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rli
robotics-codes-from-scratch
Commits
4259a8f0
Commit
4259a8f0
authored
1 year ago
by
Philip ABBET
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Fix some issues in 'iLQR_manipulator3D.py'
parent
c74ef277
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python/iLQR_manipulator3D.py
+24
-14
24 additions, 14 deletions
python/iLQR_manipulator3D.py
with
24 additions
and
14 deletions
python/iLQR_manipulator3D.py
+
24
−
14
View file @
4259a8f0
...
@@ -79,19 +79,20 @@ def logmap(f, f0):
...
@@ -79,19 +79,20 @@ def logmap(f, f0):
# Logarithmic map for S^3 manifold (with e in ambient space)
# Logarithmic map for S^3 manifold (with e in ambient space)
def
logmap_S3
(
x
,
x0
):
def
logmap_S3
(
x
,
x0
):
x0
=
x0
.
reshape
((
4
,
1
))
x
=
x
.
reshape
((
4
,
1
))
th
=
acoslog
(
x0
.
T
@
x
)
th
=
acoslog
(
x0
.
T
@
x
)
if
math
.
isnan
(
th
):
th
=
1.0
u
=
x
-
(
x0
.
T
@
x
)
*
x0
u
=
x
-
(
x0
.
T
@
x
)
*
x0
u
=
np
.
multiply
(
th
,
u
)
/
np
.
linalg
.
norm
(
u
)
if
np
.
linalg
.
norm
(
u
)
>
1e-9
:
u
=
np
.
multiply
(
th
,
u
)
/
np
.
linalg
.
norm
(
u
)
# import sys; sys.exit(0)
return
u
[:,
0
]
return
u
# Arcosine redefinition to make sure the distance between antipodal quaternions is zero
# Arcosine redefinition to make sure the distance between antipodal quaternions is zero
def
acoslog
(
x
):
def
acoslog
(
x
):
y
=
np
.
arccos
(
x
)
y
=
np
.
arccos
(
x
)
[
0
][
0
]
if
(
x
>=-
1.0
)
and
(
x
<
0
):
if
(
x
>=-
1.0
)
and
(
x
<
0
):
y
=
y
-
np
.
pi
y
=
y
-
np
.
pi
return
y
return
y
...
@@ -175,7 +176,7 @@ Q = np.eye((param.nbVarF-1) * param.nbPoints) * param.q
...
@@ -175,7 +176,7 @@ Q = np.eye((param.nbVarF-1) * param.nbPoints) * param.q
R
=
np
.
eye
((
param
.
nbData
-
1
)
*
param
.
nbVarU
)
*
param
.
r
R
=
np
.
eye
((
param
.
nbData
-
1
)
*
param
.
nbVarU
)
*
param
.
r
# Time occurrence of viapoints
# Time occurrence of viapoints
tl
=
np
.
linspace
(
0
,
param
.
nbData
,
param
.
nbPoints
+
1
)
tl
=
np
.
linspace
(
1
,
param
.
nbData
,
param
.
nbPoints
+
1
)
tl
=
np
.
rint
(
tl
[
1
:]).
astype
(
np
.
int64
)
-
1
tl
=
np
.
rint
(
tl
[
1
:]).
astype
(
np
.
int64
)
-
1
idx
=
np
.
array
([
i
+
np
.
arange
(
0
,
param
.
nbVarX
,
1
)
for
i
in
(
tl
*
param
.
nbVarX
)]).
flatten
()
idx
=
np
.
array
([
i
+
np
.
arange
(
0
,
param
.
nbVarX
,
1
)
for
i
in
(
tl
*
param
.
nbVarX
)]).
flatten
()
...
@@ -191,28 +192,37 @@ Su = Su0[idx,:] # We remove the lines that are out of interest
...
@@ -191,28 +192,37 @@ Su = Su0[idx,:] # We remove the lines that are out of interest
# iLQR
# iLQR
# ===============================
# ===============================
u
=
np
.
zeros
(
param
.
nbVarU
*
(
param
.
nbData
-
1
))
# Initial control command
u
=
np
.
zeros
(
(
param
.
nbVarU
*
(
param
.
nbData
-
1
),
1
))
# Initial control command
x0
=
np
.
array
([
0
,
0
,
0
,
-
np
.
pi
/
2
,
-
0
,
np
.
pi
/
2
,
0
])
# Initial robot pose
x0
=
np
.
array
([
0
,
0
,
0
,
-
np
.
pi
/
2
,
-
0
,
np
.
pi
/
2
,
0
])
# Initial robot pose
x0
=
x0
.
reshape
((
-
1
,
1
))
for
i
in
range
(
param
.
nbIter
):
for
i
in
range
(
param
.
nbIter
):
x
=
Su0
@
u
+
Sx0
@
x0
# System evolution
x
=
Su0
@
u
+
Sx0
@
x0
# System evolution
x
=
x
.
reshape
([
param
.
nbVarX
,
param
.
nbData
],
order
=
'
F
'
)
x
=
x
.
reshape
([
param
.
nbVarX
,
param
.
nbData
],
order
=
'
F
'
)
f
,
J
=
f_reach
(
x
[:,
tl
],
param
)
# Residuals and Jacobians
f
,
J
=
f_reach
(
x
[:,
tl
],
param
)
# Residuals and Jacobians
du
=
np
.
linalg
.
inv
(
Su
.
T
@
J
.
T
@
Q
@
J
@
Su
+
R
)
@
(
-
Su
.
T
@
J
.
T
@
Q
@
f
.
flatten
(
'
F
'
)
-
u
*
param
.
r
)
# Gauss-Newton update
f
=
f
.
reshape
((
-
1
,
1
),
order
=
'
F
'
)
du
=
np
.
linalg
.
pinv
(
Su
.
T
@
J
.
T
@
Q
@
J
@
Su
+
R
)
@
(
-
Su
.
T
@
J
.
T
@
Q
@
f
-
u
*
param
.
r
)
# Gauss-Newton update
# Estimate step size with backtracking line search method
# Estimate step size with backtracking line search method
alpha
=
1
alpha
=
1
cost0
=
f
.
flatten
(
'
F
'
).
T
@
Q
@
f
.
flatten
(
'
F
'
)
+
np
.
linalg
.
norm
(
u
)
**
2
*
param
.
r
# Cost
cost0
=
f
.
T
@
Q
@
f
+
np
.
linalg
.
norm
(
u
)
**
2
*
param
.
r
# Cost
while
True
:
while
True
:
utmp
=
u
+
du
*
alpha
utmp
=
u
+
du
*
alpha
xtmp
=
Su0
@
utmp
+
Sx0
@
x0
# System evolution
xtmp
=
Su0
@
utmp
+
Sx0
@
x0
# System evolution
xtmp
=
xtmp
.
reshape
([
param
.
nbVarX
,
param
.
nbData
],
order
=
'
F
'
)
xtmp
=
xtmp
.
reshape
([
param
.
nbVarX
,
param
.
nbData
],
order
=
'
F
'
)
ftmp
,
_
=
f_reach
(
xtmp
[:,
tl
],
param
)
# Residuals
ftmp
,
_
=
f_reach
(
xtmp
[:,
tl
],
param
)
# Residuals
cost
=
ftmp
.
flatten
(
'
F
'
).
T
@
Q
@
ftmp
.
flatten
(
'
F
'
)
+
np
.
linalg
.
norm
(
utmp
)
**
2
*
param
.
r
# Cost
ftmp
=
ftmp
.
reshape
((
-
1
,
1
),
order
=
'
F
'
)
cost
=
ftmp
.
T
@
Q
@
ftmp
+
np
.
linalg
.
norm
(
utmp
)
**
2
*
param
.
r
# Cost
if
cost
<
cost0
or
alpha
<
1e-3
:
if
cost
<
cost0
or
alpha
<
1e-3
:
u
=
utmp
print
(
"
Iteration {}, cost: {}
"
.
format
(
i
,
cost
[
0
][
0
]))
print
(
"
Iteration {}, cost: {}
"
.
format
(
i
,
cost
))
break
break
alpha
/=
2
alpha
/=
2
u
=
u
+
du
*
alpha
if
np
.
linalg
.
norm
(
du
*
alpha
)
<
1E-2
:
if
np
.
linalg
.
norm
(
du
*
alpha
)
<
1E-2
:
break
# Stop iLQR iterations when solution is reached
break
# Stop iLQR iterations when solution is reached
...
...
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