Python example with reasonable measurements, in body frame. Still a TODO left.
Frank Dellaert
parent
0219b39341
commit
97a5d5a64a
|
|
@ -0,0 +1,207 @@
|
|||
"""
|
||||
iSAM2 example with ImuFactor.
|
||||
Author: Robert Truax (C++), Frank Dellaert (Python)
|
||||
"""
|
||||
# pylint: disable=invalid-name, E1101
|
||||
|
||||
from __future__ import print_function
|
||||
|
||||
import math
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import numpy as np
|
||||
from mpl_toolkits.mplot3d import Axes3D # pylint: disable=W0611
|
||||
|
||||
import gtsam
|
||||
import gtsam.utils.plot as gtsam_plot
|
||||
|
||||
|
||||
def X(key):
|
||||
"""Create symbol for pose key."""
|
||||
return gtsam.symbol(ord('x'), key)
|
||||
|
||||
|
||||
def V(key):
|
||||
"""Create symbol for velocity key."""
|
||||
return gtsam.symbol(ord('v'), key)
|
||||
|
||||
|
||||
def vector3(x, y, z):
|
||||
"""Create 3d double numpy array."""
|
||||
return np.array([x, y, z], dtype=np.float)
|
||||
|
||||
|
||||
def create_poses(angular_velocity=np.pi,
|
||||
delta_t=0.01, radius=30.0):
|
||||
# Create the set of ground-truth poses
|
||||
poses = []
|
||||
theta = 0.0
|
||||
up = gtsam.Point3(0, 0, 1)
|
||||
target = gtsam.Point3(0, 0, 0)
|
||||
for i in range(80):
|
||||
position = gtsam.Point3(radius * math.cos(theta),
|
||||
radius * math.sin(theta), 0.0)
|
||||
camera = gtsam.SimpleCamera.Lookat(
|
||||
position, target, up, gtsam.Cal3_S2())
|
||||
poses.append(camera.pose())
|
||||
theta += delta_t * angular_velocity
|
||||
|
||||
return poses
|
||||
|
||||
|
||||
def ISAM2_plot(values):
|
||||
"""Plot poses."""
|
||||
|
||||
# Declare an id for the figure
|
||||
fignum = 0
|
||||
|
||||
fig = plt.figure(fignum)
|
||||
axes = fig.gca(projection='3d')
|
||||
plt.cla()
|
||||
|
||||
i = 0
|
||||
min_bounds = 0, 0, 0
|
||||
max_bounds = 0, 0, 0
|
||||
while values.exists(X(i)):
|
||||
pose_i = values.atPose3(X(i))
|
||||
gtsam_plot.plot_pose3(fignum, pose_i, 10)
|
||||
position = pose_i.translation().vector()
|
||||
min_bounds = [min(v1, v2) for (v1, v2) in zip(position, min_bounds)]
|
||||
max_bounds = [max(v1, v2) for (v1, v2) in zip(position, max_bounds)]
|
||||
# max_bounds = min(pose_i.x(), max_bounds[0]), 0, 0
|
||||
i += 1
|
||||
|
||||
# draw
|
||||
axes.set_xlim3d(min_bounds[0]-1, max_bounds[0]+1)
|
||||
axes.set_ylim3d(min_bounds[1]-1, max_bounds[1]+1)
|
||||
axes.set_zlim3d(min_bounds[2]-1, max_bounds[2]+1)
|
||||
plt.pause(1)
|
||||
|
||||
|
||||
I = np.eye(3)
|
||||
accCov = I * 0.1
|
||||
gyroCov = I * 0.1
|
||||
intCov = I * 0.1
|
||||
secOrder = False
|
||||
|
||||
# IMU preintegration parameters
|
||||
# Default Params for a Z-up navigation frame, such as ENU: gravity points along negative Z-axis
|
||||
g = 9.81
|
||||
PARAMS = gtsam.PreintegrationParams.MakeSharedU()
|
||||
PARAMS.setAccelerometerCovariance(accCov)
|
||||
PARAMS.setGyroscopeCovariance(gyroCov)
|
||||
PARAMS.setIntegrationCovariance(intCov)
|
||||
PARAMS.setUse2ndOrderCoriolis(secOrder)
|
||||
PARAMS.setOmegaCoriolis(vector3(0, 0, 0))
|
||||
|
||||
|
||||
def IMU_example():
|
||||
|
||||
# Create the set of ground-truth landmarks and poses
|
||||
angular_velocity = math.radians(180) # rad/sec
|
||||
delta_t = 1.0/18 # makes for 10 degrees per step
|
||||
radius = 30
|
||||
poses = create_poses(angular_velocity, delta_t, radius)
|
||||
|
||||
# Create a factor graph
|
||||
newgraph = gtsam.NonlinearFactorGraph()
|
||||
totalgraph = gtsam.NonlinearFactorGraph()
|
||||
|
||||
# Create (incremental) ISAM2 solver
|
||||
isam = gtsam.ISAM2()
|
||||
|
||||
# Create the initial estimate to the solution
|
||||
# Intentionally initialize the variables off from the ground truth
|
||||
initialEstimate = gtsam.Values()
|
||||
totalEstimate = gtsam.Values()
|
||||
|
||||
# Add a prior on pose x0. This indirectly specifies where the origin is.
|
||||
# 30cm std on x,y,z 0.1 rad on roll,pitch,yaw
|
||||
noise = gtsam.noiseModel_Diagonal.Sigmas(
|
||||
np.array([0.3, 0.3, 0.3, 0.1, 0.1, 0.1]))
|
||||
newgraph.push_back(gtsam.PriorFactorPose3(X(0), poses[0], noise))
|
||||
totalgraph.push_back(gtsam.PriorFactorPose3(X(0), poses[0], noise))
|
||||
|
||||
# Add imu priors
|
||||
biasKey = gtsam.symbol(ord('b'), 0)
|
||||
biasnoise = gtsam.noiseModel_Isotropic.Sigma(6, 0.1)
|
||||
biasprior = gtsam.PriorFactorConstantBias(biasKey, gtsam.imuBias_ConstantBias(),
|
||||
biasnoise)
|
||||
newgraph.push_back(biasprior)
|
||||
totalgraph.push_back(biasprior)
|
||||
initialEstimate.insert(biasKey, gtsam.imuBias_ConstantBias())
|
||||
totalEstimate.insert(biasKey, gtsam.imuBias_ConstantBias())
|
||||
velnoise = gtsam.noiseModel_Isotropic.Sigma(3, 0.1)
|
||||
|
||||
# Calculate with correct initial velocity
|
||||
velocity = vector3(0, angular_velocity * radius, 0)
|
||||
velprior = gtsam.PriorFactorVector(V(0), velocity, velnoise)
|
||||
newgraph.push_back(velprior)
|
||||
totalgraph.push_back(velprior)
|
||||
initialEstimate.insert(V(0), velocity)
|
||||
totalEstimate.insert(V(0), velocity)
|
||||
|
||||
accum = gtsam.PreintegratedImuMeasurements(PARAMS)
|
||||
|
||||
# Simulate poses and imu measurements, adding them to the factor graph
|
||||
for i, pose_i in enumerate(poses):
|
||||
delta = gtsam.Pose3(gtsam.Rot3.Rodrigues(0, 0, 0),
|
||||
gtsam.Point3(0.05, -0.10, 0.20))
|
||||
if i == 0: # First time add two poses
|
||||
initialEstimate.insert(X(0), poses[0].compose(delta))
|
||||
initialEstimate.insert(X(1), poses[1].compose(delta))
|
||||
totalEstimate.insert(X(0), poses[0].compose(delta))
|
||||
totalEstimate.insert(X(1), poses[1].compose(delta))
|
||||
elif i >= 2: # Add more poses as necessary
|
||||
initialEstimate.insert(X(i), pose_i.compose(delta))
|
||||
totalEstimate.insert(X(i), pose_i.compose(delta))
|
||||
|
||||
if i > 0:
|
||||
# Add Bias variables periodically
|
||||
if i % 5 == 0:
|
||||
biasKey += 1
|
||||
b1 = biasKey - 1
|
||||
b2 = biasKey
|
||||
cov = gtsam.noiseModel_Isotropic.Variance(6, 0.1)
|
||||
f = gtsam.BetweenFactorConstantBias(
|
||||
b1, b2, gtsam.imuBias_ConstantBias(), cov)
|
||||
newgraph.add(f)
|
||||
totalgraph.add(f)
|
||||
initialEstimate.insert(biasKey, gtsam.imuBias_ConstantBias())
|
||||
totalEstimate.insert(biasKey, gtsam.imuBias_ConstantBias())
|
||||
|
||||
# Predict acceleration and gyro measurements in (actual) body frame
|
||||
# TODO: calculate correct acceleration due to circular trajectory
|
||||
nRb = pose_i.rotation().matrix()
|
||||
bRn = np.transpose(nRb)
|
||||
measuredAcc = - np.dot(bRn, vector3(0, 0, -g))
|
||||
measuredOmega = np.dot(bRn, vector3(0, 0, angular_velocity))
|
||||
accum.integrateMeasurement(measuredAcc, measuredOmega, delta_t)
|
||||
|
||||
# Add Imu Factor
|
||||
imufac = gtsam.ImuFactor(
|
||||
X(i - 1), V(i - 1), X(i), V(i), biasKey, accum)
|
||||
newgraph.add(imufac)
|
||||
totalgraph.add(imufac)
|
||||
|
||||
# insert new velocity
|
||||
initialEstimate.insert(V(i), velocity)
|
||||
totalEstimate.insert(V(i), velocity)
|
||||
accum.resetIntegration()
|
||||
|
||||
# Batch solution
|
||||
isam_full = gtsam.ISAM2()
|
||||
isam_full.update(totalgraph, totalEstimate)
|
||||
result = isam_full.calculateEstimate()
|
||||
|
||||
# Incremental solution
|
||||
isam.update(newgraph, initialEstimate)
|
||||
result = isam.calculateEstimate()
|
||||
newgraph = gtsam.NonlinearFactorGraph()
|
||||
initialEstimate.clear()
|
||||
|
||||
# ISAM2_plot(result)
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
IMU_example()
|
||||
Loading…
Reference in New Issue