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efvega
Mobile-robotics
Commits
804b8c98
Commit
804b8c98
authored
2 years ago
by
ziminlu
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804b8c98
import
numpy
as
np
import
math
import
matplotlib.pyplot
as
plt
from
extended_kalman_filter_project
import
extended_kalman_filter
import
json
class
myStruct
:
pass
def
process_model
(
x
):
"""
Think this makes sense because we don
'
t move at all
:param x:
:return:
"""
f
=
np
.
array
([
x
[
0
,
0
],
x
[
1
,
0
],
x
[
2
,
0
]],
dtype
=
float
)
return
f
.
reshape
([
3
,
1
])
def
wraptopi
(
x
):
# wraps angles in x, in radians, to the interval [−pi, pi] such that pi maps to pi and −pi maps to −pi.
# In general, odd, positive multiples of pi map to pi and odd, negative multiples of pi map to −pi.
pi
=
np
.
pi
x
=
x
-
np
.
floor
(
x
/
(
2
*
pi
))
*
2
*
pi
print
(
'
x
'
,
x
)
if
x
>=
pi
:
x
=
x
-
2
*
pi
else
:
x
=
x
return
float
(
x
)
def
measurement
(
Z_landmark
):
# use this function to transform the [x, y, z] 3D coordinate got from pixel position measurement to the 2D bearing and range measurement
# mx, my is the x, y coordinate of the image 1 (the image at time t/t+1), it is the coordinate of the landmark.
# landmarks at t are only used for getting the bearing_range measurement.
Z_landmark
=
Z_landmark
.
reshape
((
3
,
1
))
Z_2D
=
Z_landmark
[
0
:
2
,
0
]
mx
=
Z_2D
[
0
]
print
(
'
mx
'
,
mx
)
my
=
Z_2D
[
1
]
z_br
=
np
.
array
([[
math
.
atan2
(
my
,
mx
)],[
np
.
sqrt
(
my
**
2
+
mx
**
2
)]])
# z_bearing_range
return
z_br
.
reshape
([
2
,
1
])
def
measurement_model
(
x_hat
,
mx_t_minus_1
,
my_t_minus_1
):
# hfun
# mx_t_minus_1 is the x coordinate of the image 1 at time t-1, it is the coordinate of the landmark.
# x_hat is the estimated state by the process_model
"""
:param mx_t_minus_1, my_t_minus_1: the x, y coordinate of the image 1 (the image at time t-1), it is the coordinate of the landmark.
:param x_hat: the estimated state by the process_model, [x, y ,theta]
:return: h
"""
x_hat
=
x_hat
.
reshape
((
-
1
,
1
))
mx
=
mx_t_minus_1
my
=
my_t_minus_1
h
=
np
.
array
([[
wraptopi
(
math
.
atan2
(
my
-
x_hat
[
1
,
0
],
mx
-
x_hat
[
0
,
0
]))
-
x_hat
[
2
,
0
]],
[
np
.
sqrt
((
my
-
x_hat
[
1
,
0
])
**
2
+
(
mx
-
x_hat
[
0
,
0
])
**
2
)]])
# sys.hfun = @(landmark_x, landmark_y, mu_pred) [...
# wrapToPi(atan2(landmark_y - mu_pred(2), landmark_x - mu_pred(1)) - mu_pred(3));
# sqrt((landmark_y - mu_pred(2))^2 + (landmark_x - mu_pred(1))^2)];
temp
=
math
.
atan2
(
my
-
x_hat
[
1
,
0
],
mx
-
x_hat
[
0
,
0
])
print
(
'
hfun
'
,
temp
)
print
(
'
wrap
'
,
wraptopi
(
temp
))
return
h
.
reshape
([
2
,
1
])
def
measurment_Jacobain
(
landmark_x
,
landmark_y
,
mu_pred
,
z_hat
):
# Hfun
"""
:param landmark_x, landmark_y: the x, y coordinate of the image 1 (the image at time t-1), it is the coordinate of the landmark. matrix
:param mu_pred: the estimated state by the process_model, [x, y ,theta]. matrix
:param z_hat: hfun. matrix
:return: mesaurment jacobian
"""
z_hat
=
z_hat
.
reshape
((
-
1
,))
mu_pred
=
mu_pred
.
reshape
((
-
1
,))
Hfun
=
np
.
array
([[(
landmark_y
-
mu_pred
[
1
])
/
(
z_hat
[
1
]
**
2
),
-
(
landmark_x
-
mu_pred
[
0
])
/
(
z_hat
[
1
]
**
2
),
-
1
],
[
-
(
landmark_x
-
mu_pred
[
0
])
/
z_hat
[
1
],
-
(
landmark_y
-
mu_pred
[
1
])
/
z_hat
[
1
],
0
]])
# print('Hfun', Hfun)
return
Hfun
.
reshape
((
2
,
3
))
if
__name__
==
"
__main__
"
:
# Opening JSON file
f
=
open
(
'
dict.json
'
)
# returns JSON object as a dictionary
data
=
json
.
load
(
f
)
xyz_t
=
data
[
'
Frame_t+1
'
]
xyz_t_1
=
data
[
'
Frame_t
'
]
f
.
close
()
z_1
=
np
.
zeros
((
len
(
xyz_t
),
2
))
z_2
=
np
.
zeros
((
len
(
xyz_t
),
2
))
z_3
=
np
.
zeros
((
len
(
xyz_t
),
2
))
landmark1
=
np
.
zeros
((
len
(
xyz_t
),
2
))
landmark2
=
np
.
zeros
((
len
(
xyz_t
),
2
))
landmark3
=
np
.
zeros
((
len
(
xyz_t
),
2
))
for
i
in
range
(
len
(
xyz_t
)):
z_xyz_1
=
np
.
array
([
xyz_t
[
i
][
0
][
10
],
xyz_t
[
i
][
1
][
10
],
xyz_t
[
i
][
2
][
10
]])
z_xyz_2
=
np
.
array
([
xyz_t
[
i
][
0
][
-
15
],
xyz_t
[
i
][
1
][
-
15
],
xyz_t
[
i
][
2
][
-
15
]])
z_xyz_3
=
np
.
array
([
xyz_t
[
i
][
0
][
0
],
xyz_t
[
i
][
1
][
0
],
xyz_t
[
i
][
2
][
0
]])
# t-1
z_xyz_1_1
=
np
.
array
([
xyz_t_1
[
i
][
0
][
10
],
xyz_t_1
[
i
][
1
][
10
],
xyz_t_1
[
i
][
2
][
10
]])
z_xyz_2_1
=
np
.
array
([
xyz_t_1
[
i
][
0
][
-
15
],
xyz_t_1
[
i
][
1
][
-
15
],
xyz_t_1
[
i
][
2
][
-
15
]])
z_xyz_3_1
=
np
.
array
([
xyz_t_1
[
i
][
0
][
0
],
xyz_t_1
[
i
][
1
][
0
],
xyz_t_1
[
i
][
2
][
0
]])
landmark1
[
i
,:]
=
z_xyz_1_1
[
0
:
2
]
landmark2
[
i
,:]
=
z_xyz_2_1
[
0
:
2
]
landmark3
[
i
,:]
=
z_xyz_3_1
[
0
:
2
]
z_1_i
=
measurement
(
z_xyz_1
)
z_2_i
=
measurement
(
z_xyz_2
)
z_3_i
=
measurement
(
z_xyz_3
)
# print('z1i',type(z_1_i[0,0]))
z_1
[
i
,
:]
=
z_1_i
.
reshape
((
2
,))
z_2
[
i
,
:]
=
z_2_i
.
reshape
((
2
,))
z_3
[
i
,
:]
=
z_3_i
.
reshape
((
2
,))
t
=
list
(
range
(
len
(
xyz_t
)))
t
=
[
float
(
x
)
for
x
in
t
]
# initialize the state using the first measurement
init
=
myStruct
()
init
.
x1
=
np
.
zeros
([
3
,
1
])
# init.x1[0,0] = 46.6
# init.x1[1,0] = -33.7
# init.x1[2, 0] = -1.95
init
.
x1
[
0
,
0
]
=
0
init
.
x1
[
1
,
0
]
=
0
init
.
x1
[
2
,
0
]
=
0
init
.
Sigma
=
np
.
eye
(
3
)
#Tune
# Build the system
sys
=
myStruct
()
sys
.
A
=
np
.
eye
(
3
)
# double check size
sys
.
B
=
[]
# no input because the object is static
sys
.
f
=
process_model
sys
.
H
=
measurment_Jacobain
# 2 by3
# sys.H2 = measurment_Jacobain_2 # # 2by 3
sys
.
R1
=
np
.
cov
(
z_1
,
rowvar
=
False
)
# double check 2by 2
sys
.
R2
=
np
.
cov
(
z_2
,
rowvar
=
False
)
# double check 2 by 2
sys
.
R3
=
np
.
cov
(
z_3
,
rowvar
=
False
)
# double check 2 by 2
sys
.
h
=
measurement_model
# sys.Q1 = 0.01*np.array([[0.03, 0.02, 0.01],
# [0.02, 0.04, 0.01],
# [0.01, 0.01, 0.05]]).reshape((3, 3)) # vibrations M
sys
.
Q1
=
10
*
np
.
eye
(
3
)
# vibrations M
# sys.Q1 = 50*np.array([[0.03, 0.02, 0.01],
# [0.02, 0.03, 0.02],
# [0.02, 0.01, 0.01]]).reshape((3, 3)) # vibrations M good
# sys.Q1 = 10*np.array([[0.03, 0.02, 0.015],
# [0.02, 0.3, 0.015],
# [0.015, 0.015, 0.1]]).reshape((3, 3)) # vibrations M
sys
.
Q1
=
1
*
np
.
array
([[
0.03
,
0.02
,
0.015
],
[
0.02
,
0.3
,
0.015
],
[
0.015
,
0.015
,
0.1
]]).
reshape
((
3
,
3
))
# vibrations M
# sys.Q1 = np.zeros((3,3))
# ################################################
# implement ekf
ekf_1b
=
extended_kalman_filter
(
sys
,
init
)
x1_b
=
[]
x1_b
.
append
(
init
.
x1
)
# started from 0 instead cuz picked random init
for
i
in
range
(
0
,
np
.
shape
(
z_1
)[
0
],
1
):
# print('typez1',type(z_1[0,0]))
ekf_1b
.
prediction_1
()
zstack
=
np
.
append
(
z_1
[
i
,
:],
z_2
[
i
,
:]).
reshape
((
-
1
,
1
))
zstack
=
np
.
append
(
zstack
,
z_3
[
i
,
:]).
reshape
((
-
1
,
1
))
print
(
'
zstack
'
,
zstack
)
# print(zstack)
ekf_1b
.
correction_batch
(
zstack
,
landmark1
[
i
,
:],
landmark2
[
i
,
:],
landmark3
[
i
,
:])
# since the ekf_1b.x1 is the relative location to the x0, we add it to the x0 location.
# double check for the covariance.
x1_b
.
append
(
x1_b
[
-
1
]
+
ekf_1b
.
x1
)
# change the axes and add the initilization point.
x1_b
=
np
.
array
(
x1_b
).
reshape
((
-
1
,
3
))
x1_b_1
=
np
.
zeros
(
x1_b
.
shape
)
x1_b_1
[:,
0
]
=
-
x1_b
[:,
1
]
x1_b_1
[:,
1
]
=
x1_b
[:,
0
]
# x1_b = x1_b_1
# x1_b[:,0] = -x1_b[:,0]
true_initialization
=
np
.
array
([
46.6
,
-
33.7
,
-
1.95
])
# true_initialization = np.array([85, 15, -1.95])
x1_b_1
=
x1_b_1
+
true_initialization
x1_b_1
=
x1_b_1
.
reshape
((
-
1
,
3
))
# Final Label
print
(
'
Final x: %.4f, y: %.4f, z: %.4f
'
%
(
x1_b
[
-
1
,
0
],
x1_b
[
-
1
,
1
],
x1_b
[
-
1
,
2
]))
# plotting
fig
=
plt
.
figure
()
plt
.
plot
(
x1_b_1
[:,
0
],
x1_b_1
[:,
1
])
plt
.
xlabel
(
r
'
x
'
)
plt
.
ylabel
(
r
'
y
'
)
# plt.legend()
plt
.
title
(
'
EKF Batch Measurement
'
)
plt
.
show
()
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