ImuFactorISAM2Example.py

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"""
ImuFactor example with iSAM2.
Authors: Robert Truax (C++), Frank Dellaert, Varun Agrawal (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
from gtsam import (ISAM2, BetweenFactorConstantBias, Cal3_S2,
                   ConstantTwistScenario, ImuFactor, NonlinearFactorGraph,
                   PinholeCameraCal3_S2, Point3, Pose3,
                   PriorFactorConstantBias, PriorFactorPose3,
                   PriorFactorVector, Rot3, Values)
from gtsam.symbol_shorthand import B, V, X
from gtsam.utils import plot
 
 
def vector3(x, y, z):
    """Create 3d double numpy array."""
    return np.array([x, y, z], dtype=float)
 
 
g = 9.81
n_gravity = vector3(0, 0, -g)
 
 
def preintegration_parameters():
    # IMU preintegration parameters
    # Default Params for a Z-up navigation frame, such as ENU: gravity points along negative Z-axis
    PARAMS = gtsam.PreintegrationParams.MakeSharedU(g)
    I = np.eye(3)
    PARAMS.setAccelerometerCovariance(I * 0.1)
    PARAMS.setGyroscopeCovariance(I * 0.1)
    PARAMS.setIntegrationCovariance(I * 0.1)
    PARAMS.setUse2ndOrderCoriolis(False)
    PARAMS.setOmegaCoriolis(vector3(0, 0, 0))
 
    BIAS_COVARIANCE = gtsam.noiseModel.Isotropic.Variance(6, 0.1)
    DELTA = Pose3(Rot3.Rodrigues(0, 0, 0),
                  Point3(0.05, -0.10, 0.20))
 
    return PARAMS, BIAS_COVARIANCE, DELTA
 
 
def get_camera(radius):
    up = Point3(0, 0, 1)
    target = Point3(0, 0, 0)
    position = Point3(radius, 0, 0)
    camera = PinholeCameraCal3_S2.Lookat(position, target, up, Cal3_S2())
    return camera
 
 
def get_scenario(radius, pose_0, angular_velocity, delta_t):
    """Create the set of ground-truth landmarks and poses"""
    angular_velocity_vector = vector3(0, -angular_velocity, 0)
    linear_velocity_vector = vector3(radius * angular_velocity, 0, 0)
    scenario = ConstantTwistScenario(
        angular_velocity_vector, linear_velocity_vector, pose_0)
 
    return scenario
 
 
def IMU_example():
    """Run iSAM 2 example with IMU factor."""
 
    # Start with a camera on x-axis looking at origin
    radius = 30
    camera = get_camera(radius)
    pose_0 = camera.pose()
 
    delta_t = 1.0/18  # makes for 10 degrees per step
    angular_velocity = math.radians(180)  # rad/sec
    scenario = get_scenario(radius, pose_0, angular_velocity, delta_t)
 
    PARAMS, BIAS_COVARIANCE, DELTA = preintegration_parameters()
 
    # Create a factor graph
    graph = NonlinearFactorGraph()
 
    # Create (incremental) ISAM2 solver
    isam = ISAM2()
 
    # Create the initial estimate to the solution
    # Intentionally initialize the variables off from the ground truth
    initialEstimate = 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([0.1, 0.1, 0.1, 0.3, 0.3, 0.3]))
    graph.push_back(PriorFactorPose3(X(0), pose_0, noise))
 
    # Add imu priors
    biasKey = B(0)
    biasnoise = gtsam.noiseModel.Isotropic.Sigma(6, 0.1)
    biasprior = PriorFactorConstantBias(biasKey, gtsam.imuBias.ConstantBias(),
                                        biasnoise)
    graph.push_back(biasprior)
    initialEstimate.insert(biasKey, gtsam.imuBias.ConstantBias())
    velnoise = gtsam.noiseModel.Isotropic.Sigma(3, 0.1)
 
    # Calculate with correct initial velocity
    n_velocity = vector3(0, angular_velocity * radius, 0)
    velprior = PriorFactorVector(V(0), n_velocity, velnoise)
    graph.push_back(velprior)
    initialEstimate.insert(V(0), n_velocity)
 
    accum = gtsam.PreintegratedImuMeasurements(PARAMS)
 
    # Simulate poses and imu measurements, adding them to the factor graph
    for i in range(80):
        t = i * delta_t  # simulation time
        if i == 0:  # First time add two poses
            pose_1 = scenario.pose(delta_t)
            initialEstimate.insert(X(0), pose_0.compose(DELTA))
            initialEstimate.insert(X(1), pose_1.compose(DELTA))
        elif i >= 2:  # Add more poses as necessary
            pose_i = scenario.pose(t)
            initialEstimate.insert(X(i), pose_i.compose(DELTA))
 
        if i > 0:
            # Add Bias variables periodically
            if i % 5 == 0:
                biasKey += 1
                factor = BetweenFactorConstantBias(
                    biasKey - 1, biasKey, gtsam.imuBias.ConstantBias(), BIAS_COVARIANCE)
                graph.add(factor)
                initialEstimate.insert(biasKey, gtsam.imuBias.ConstantBias())
 
            # Predict acceleration and gyro measurements in (actual) body frame
            nRb = scenario.rotation(t).matrix()
            bRn = np.transpose(nRb)
            measuredAcc = scenario.acceleration_b(t) - np.dot(bRn, n_gravity)
            measuredOmega = scenario.omega_b(t)
            accum.integrateMeasurement(measuredAcc, measuredOmega, delta_t)
 
            # Add Imu Factor
            imufac = ImuFactor(X(i - 1), V(i - 1), X(i), V(i), biasKey, accum)
            graph.add(imufac)
 
            # insert new velocity, which is wrong
            initialEstimate.insert(V(i), n_velocity)
            accum.resetIntegration()
 
        # Incremental solution
        isam.update(graph, initialEstimate)
        result = isam.calculateEstimate()
        plot.plot_incremental_trajectory(0, result,
                                         start=i, scale=3, time_interval=0.01)
 
        # reset
        graph = NonlinearFactorGraph()
        initialEstimate.clear()
 
    plt.show()
 
 
if __name__ == '__main__':
    IMU_example()