291 lines
6.3 KiB
Python
291 lines
6.3 KiB
Python
# -*- coding: utf-8 -*-
|
|
"""
|
|
Created on Sun May 24 08:39:36 2015
|
|
|
|
@author: Roger
|
|
"""
|
|
|
|
#x = x x' y y' theta
|
|
|
|
from math import cos, sin, sqrt, atan2
|
|
import numpy as np
|
|
from numpy import array, dot
|
|
from numpy.linalg import pinv
|
|
|
|
|
|
def print_x(x):
|
|
print(x[0, 0], x[1, 0], np.degrees(x[2, 0]))
|
|
|
|
|
|
def control_update(x, u, dt):
|
|
""" x is [x, y, hdg], u is [vel, omega] """
|
|
|
|
v = u[0]
|
|
w = u[1]
|
|
if w == 0:
|
|
# approximate straight line with huge radius
|
|
w = 1.e-30
|
|
r = v/w # radius
|
|
|
|
|
|
return x + np.array([[-r*sin(x[2]) + r*sin(x[2] + w*dt)],
|
|
[ r*cos(x[2]) - r*cos(x[2] + w*dt)],
|
|
[w*dt]])
|
|
|
|
|
|
a1 = 0.001
|
|
a2 = 0.001
|
|
a3 = 0.001
|
|
a4 = 0.001
|
|
|
|
sigma_r = 0.1
|
|
sigma_h = a_error = np.radians(1)
|
|
sigma_s = 0.00001
|
|
|
|
def normalize_angle(x, index):
|
|
if x[index] > np.pi:
|
|
x[index] -= 2*np.pi
|
|
if x[index] < -np.pi:
|
|
x[index] = 2*np.pi
|
|
|
|
|
|
def ekfloc_predict(x, P, u, dt):
|
|
|
|
h = x[2]
|
|
v = u[0]
|
|
w = u[1]
|
|
|
|
if w == 0:
|
|
# approximate straight line with huge radius
|
|
w = 1.e-30
|
|
r = v/w # radius
|
|
|
|
sinh = sin(h)
|
|
sinhwdt = sin(h + w*dt)
|
|
cosh = cos(h)
|
|
coshwdt = cos(h + w*dt)
|
|
|
|
G = array(
|
|
[[1, 0, -r*cosh + r*coshwdt],
|
|
[0, 1, -r*sinh + r*sinhwdt],
|
|
[0, 0, 1]])
|
|
|
|
V = array(
|
|
[[(-sinh + sinhwdt)/w, v*(sin(h)-sinhwdt)/(w**2) + v*coshwdt*dt/w],
|
|
[(cosh - coshwdt)/w, -v*(cosh-coshwdt)/(w**2) + v*sinhwdt*dt/w],
|
|
[0, dt]])
|
|
|
|
|
|
# covariance of motion noise in control space
|
|
M = array([[a1*v**2 + a2*w**2, 0],
|
|
[0, a3*v**2 + a4*w**2]])
|
|
|
|
|
|
|
|
x = x + array([[-r*sinh + r*sinhwdt],
|
|
[r*cosh - r*coshwdt],
|
|
[w*dt]])
|
|
|
|
P = dot(G, P).dot(G.T) + dot(V, M).dot(V.T)
|
|
|
|
return x, P
|
|
|
|
def ekfloc(x, P, u, zs, c, m, dt):
|
|
|
|
h = x[2]
|
|
v = u[0]
|
|
w = u[1]
|
|
|
|
if w == 0:
|
|
# approximate straight line with huge radius
|
|
w = 1.e-30
|
|
r = v/w # radius
|
|
|
|
sinh = sin(h)
|
|
sinhwdt = sin(h + w*dt)
|
|
cosh = cos(h)
|
|
coshwdt = cos(h + w*dt)
|
|
|
|
F = array(
|
|
[[1, 0, -r*cosh + r*coshwdt],
|
|
[0, 1, -r*sinh + r*sinhwdt],
|
|
[0, 0, 1]])
|
|
|
|
V = array(
|
|
[[(-sinh + sinhwdt)/w, v*(sin(h)-sinhwdt)/(w**2) + v*coshwdt*dt/w],
|
|
[(cosh - coshwdt)/w, -v*(cosh-coshwdt)/(w**2) + v*sinhwdt*dt/w],
|
|
[0, dt]])
|
|
|
|
|
|
# covariance of motion noise in control space
|
|
M = array([[a1*v**2 + a2*w**2, 0],
|
|
[0, a3*v**2 + a4*w**2]])
|
|
|
|
|
|
x = x + array([[-r*sinh + r*sinhwdt],
|
|
[r*cosh - r*coshwdt],
|
|
[w*dt]])
|
|
|
|
P = dot(F, P).dot(F.T) + dot(V, M).dot(V.T)
|
|
|
|
|
|
R = np.diag([sigma_r**2, sigma_h**2, sigma_s**2])
|
|
|
|
for i, z in enumerate(zs):
|
|
j = c[i]
|
|
|
|
q = (m[j][0] - x[0, 0])**2 + (m[j][1] - x[1, 0])**2
|
|
|
|
z_est = array([sqrt(q),
|
|
atan2(m[j][1] - x[1, 0], m[j][0] - x[0, 0]) - x[2, 0],
|
|
0])
|
|
|
|
|
|
H = array(
|
|
[[-(m[j, 0] - x[0, 0]) / sqrt(q), -(m[j, 1] - x[1, 0]) / sqrt(q), 0],
|
|
[ (m[j, 1] - x[1, 0]) / q, -(m[j, 0] - x[0, 0]) / q, -1],
|
|
[0, 0, 0]])
|
|
|
|
|
|
|
|
S = dot(H, P).dot(H.T) + R
|
|
|
|
#print('S', S)
|
|
K = dot(P, H.T).dot(pinv(S))
|
|
y = z - z_est
|
|
normalize_angle(y, 1)
|
|
y = array([y]).T
|
|
#print('y', y)
|
|
|
|
x = x + dot(K, y)
|
|
I = np.eye(P.shape[0])
|
|
I_KH = I - dot(K, H)
|
|
#print('i', I_KH)
|
|
|
|
P = dot(I_KH, P).dot(I_KH.T) + dot(K, R).dot(K.T)
|
|
|
|
return x, P
|
|
|
|
|
|
|
|
def ekfloc2(x, P, u, zs, c, m, dt):
|
|
|
|
h = x[2]
|
|
v = u[0]
|
|
w = u[1]
|
|
|
|
if w == 0:
|
|
# approximate straight line with huge radius
|
|
w = 1.e-30
|
|
r = v/w # radius
|
|
|
|
sinh = sin(h)
|
|
sinhwdt = sin(h + w*dt)
|
|
cosh = cos(h)
|
|
coshwdt = cos(h + w*dt)
|
|
|
|
F = array(
|
|
[[1, 0, -r*cosh + r*coshwdt],
|
|
[0, 1, -r*sinh + r*sinhwdt],
|
|
[0, 0, 1]])
|
|
|
|
V = array(
|
|
[[(-sinh + sinhwdt)/w, v*(sin(h)-sinhwdt)/(w**2) + v*coshwdt*dt/w],
|
|
[(cosh - coshwdt)/w, -v*(cosh-coshwdt)/(w**2) + v*sinhwdt*dt/w],
|
|
[0, dt]])
|
|
|
|
|
|
# covariance of motion noise in control space
|
|
M = array([[a1*v**2 + a2*w**2, 0],
|
|
[0, a3*v**2 + a4*w**2]])
|
|
|
|
|
|
x = x + array([[-r*sinh + r*sinhwdt],
|
|
[r*cosh - r*coshwdt],
|
|
[w*dt]])
|
|
|
|
|
|
P = dot(F, P).dot(F.T) + dot(V, M).dot(V.T)
|
|
|
|
|
|
|
|
R = np.diag([sigma_r**2, sigma_h**2])
|
|
|
|
for i, z in enumerate(zs):
|
|
j = c[i]
|
|
|
|
q = (m[j][0] - x[0, 0])**2 + (m[j][1] - x[1, 0])**2
|
|
|
|
z_est = array([sqrt(q),
|
|
atan2(m[j][1] - x[1, 0], m[j][0] - x[0, 0]) - x[2, 0]])
|
|
|
|
H = array(
|
|
[[-(m[j, 0] - x[0, 0]) / sqrt(q), -(m[j, 1] - x[1, 0]) / sqrt(q), 0],
|
|
[ (m[j, 1] - x[1, 0]) / q, -(m[j, 0] - x[0, 0]) / q, -1]])
|
|
|
|
|
|
S = dot(H, P).dot(H.T) + R
|
|
|
|
#print('S', S)
|
|
K = dot(P, H.T).dot(pinv(S))
|
|
y = z - z_est
|
|
normalize_angle(y, 1)
|
|
y = array([y]).T
|
|
#print('y', y)
|
|
|
|
x = x + dot(K, y)
|
|
print('x', x)
|
|
I = np.eye(P.shape[0])
|
|
I_KH = I - dot(K, H)
|
|
|
|
P = dot(I_KH, P).dot(I_KH.T) + dot(K, R).dot(K.T)
|
|
|
|
return x, P
|
|
|
|
m = array([[5, 5],
|
|
[7,6],
|
|
[4, 8]])
|
|
|
|
x = array([[2, 6, .3]]).T
|
|
u = array([.5, .01])
|
|
P = np.diag([1., 1., 1.])
|
|
c = [0, 1, 2]
|
|
|
|
|
|
|
|
import matplotlib.pyplot as plt
|
|
from numpy.random import randn
|
|
from filterpy.common import plot_covariance_ellipse
|
|
from filterpy.kalman import KalmanFilter
|
|
plt.figure()
|
|
plt.plot(m[:, 0], m[:, 1], 'o')
|
|
plt.plot(x[0], x[1], 'x', color='b', ms=20)
|
|
|
|
xp = x.copy()
|
|
dt = 0.1
|
|
np.random.seed(1234)
|
|
|
|
for i in range(1000):
|
|
xp, _ = ekfloc_predict(xp, P, u, dt)
|
|
plt.plot(xp[0], xp[1], 'x', color='g', ms=20)
|
|
|
|
if i % 10 == 0:
|
|
zs = []
|
|
|
|
for lmark in m:
|
|
d = sqrt((lmark[0] - xp[0, 0])**2 + (lmark[1] - xp[1, 0])**2) + randn()*sigma_r
|
|
a = atan2(lmark[1] - xp[1, 0], lmark[0] - xp[0, 0]) - xp[2, 0] + randn()*sigma_h
|
|
zs.append(np.array([d, a]))
|
|
|
|
x, P = ekfloc2(x, P, u, zs, c, m, dt*10)
|
|
|
|
|
|
if P[0,0] < 10000:
|
|
plot_covariance_ellipse((x[0,0], x[1,0]), P[0:2, 0:2], std=2,
|
|
facecolor='g', alpha=0.3)
|
|
|
|
plt.plot(x[0], x[1], 'x', color='r')
|
|
|
|
plt.axis('equal')
|
|
plt.show()
|