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state_estimation.py
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import numpy as np
import scipy.linalg
import pdb
def state_estimation(dt,xhat,u,z_measurement,P):
# x_dot=Ax+Bu
# y=Cx
# Set A matrix
A = np.identity(18)
A[0:3,3:6] = dt * np.identity(3)
# Set B matrix
B = np.zeros([18,3])
B[3:6,0:3] = np.identity(3) * dt
# Set C matrix
C = np.zeros([28,18])
C[0:3,0:3] = -1 * np.identity(3)
C[3:6,0:3] = -1 * np.identity(3)
C[6:9,0:3] = -1 * np.identity(3)
C[9:12,0:3] = -1 * np.identity(3)
C[0:12,6:18] = np.identity(12)
C[12:15,3:6] = -1 * np.identity(3)
C[15:18,3:6] = -1 * np.identity(3)
C[18:21,3:6] = -1 * np.identity(3)
C[21:24,3:6] = -1 * np.identity(3)
C[27,17] = 1
C[26,14] = 1
C[25,11] = 1
C[24,8] = 1
# Some noise parameters
process_noise_pimu = 0.02
process_noise_vimu = 0.02
process_noise_pfoot = 0.002
sensor_noise_pimu_rel_foot = 1000000.01
sensor_noise_vimu_rel_foot = 1000000.01
sensor_noise_zfoot = 100000.01
# Set process covariance
Q = np.identity(18)
Q[0:3,0:3] = process_noise_pimu * (dt / 20) * np.identity(3)
Q[3:6,3:6] = process_noise_vimu * (dt / 20) * np.identity(3)
Q[6:18,6:18] = process_noise_pfoot * dt * np.identity(12)
# Set measurement covariance
R = np.identity(28)
R[0:12,0:12] = sensor_noise_pimu_rel_foot * np.identity(12)
R[12:24,12:24] = sensor_noise_vimu_rel_foot * np.identity(12)
R[24:28,24:28] = sensor_noise_zfoot * np.identity(4)
# Get acceleration from accelerometer
#g = np.array([0,0,-9.81])
# Get elements of y
p0 = np.array([xhat[0],xhat[1],xhat[2]])
v0 = np.array([xhat[3],xhat[4],xhat[5]])
#z_model = np.concatenate((ps, vs, pzs),axis=None)
# Kalman filter estimatiion
#########################################################
# predict
xhat = np.dot(A,xhat) + np.dot(B,u)
At = A.T
Pm = np.dot(A,np.dot(P,At)) + Q
#########################################################
##########################################################
# update
Ct = C.T
z_model = np.dot(C,xhat)
y = z_model - z_measurement
S = np.dot(C,np.dot(P,Ct))+R
K = np.dot(P,np.dot(Ct,np.linalg.inv(S)))
xhat = xhat+np.dot(K,y)
P=np.dot((np.eye(18)-np.dot(K,C)),Pm)
y= np.dot(C,xhat)-z_measurement
##########################################################
#print(np.linalg.norm(ey))
#S = C @ Pm @ Ct + R
#LU = scipy.linalg.lu_factor(S)
#K = Pm @ Ct @ np.linalg.inv(S)
#xhat += K @ ey
#S_ey = scipy.linalg.lu_solve(LU,ey)
#xhat += Pm @ Ct @ S_ey
#I = np.identity(18)
#S_C = scipy.linalg.lu_solve(LU,C)
#P = (I - Pm @ Ct @ S_C) @ Pm
#P = (I - K @ C) @ Pm
#Pt = P.T
#P = (P + Pt) / 2
#print(scipy.linalg.norm(P))
#pdb.set_trace()
#if np.linalg.det(P[0:2,0:2]) > 0.00001:
# P[0:2,2:18] = np.zeros((2,16))
# P[2:18,0:2] = np.zeros((16,2))
# P[0:2,0:2] /= 10
return xhat,P
def state_estimation_god_view(dt,xhat,u,z_measurement,P):
# Set A matrix
A = np.identity(18)
A[0:3,3:6] = dt * np.identity(3)
# Set B matrix
B = np.zeros([18,3])
B[3:6,0:3] = np.identity(3) * dt
# Set C matrix
C = np.zeros([15,18])
C[0:3,0:3]=np.eye(3)
C[3:6,6:9]=np.eye(3)
C[6:9,9:12]=np.eye(3)
C[9:12,12:15]=np.eye(3)
C[12:15,15:18]=np.eye(3)
# Some noise parameters
scale = 0.001
process_noise_pimu = 0.02*scale
process_noise_vimu = 0.02*scale
process_noise_pfoot = 0.02*scale
sensor_noise_position = 0.01
sensor_noise_foot_position = 0.01
# Set process covariance
Q = np.identity(18)
Q[0:3,0:3] = process_noise_pimu * np.identity(3)
Q[3:6,3:6] = process_noise_vimu * np.identity(3)
Q[6:18,6:18] = process_noise_pfoot * np.identity(12)
# Set measurement covariance
R = np.identity(15)
R[0:3,0:3] = sensor_noise_position * np.identity(3)
R[3:15,3:15] = sensor_noise_foot_position * np.identity(12)
# Kalman filter estimatiion
#########################################################
# predict
xhat = np.dot(A,xhat) + np.dot(B,u)
P=np.dot(A,np.dot(P,A.T))+Q
#########################################################
#pdb.set_trace()
#######################
# update
y = z_measurement-np.dot(C,xhat)
S=np.dot(C,np.dot(P,C.T))+R
K = np.dot(P,np.dot(C.T,np.linalg.inv(S)))
xhat = xhat + np.dot(K,y)
#print(x_hat)
P = np.dot((np.eye(len(xhat))-np.dot(K,C)),P)
#########################
#pdb.set_trace()
return xhat,P
def state_estimation_simple_version(dt,xhat,u,z_measurement,P):
A = np.identity(6)
A[0:3,3:6] = dt * np.identity(3)
B = np.zeros([6,3])
B[0:3,0:3] = np.identity(3) * dt**2/2
B[3:6,0:3] = np.identity(3) * dt
C = np.zeros([3,6])
C[0:3,0:3]=np.eye(3)
scale = 1
process_noise_pimu = 0.02*scale
sensor_noise_position = 1
Q = np.identity(6)
Q[0:3,0:3] = process_noise_pimu * np.identity(3)
# Set measurement covariance
R = np.identity(3)
R[0:3,0:3] = sensor_noise_position * np.identity(3)
# Kalman filter estimatiion
#########################################################
# predict
xhat = np.dot(A,xhat) + np.dot(B,u)
P=np.dot(A,np.dot(P,A.T))+Q
#########################################################
#pdb.set_trace()
#######################
# update
y = z_measurement-np.dot(C,xhat)
S=np.dot(C,np.dot(P,C.T))+R
K = np.dot(P,np.dot(C.T,np.linalg.inv(S)))
xhat = xhat + np.dot(K,y)
#print('norm K')
#print(np.linalg.norm(K))
P = np.dot((np.eye(len(xhat))-np.dot(K,C)),P)
#########################
#pdb.set_trace()
return xhat,P
def state_estimation_simple_velocity_version(dt,xhat,u,z_measurement,P):
A = np.identity(6)
A[0:3,3:6] = dt * np.identity(3)
B = np.zeros([6,3])
B[0:3,0:3] = np.identity(3) * dt**2/2
B[3:6,0:3] = np.identity(3) * dt
C = np.zeros([3,6])
C[0:3,3:6]=np.eye(3)
scale = 1
process_noise_pimu = 0.01*scale
sensor_noise_position = 0.01
Q = np.identity(6)
Q[0:3,0:3] = process_noise_pimu * np.identity(3)
# Set measurement covariance
R = np.identity(3)
R[0:3,0:3] = sensor_noise_position * np.identity(3)
# Kalman filter estimatiion
#########################################################
# predict
xhat = np.dot(A,xhat) + np.dot(B,u)
P=np.dot(A,np.dot(P,A.T))+Q
#########################################################
#pdb.set_trace()
#######################
# update
y = z_measurement-np.dot(C,xhat)
S=np.dot(C,np.dot(P,C.T))+R
K = np.dot(P,np.dot(C.T,np.linalg.inv(S)))
xhat = xhat + np.dot(K,y)
print('norm K')
print(np.linalg.norm(K))
P = np.dot((np.eye(len(xhat))-np.dot(K,C)),P)
#########################
#pdb.set_trace()
return xhat,P
def Cheetah3KalmanFilter(dt,xhat,u,z_measurement,P,contacts):
# Set A matrix
A = np.identity(18)
A[0:3,3:6] = dt * np.identity(3)
# Set B matrix
B = np.zeros([18,3])
B[3:6,0:3] = np.identity(3) * dt
# Set C matrix
C = np.zeros([15,18])
C[0:3,3:6]=np.eye(3)
C[3:6,0:3]=-np.eye(3)
C[6:9,0:3]=-np.eye(3)
C[9:12,0:3]=-np.eye(3)
C[12:15,0:3]=-np.eye(3)
C[3:6,6:9]=np.eye(3)
C[6:9,9:12]=np.eye(3)
C[9:12,12:15]=np.eye(3)
C[12:15,15:18]=np.eye(3)
# Some noise parameters
scale = 10000
process_noise_pimu = 0.02
process_noise_vimu = 0.02
if len(contacts[0])==0:
process_noise_p_FL = 100000000
elif len(contacts[0])!=0:
process_noise_p_FL = 0.00001
if len(contacts[1])==0:
process_noise_p_FR = 100000000
elif len(contacts[1])!=0:
process_noise_p_FR = 0.00001
if len(contacts[2])==0:
process_noise_p_RL = 100000000
elif len(contacts[2])!=0:
process_noise_p_RL = 0.00001
if len(contacts[3])==0:
process_noise_p_RR = 100000000
elif len(contacts[3])!=0:
process_noise_p_RR = 0.00001
sensor_noise_velocity = 0.0001
sensor_noise_foot_position = 0.0001
# Set process covariance
Q = np.identity(18)
Q[0:3,0:3] = process_noise_pimu * np.identity(3)
Q[3:6,3:6] = process_noise_vimu * np.identity(3)
Q[6:9,6:9] = process_noise_p_FL * np.identity(3)
Q[9:12,9:12] = process_noise_p_FR * np.identity(3)
Q[12:15,12:15] = process_noise_p_RL * np.identity(3)
Q[15:18,15:18] = process_noise_p_RR * np.identity(3)
# Set measurement covariance
R = np.identity(15)
R[0:3,0:3] = sensor_noise_velocity * np.identity(3)
R[3:15,3:15] = sensor_noise_foot_position * np.identity(12)
# Kalman filter estimatiion
#########################################################
# predict
xhat = np.dot(A,xhat) + np.dot(B,u)
P=np.dot(A,np.dot(P,A.T))+Q
#########################################################
#pdb.set_trace()
#######################
# update
y = z_measurement-np.dot(C,xhat)
S=np.dot(C,np.dot(P,C.T))+R
K = np.dot(P,np.dot(C.T,np.linalg.inv(S)))
xhat = xhat + np.dot(K,y)
#print(x_hat)
P = np.dot((np.eye(len(xhat))-np.dot(K,C)),P)
#########################
#pdb.set_trace()
return xhat,P
def state_estimation_god_view_relative(dt,xhat,u,z_measurement,P):
# Set A matrix
A = np.identity(18)
A[0:3,3:6] = dt * np.identity(3)
# Set B matrix
B = np.zeros([18,3])
B[3:6,0:3] = np.identity(3) * dt
# Set C matrix
C = np.zeros([15,18])
C[0:3,0:3]=np.eye(3)
C[3:6,0:3]=-np.eye(3)
C[6:9,0:3]=-np.eye(3)
C[9:12,0:3]=-np.eye(3)
C[12:15,0:3]=-np.eye(3)
C[3:6,6:9]=np.eye(3)
C[6:9,9:12]=np.eye(3)
C[9:12,12:15]=np.eye(3)
C[12:15,15:18]=np.eye(3)
# Some noise parameters
scale = 0.001
process_noise_pimu = 0.02*scale
process_noise_vimu = 0.02*scale
process_noise_pfoot = 0.02*scale
sensor_noise_position = 0.01
sensor_noise_foot_position = 0.01
# Set process covariance
Q = np.identity(18)
Q[0:3,0:3] = process_noise_pimu * np.identity(3)
Q[3:6,3:6] = process_noise_vimu * np.identity(3)
Q[6:18,6:18] = process_noise_pfoot * np.identity(12)
# Set measurement covariance
R = np.identity(15)
R[0:3,0:3] = sensor_noise_position * np.identity(3)
R[3:15,3:15] = sensor_noise_foot_position * np.identity(12)
# Kalman filter estimatiion
#########################################################
# predict
xhat = np.dot(A,xhat) + np.dot(B,u)
P=np.dot(A,np.dot(P,A.T))+Q
#########################################################
#pdb.set_trace()
#######################
# update
y = z_measurement-np.dot(C,xhat)
S=np.dot(C,np.dot(P,C.T))+R
K = np.dot(P,np.dot(C.T,np.linalg.inv(S)))
xhat = xhat + np.dot(K,y)
#print(x_hat)
P = np.dot((np.eye(len(xhat))-np.dot(K,C)),P)
#########################
#pdb.set_trace()
return xhat,P