Add B-Spline on SE(3)

data/README.md

@@ -0,0 +1,16 @@
+## navlie data
+
+This folder contains groundtruth data useful for generating simulated
+trajectories in 3D space to test estimators on, using the B-Spline simulator
+included in navlie. For an example of how to load in the data and use it to
+generate simulated trajectories, see the example `ex_simulated_kitti.py`.
+
+To generate your own simulated dataset from a custom trajectory, ensure that the
+trajectory file is in TUM format, where each line is formatted as follows:
+```
+timestamp tx ty tz qx qy qz qw
+```
+
+where `timestamp` is the time in seconds, `tx ty tz` are the components of the translation,
+and `qx qy qz qw` are the components quaternion that represents the orientation of the platform.
+It is assumed that the quaternion corresponds to `C_ab`.

docs/source/api.rst

@@ -10,8 +10,8 @@ Below is a list of all the modules in the navlie package.  Click on any of the l
    navlie.composite
    navlie.datagen
    navlie.filters
-   navlie.imm
    navlie.types
    navlie.utils
    navlie.batch
-   navlie.lib
+   navlie.lib
+   navlie.bspline

examples/ex_simulated_bspline.py

@@ -0,0 +1,287 @@
+"""This script will show how to use the B-Spline simulator to simulate robot
+trajectories in 3D space, and to generate measurements along the trajectory
+to then run estimation algorithms on.
+
+The script simulates a trajectory based on a sequence from the Euroc dataset,
+where the groundtruth file is provided under navlie/data/MH_01_easy.txt. 
+
+The B-Spline simulator is used to generate IMU measurements and absolute
+position measurements along the trajectory, and then an EKF is used to fuse them. 
+"""
+
+import os
+import numpy as np
+import typing
+
+from pymlg import SE23
+from navlie.lib.states import SE3State
+from navlie.bspline import SE3Bspline
+from navlie.utils.common import load_tum_trajectory, randvec
+from navlie.lib.imu import IMU, IMUState, IMUKinematics
+from navlie.lib.models import AbsolutePosition
+from navlie.types import Measurement
+import navlie as nav
+
+import matplotlib.pyplot as plt
+
+cur_dir = os.path.dirname(os.path.realpath(__file__))
+
+
+def generate_bspline_dataset(
+    traj_file: str,
+    input_freq: int = 200,
+    meas_freq: int = 5,
+    t_end: float = 100,
+    Q_c: np.ndarray = None,
+    R: np.ndarray = None,
+    gravity_mag: float = 9.80665,
+) -> typing.Dict[str, typing.Any]:
+    """This function generates simulated trajectory using the
+    SE(3) B-Spline simulator found in the module bspline.py.
+
+    In addition, this function generates simulated noisy, biased
+    IMU measurements and noisy GPS measurements along the trajectory.
+
+    Parameters
+    ----------
+    traj_file : str
+        The path to the TUM trajectory file to load
+    input_freq : int, optional
+        The frequency of the IMU measurements, by default 200.
+    meas_freq : int, optional
+        The frequency of the GPS position measurements, by default 5.
+    t_end : float, optional
+        The duration of the trajectory to simulate, by default 100.
+    Q_c : np.ndarray, optional
+        The continuous-time IMU process noise covariance, by default None.
+        This should be a 12x12 matrix, where the ordering is
+            gyro_white_noise, accel_white_noise,
+            gyro_bias_white_noise, accel_bias_white_noise.
+    R : np.ndarray, optional
+        The measurement noise covariance for the GPS measurements, by default None.
+    gravity_mag : float, optional
+        The magnitude of the gravity vector, by default 9.80665.
+
+    Returns:
+        typing.Dict[str, typing.Any]: A dictionary containing the following
+        keys:
+            - gt_states: A list of the groundtruth IMU states
+            - imu_meas: A list of the noisy IMU measurements
+            - abs_pos_meas: A list of the noisy GPS measurements
+            - process_noise: The discrete-time process noise covariance
+    """
+    # Load the trajectory until the end time
+    raw_traj = load_tum_trajectory(traj_file)
+    start_stamp = raw_traj[0].stamp
+    end_stamp = start_stamp + t_end
+
+    trajectory = []
+    for pose in raw_traj:
+        if pose.stamp < end_stamp:
+            trajectory.append(pose)
+        else:
+            break
+
+    # Create the B-Spline from the raw trajectory
+    bspline = SE3Bspline(trajectory, verbose=True)
+
+    # Query the B-Spline to get the poses and velocities at a set of times
+    dt = 1.0 / input_freq
+    t_eval = np.arange(bspline.start_time, bspline.end_time, dt)
+    poses_gt: typing.List[SE3State] = []
+    angular_vels: typing.List[np.ndarray] = []
+    linear_vels: typing.List[np.ndarray] = []
+    linear_accels: typing.List[np.ndarray] = []
+    stamps: typing.List[float] = []
+    for t in t_eval:
+        pose = bspline.get_pose(t)
+        omega_b_ba, v_a_ba = bspline.get_velocity(t)
+        _, a_a_ba = bspline.get_acceleration(t)
+
+        if pose is not None and omega_b_ba is not None:
+            poses_gt.append(pose)
+            angular_vels.append(omega_b_ba)
+            linear_vels.append(v_a_ba)
+            linear_accels.append(a_a_ba)
+            stamps.append(t)
+
+    # Set the continuous-time IMU noise covariance
+    if Q_c is None:
+        Q_c = np.identity(12)
+        Q_c[0:3, 0:3] = np.identity(3) * 0.0001
+        Q_c[3:6, 3:6] = np.identity(3) * 0.001
+        Q_c[6:9, 6:9] = np.identity(3) * 0.0001
+        Q_c[9:, 9:] = np.identity(3) * 0.0001
+    if R is None:
+        R = np.identity(3) * 0.01
+    # Convert the continuous-time noise to discrete-time
+    Q_d = Q_c / dt
+
+    # Extract the relevant subblocks of the process noise to generate
+    # the measurements
+    Qd_gyro = Q_d[0:3, 0:3]
+    Qd_accel = Q_d[3:6, 3:6]
+    Qd_gyro_bias = Q_d[6:9, 6:9]
+    Qd_accel_bias = Q_d[9:, 9:]
+
+    # Propagate forward the IMU biases using a first order random walk
+    init_gyro_bias = np.array([0.02, 0.03, -0.03])
+    init_accel_bias = np.array([0.02, -0.06, 0.04])
+    gyro_biases: typing.List[np.ndarray] = [init_gyro_bias]
+    accel_biases: typing.List[np.ndarray] = [init_accel_bias]
+    for i in range(0, len(poses_gt) - 1):
+        next_gyro_bias = gyro_biases[i] + dt * randvec(Qd_gyro_bias).ravel()
+        next_accel_bias = accel_biases[i] + dt * randvec(Qd_accel_bias).ravel()
+        gyro_biases.append(next_gyro_bias)
+        accel_biases.append(next_accel_bias)
+
+    # Create a list of the groundtruth states
+    gt_imu_states: typing.List[IMUState] = []
+    for i in range(len(poses_gt)):
+        pose_gt = poses_gt[i]
+        vel_gt = linear_vels[i]
+        gyro_bias_gt = gyro_biases[i]
+        accel_bias_gt = accel_biases[i]
+        stamp = stamps[i]
+        nav_state = SE23.from_components(pose_gt.attitude, vel_gt, pose_gt.position)
+        imu_state = IMUState(
+            nav_state=nav_state,
+            bias_gyro=gyro_bias_gt,
+            bias_accel=accel_bias_gt,
+            stamp=stamp,
+        )
+        gt_imu_states.append(imu_state)
+
+    # Generate the noisy, biases IMU measurements
+    # Note that the gyro measurements are of the form
+    #   u_gyro = omega_b_ba + bias_gyro + noise,
+    # and the accel measurements are of the form
+    #   u_accel = C_ab.T * (accel_a - gravity) + bias_accel + noise
+    gravity = np.array([0, 0, -gravity_mag])
+    imu_meas_list: typing.List[IMU] = []
+    for i in range(len(gt_imu_states)):
+        cur_state = gt_imu_states[i]
+        omega_b_ba = angular_vels[i].ravel()
+        accel_a = linear_accels[i].ravel()
+        gyro_meas = omega_b_ba + cur_state.bias_gyro + randvec(Qd_gyro).ravel()
+        accel_meas = (
+            cur_state.attitude.T @ (accel_a - gravity)
+            + cur_state.bias_accel
+            + randvec(Qd_accel).ravel()
+        )
+        imu_meas = IMU(
+            gyro=gyro_meas,
+            accel=accel_meas,
+            stamp=cur_state.stamp,
+        )
+        imu_meas_list.append(imu_meas)
+
+    # Generate the noisy absolute position measurements at the correct timestamps
+    time_last_meas = stamps[0]
+    meas_dt = 1 / meas_freq
+    meas_model = AbsolutePosition(R)
+    meas_list: typing.List[Measurement] = []
+    for i in range(len(gt_imu_states)):
+        cur_stamp = gt_imu_states[i].stamp
+        if (cur_stamp - time_last_meas) > meas_dt:
+            # Generate a measurement
+            time_last_meas = cur_stamp
+            pos_meas = gt_imu_states[i].position + randvec(R).ravel()
+            meas = Measurement(
+                model=meas_model,
+                value=pos_meas,
+                stamp=cur_stamp,
+            )
+            meas_list.append(meas)
+
+    # Return the dataset
+    out_dict = {
+        "gt_states": gt_imu_states,
+        "imu_meas": imu_meas_list,
+        "abs_pos_meas": meas_list,
+        "process_noise": Q_d,
+    }
+    return out_dict
+
+
+def main(traj_file: str) -> nav.GaussianResultList:
+    # Generate the simualted dataset
+    dataset = generate_bspline_dataset(
+        traj_file,
+        input_freq=200,
+        meas_freq=10,
+        t_end=300,
+    )
+
+    # Plot the IMU measurements along the trajectory 
+    fig, ax = plt.subplots(2, 1, figsize=(10, 6))
+    stamps = np.array([m.stamp for m in dataset["imu_meas"]])
+    gyro_meas = np.array([m.gyro for m in dataset["imu_meas"]])
+    accel_meas = np.array([m.accel for m in dataset["imu_meas"]])
+    ax[0].plot(stamps, gyro_meas, label="Gyro Meas")
+    ax[0].set_ylabel("Gyro Meas (rad/s)")
+    ax[1].plot(stamps, accel_meas, label="Accel Meas")
+    ax[1].set_ylabel("Accel Meas (m/s^2)")
+    ax[1].set_xlabel("Time (s)")
+    fig.tight_layout()
+
+    # Run a filter on the data!
+    gt_states = dataset["gt_states"]
+    imu_meas = dataset["imu_meas"]
+    abs_pos_meas = dataset["abs_pos_meas"]
+    Q_d = dataset["process_noise"]
+
+    # Create the process model
+    process_model = IMUKinematics(Q_d)
+
+    # Filter initialization
+    P0 = np.eye(15)
+    P0[0:3, 0:3] *= 0.01**2
+    P0[3:6, 3:6] *= 0.01**2
+    P0[6:9, 6:9] *= 0.01**2
+    P0[9:12, 9:12] *= 0.01**2
+    P0[12:15, 12:15] *= 0.01**2
+    x0 = gt_states[0].plus(randvec(P0))
+
+    # ###########################################################################
+    # Run filter
+    ekf = nav.ExtendedKalmanFilter(process_model)
+    estimate_list = nav.run_filter(ekf, x0, P0, imu_meas, abs_pos_meas)
+    return nav.GaussianResultList.from_estimates(estimate_list, gt_states)
+
+
+if __name__ == "__main__":
+    # Select the trajecotry file to use
+    traj_file = os.path.join(cur_dir, "../data", "MH_01_easy.txt")
+    results = main(traj_file)
+    # Plot results
+    fig = plt.figure()
+    ax = plt.axes(projection="3d")
+    nav.plot_poses(
+        results.state,
+        ax,
+        line_color="tab:blue",
+        step=None,
+        label="Estimate",
+    )
+    nav.plot_poses(
+        results.state_true,
+        ax,
+        line_color="tab:red",
+        step=None,
+        label="Groundtruth",
+    )
+    ax.legend()
+    ax.set_xlabel("x (m)")
+    ax.set_ylabel("y (m)")
+    ax.set_zlabel("z (m)")
+
+    fig, axs = nav.plot_error(results)
+    axs[0, 0].set_title("Attitude")
+    axs[0, 1].set_title("Velocity")
+    axs[0, 2].set_title("Position")
+    axs[0, 3].set_title("Gyro bias")
+    axs[0, 4].set_title("Accel bias")
+    axs[-1, 2]
+
+    plt.show()

navlie/__init__.py

@@ -27,6 +27,8 @@
 
 from .datagen import DataGenerator, generate_measurement
 
+from .bspline import SE3Bspline
+
 from .composite import (
     CompositeState,
     CompositeProcessModel,

navlie/batch/estimator.py

@@ -1,4 +1,5 @@
-"""Batch estimator to construct batch problems composed of prior residuals, process residuals, and 
+"""
+Batch estimator to construct batch problems composed of prior residuals, process residuals, and 
 measurement residuals.
 
 The BatchEstimator.solve() method constructs and solves a batch problem over a sequence