192 lines
4.4 KiB
Python
192 lines
4.4 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Created on Mon May 25 18:18:54 2015
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@author: rlabbe
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"""
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from math import cos, sin, sqrt, atan2
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import matplotlib.pyplot as plt
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import numpy as np
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from numpy import array, dot
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from numpy.linalg import pinv
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from numpy.random import randn
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from filterpy.common import plot_covariance_ellipse
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from filterpy.kalman import ExtendedKalmanFilter as EKF
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def print_x(x):
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print(x[0, 0], x[1, 0], np.degrees(x[2, 0]))
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def normalize_angle(x, index):
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if x[index] > np.pi:
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x[index] -= 2*np.pi
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if x[index] < -np.pi:
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x[index] = 2*np.pi
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def residual(a,b):
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y = a - b
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normalize_angle(y, 1)
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return y
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def control_update(x, u, dt):
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""" x is [x, y, hdg], u is [vel, omega] """
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v = u[0]
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w = u[1]
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if w == 0:
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# approximate straight line with huge radius
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w = 1.e-30
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r = v/w # radius
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return x + np.array([[-r*sin(x[2]) + r*sin(x[2] + w*dt)],
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[ r*cos(x[2]) - r*cos(x[2] + w*dt)],
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[w*dt]])
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a1 = 0.001
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a2 = 0.001
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a3 = 0.001
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a4 = 0.001
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sigma_r = 0.1
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sigma_h = a_error = np.radians(1)
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sigma_s = 0.00001
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def normalize_angle(x, index):
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if x[index] > np.pi:
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x[index] -= 2*np.pi
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if x[index] < -np.pi:
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x[index] = 2*np.pi
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class RobotEKF(EKF):
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def __init__(self, dt):
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EKF.__init__(self, 3, 2, 2)
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self.dt = dt
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def predict_x(self, u):
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self.x = self.move(self.x, u, self.dt)
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def move(self, x, u, dt):
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h = x[2, 0]
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v = u[0]
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w = u[1]
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if w == 0:
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# approximate straight line with huge radius
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w = 1.e-30
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r = v/w # radius
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sinh = sin(h)
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sinhwdt = sin(h + w*dt)
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cosh = cos(h)
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coshwdt = cos(h + w*dt)
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return x + array([[-r*sinh + r*sinhwdt],
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[r*cosh - r*coshwdt],
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[w*dt]])
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def H_of(x, landmark_pos):
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""" compute Jacobian of H matrix for state x """
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mx = landmark_pos[0]
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my = landmark_pos[1]
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q = (mx - x[0, 0])**2 + (my - x[1, 0])**2
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H = array(
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[[-(mx - x[0, 0]) / sqrt(q), -(my - x[1, 0]) / sqrt(q), 0],
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[ (my - x[1, 0]) / q, -(mx - x[0, 0]) / q, -1]])
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return H
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def Hx(x, landmark_pos):
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""" takes a state variable and returns the measurement that would
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correspond to that state.
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"""
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mx = landmark_pos[0]
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my = landmark_pos[1]
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q = (mx - x[0, 0])**2 + (my - x[1, 0])**2
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Hx = array([[sqrt(q)],
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[atan2(my - x[1, 0], mx - x[0, 0]) - x[2, 0]]])
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return Hx
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dt = 1.0
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ekf = RobotEKF(dt)
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#np.random.seed(1234)
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m = array([[5, 10],
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[10, 5],
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[15, 15]])
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ekf.x = array([[2, 6, .3]]).T
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u = array([.5, .01])
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ekf.P = np.diag([1., 1., 1.])
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ekf.R = np.diag([sigma_r**2, sigma_h**2])
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c = [0, 1, 2]
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xp = ekf.x.copy()
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plt.scatter(m[:, 0], m[:, 1])
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for i in range(300):
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xp = ekf.move(xp, u, dt/10.) # simulate robot
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plt.plot(xp[0], xp[1], ',', color='g')
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if i % 10 == 0:
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h = ekf.x[2, 0]
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v = u[0]
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w = u[1]
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if w == 0:
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# approximate straight line with huge radius
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w = 1.e-30
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r = v/w # radius
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sinh = sin(h)
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sinhwdt = sin(h + w*dt)
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cosh = cos(h)
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coshwdt = cos(h + w*dt)
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ekf.F = array(
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[[1, 0, -r*cosh + r*coshwdt],
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[0, 1, -r*sinh + r*sinhwdt],
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[0, 0, 1]])
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V = array(
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[[(-sinh + sinhwdt)/w, v*(sin(h)-sinhwdt)/(w**2) + v*coshwdt*dt/w],
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[(cosh - coshwdt)/w, -v*(cosh-coshwdt)/(w**2) + v*sinhwdt*dt/w],
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[0, dt]])
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# covariance of motion noise in control space
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M = array([[a1*v**2 + a2*w**2, 0],
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[0, a3*v**2 + a4*w**2]])
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ekf.Q = dot(V, M).dot(V.T)
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ekf.predict(u=u)
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for lmark in m:
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d = sqrt((lmark[0] - xp[0, 0])**2 + (lmark[1] - xp[1, 0])**2) + randn()*sigma_r
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a = atan2(lmark[1] - xp[1, 0], lmark[0] - xp[0, 0]) - xp[2, 0] + randn()*sigma_h
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z = np.array([[d], [a]])
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ekf.update(z, HJacobian=H_of, Hx=Hx, residual=residual,
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args=(lmark), hx_args=(lmark))
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plot_covariance_ellipse((ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], std=10,
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facecolor='g', alpha=0.3)
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#plt.plot(ekf.x[0], ekf.x[1], 'x', color='r')
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plt.axis('equal')
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plt.show()
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