0 5:
ω
i+1
=R
i
i +1
ω
i
+
˙
θ
i+1
Z
i +1
i +1
(
1
)
˙ω
i+1
=R
i
i +1
˙ω
i
+R
i
i+1
ω
i
×
˙
θ
i+1
Z
i+1
i+1
+
¨
θ
i +1
Z
i+1
i+1
(
2
)
˙
v
i +1
=R
i
i +1
[
˙
ω
i
× P
i+1
i
+ω
i
×
(
ω
i
× P
i+1
i
)
+
˙
v
i
]
(
3
)
˙
v
ci+1
=
˙
ω
i+1
× P
ci+1
i+1
+ω
i + 1
×
(
ω
i+1
× P
ci+1
i+1
)
+
˙
v
i+1
(
4
)
F
i+1
= m
i+1
˙
v
ci + 1
(
5
)
N
i+ 1
=I
i +1
c
i+1
˙
ω
i+1
+ω
i+1
× I
i +1
c
i+1
ω
i+1
(
6
)
With
ω
0
=
˙
ω
0
=0
The backward recursions, from 6 1:
f
i
=R
i+ 1
i
f
i+1
+F
i
(
7
)
n
i
=N
i
+R
i+1
i
n
i+1
+P
ci
i
× F
i
+P
i+ 1
i
× R
i +1
i
f
i+1
(
8
)
τ
i
=
(
n
i
)
T
Z
i
i
(
9
)
Here:
R
i
i + 1
is the rotation matrix from link
i
to link
i+1
˙
θ
i
and
¨
θ
i
are the unit angle speed and acceleration of link
i
respectively
ω
i
is the angular velocity vector of the link
i
˙
ω
i
is the angular acceleration vector of the link
i
˙
v
i
is the line acceleration of the origin of the link coordination system
˙
v
ci
is the linear acceleration of the center of mass of the link
i
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