From 3e47e1af1f1e1322d84abae32238cd20b0aab12e Mon Sep 17 00:00:00 2001 From: Mitchell Cohen Date: Thu, 6 Feb 2025 16:58:45 -0500 Subject: [PATCH 1/2] Add B-Spline simulator, example, and test --- data/MH_01_easy.txt | 36383 +++++++++++++++++++++++++++++ data/README.md | 14 + docs/source/api.rst | 4 +- examples/ex_simulated_bspline.py | 287 + navlie/__init__.py | 2 + navlie/batch/estimator.py | 3 +- navlie/bspline.py | 290 + navlie/utils/common.py | 30 + tests/unit/test_bspline.py | 61 + 9 files changed, 37071 insertions(+), 3 deletions(-) create mode 100644 data/MH_01_easy.txt create mode 100644 data/README.md create mode 100644 examples/ex_simulated_bspline.py create mode 100644 navlie/bspline.py create mode 100644 tests/unit/test_bspline.py diff --git a/data/MH_01_easy.txt b/data/MH_01_easy.txt new file mode 100644 index 00000000..7f0ca2f9 --- /dev/null +++ b/data/MH_01_easy.txt @@ -0,0 +1,36383 @@ +# timestamp(s) tx ty tz qx qy qz qw +1403636580.83856 4.688319 -1.786938 0.783338 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/dev/null +++ b/data/README.md @@ -0,0 +1,14 @@ +## 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 translation \ No newline at end of file diff --git a/docs/source/api.rst b/docs/source/api.rst index 4870a37d..6dd31055 100644 --- a/docs/source/api.rst +++ b/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 \ No newline at end of file + navlie.lib + navlie.bspline \ No newline at end of file diff --git a/examples/ex_simulated_bspline.py b/examples/ex_simulated_bspline.py new file mode 100644 index 00000000..dda20b03 --- /dev/null +++ b/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() diff --git a/navlie/__init__.py b/navlie/__init__.py index 8050a63a..a0754fdf 100644 --- a/navlie/__init__.py +++ b/navlie/__init__.py @@ -27,6 +27,8 @@ from .datagen import DataGenerator, generate_measurement +from .bspline import SE3Bspline + from .composite import ( CompositeState, CompositeProcessModel, diff --git a/navlie/batch/estimator.py b/navlie/batch/estimator.py index a0a6da90..f6490102 100644 --- a/navlie/batch/estimator.py +++ b/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 diff --git a/navlie/bspline.py b/navlie/bspline.py new file mode 100644 index 00000000..a47df874 --- /dev/null +++ b/navlie/bspline.py @@ -0,0 +1,290 @@ +""" +A B-Spline on SE(3), useful for generating simulated trajectories +in 3D space and interoceptive measurements (like IMU measurements) +along the trajectory. + +This is essentially a Python implementation of the C++ code found in OpenVINS here: +https://github.com/rpng/open_vins/blob/master/ov_core/src/sim/BsplineSE3.h + +The core idea is to utilize cubic B-splines to interpolate between a set of control +point poses. Denoting :math:`\mathbf{T}_{ab} \in SE(3)` as the vehicle pose, the B-Spline is +parameterized by an evenly spaced set of control points :math:`\mathbf{T}_{ab_i}`. The value +of the spline curve at any time :math:`t` is purely a function of four bounding control points, such that + + .. math:: + \mathbf{T}_{ab} (t) = \exp \left( \\tilde{B}_{0, 4} (t) \log \left(\mathbf{T}_{ab_0} \\right) \\right) \prod_{n=1}^3 \exp \left( \\tilde{B}_{i, 4} \\log \left(\mathbf{T}_{ab_{i-1}}^{-1} \mathbf{T}_{ab_i} \\right) \\right) + +where :math:`\\tilde{B}_{i, 4}` are the cumulative basis functions. +For detailed derivations for the key equations behind the B-Spline simulator, see + E. Mueggler, G. Gallego, H. Rebecq, and D. Scaramuzza. Continuous-Time Visual-Inertial Odometry for Event Cameras. + IEEE Transactions on Robotics, pages 1–16, 2018. +""" + +import numpy as np +import typing +from navlie.lib.states import SE3State +from navlie.utils.common import state_interp +from pymlg import SO3, SE3 + + +class SE3Bspline: + def __init__( + self, + traj_points: typing.List[SE3State], + verbose: bool = False, + max_dt: float = 0.1, + ): + self.traj_points = traj_points + # self.verbose = verbose + + # Find the average frequency to use as our uniform points + dts = [ + traj_points[i].stamp - traj_points[i - 1].stamp + for i in range(1, len(traj_points)) + ] + average_dt = np.mean(dts) + self.dt = average_dt if average_dt > max_dt else max_dt + + # Get the trajectory start and end points + start_time = traj_points[0].stamp + self.end_time = traj_points[-1].stamp + + # Create the spline control points + self.control_points: typing.List[SE3State] = [] + + # Interpolate the control points at uniform intervals + cur_time = start_time + if verbose: + print( + "Generating evenly spaced control points along the trajectory..." + ) + + while True: + # Get the bounding poses + idx_poses = self._find_bounding_poses(cur_time, traj_points) + + if idx_poses is None: + break + + poses = [traj_points[i] for i in idx_poses] + # Linear interpolate and append to our control points + cur_control_point = state_interp(cur_time, poses) + self.control_points.append(cur_control_point) + cur_time += self.dt + + self.start_time = start_time + 2 * self.dt + + if verbose: + print(f"Number of control points: {len(traj_points)}") + print( + f"Trajectory length in seconds: {(self.end_time - start_time):.3f}" + ) + print(f"Trajectory start time: {self.start_time:.3f}") + print(f"Trajectory end time: {self.end_time:.3f}") + + def get_pose(self, stamp: float) -> SE3State: + """Query the B-Spline to get the pose at a given timestamp.""" + # Get the bounding control points + control_points = self._find_bounding_control_points( + stamp, self.control_points + ) + if control_points is None: + return None + + pose0, pose1, pose2, pose3 = control_points + t2 = pose2.stamp + t1 = pose1.stamp + + # De Boor-Cox matrix scalars + DT = t2 - t1 + u = (stamp - t1) / DT + b0, b1, b2 = self._compute_basis_functions(u) + + # Calculate interpolated poses + A0 = SE3.Exp(b0 * SE3.Log(SE3.inverse(pose0.value) @ pose1.value)) + A1 = SE3.Exp(b1 * SE3.Log(SE3.inverse(pose1.value) @ pose2.value)) + A2 = SE3.Exp(b2 * SE3.Log(SE3.inverse(pose2.value) @ pose3.value)) + pose_interp_np = pose0.value @ A0 @ A1 @ A2 + pose_interp = SE3State( + value=pose_interp_np, + stamp=stamp, + ) + return pose_interp + + def get_velocity(self, stamp) -> typing.Tuple[np.ndarray, np.ndarray]: + """Gets the angular and translational velocity at a given timestamp. + + The returned quantity is a tuple of numpy arrays, where the first + quantity is the angular velocity :math:`\mathbf{\omega}_b^{ba}`, + resolved in the body frame. The second quantity is the translational + velocity resolved in the inertial frame :math:`\mathbf{v}_a^{ba}`. + """ + + control_points = self._find_bounding_control_points( + stamp, self.control_points + ) + + if control_points is None: + return None, None + + # De Boor-Cox matrix scalars + pose0, pose1, pose2, pose3 = control_points + t2 = pose2.stamp + t1 = pose1.stamp + + # De Boor-Cox matrix scalars + DT = t2 - t1 + u = (stamp - t1) / DT + b0, b1, b2 = self._compute_basis_functions(u) + b0dot, b1dot, b2dot = self._compute_basis_functions_dot(u, DT) + + # Calculate interpolated poses + omega_10 = SE3.Log(SE3.inverse(pose0.value) @ pose1.value) + omega_21 = SE3.Log(SE3.inverse(pose1.value) @ pose2.value) + omega_32 = SE3.Log(SE3.inverse(pose2.value) @ pose3.value) + A0 = SE3.Exp(b0 * omega_10) + A1 = SE3.Exp(b1 * omega_21) + A2 = SE3.Exp(b2 * omega_32) + A0dot = b0dot * SE3.wedge(omega_10) @ A0 + A1dot = b1dot * SE3.wedge(omega_21) @ A1 + A2dot = b2dot * SE3.wedge(omega_32) @ A2 + + # Get the interpolated pose and the interpolated velocities + pose_interp_np = pose0.value @ A0 @ A1 @ A2 + vel_interp_mat = pose0.value @ ( + A0dot @ A1 @ A2 + A0 @ A1dot @ A2 + A0 @ A1 @ A2dot + ) + + # Extract the angular and translational velocities + omega_b_ba = SO3.vee(pose_interp_np[0:3, 0:3].T @ vel_interp_mat[0:3, 0:3]) + vel_a_ba = vel_interp_mat[0:3, 3].reshape((-1, 1)) + return omega_b_ba, vel_a_ba + + def get_acceleration(self, stamp) -> typing.Tuple[np.ndarray, np.ndarray]: + """Computes the angular and translational acceleration at a given + timestamp. + + The returned quantity is a tuple of numpy array with dimension [6 x 1], + where the first entry is the angular acceleration :math:`\alpha_b^{ba}`, + and the second entry is the translational acceleration resolved in the + global frame, :math:`\mathbf{a}_a^{ba}`. + """ + control_points = self._find_bounding_control_points( + stamp, self.control_points + ) + + if control_points is None: + return None, None + + # De Boor-Cox matrix scalars + pose0, pose1, pose2, pose3 = control_points + t2 = pose2.stamp + t1 = pose1.stamp + + # De Boor-Cox matrix scalars + DT = t2 - t1 + u = (stamp - t1) / DT + b0, b1, b2 = self._compute_basis_functions(u) + b0dot, b1dot, b2dot = self._compute_basis_functions_dot(u, DT) + b0ddot, b1ddot, b2ddot = self._compute_basis_functions_ddot(u, DT) + + # Calculate interpolated poses + omega_10 = SE3.Log(SE3.inverse(pose0.value) @ pose1.value) + omega_21 = SE3.Log(SE3.inverse(pose1.value) @ pose2.value) + omega_32 = SE3.Log(SE3.inverse(pose2.value) @ pose3.value) + omega_10_hat = SE3.wedge(omega_10) + omega_21_hat = SE3.wedge(omega_21) + omega_32_hat = SE3.wedge(omega_32) + + A0 = SE3.Exp(b0 * omega_10) + A1 = SE3.Exp(b1 * omega_21) + A2 = SE3.Exp(b2 * omega_32) + A0dot = b0dot * SE3.wedge(omega_10) @ A0 + A1dot = b1dot * SE3.wedge(omega_21) @ A1 + A2dot = b2dot * SE3.wedge(omega_32) @ A2 + A0ddot = b0dot * omega_10_hat @ A0dot + b0ddot * omega_10_hat @ A0 + A1ddot = b1dot * omega_21_hat @ A1dot + b1ddot * omega_21_hat @ A1 + A2ddot = b2dot * omega_32_hat @ A2dot + b2ddot * omega_32_hat @ A2 + + # Get the interpolated pose and velocities + pose_interp_np = pose0.value @ A0 @ A1 @ A2 + vel_interp_mat = pose0.value @ ( + A0dot @ A1 @ A2 + A0 @ A1dot @ A2 + A0 @ A1 @ A2dot + ) + acc_interp_mat = pose0.value @ ( + A0ddot @ A1 @ A2 + A0 @ A1ddot @ A2 + A0 @ A1 @ A2ddot + 2 * A0dot @ A1dot @ A2 + + 2 * A0 @ A1dot @ A2dot + 2 * A0dot @ A1 @ A2dot + ) + + omega_skew = pose_interp_np[0:3, 0:3].T @ vel_interp_mat[0:3, 0:3] + alpha = SO3.vee(pose_interp_np[0:3, 0:3].T @ (acc_interp_mat[0:3, 0:3] - vel_interp_mat[0:3, 0:3] @ omega_skew)) + a_a_ba = acc_interp_mat[0:3, 3].reshape((-1, 1)) + return alpha, a_a_ba + + + def _find_bounding_control_points( + self, + stamp: float, + control_points: typing.List[SE3State], + ) -> typing.List[SE3State]: + # Get the two bounding poses for the timestamp + idx_poses = self._find_bounding_poses( + stamp, + control_points, + ) + if idx_poses is None: + return None + + if idx_poses[0] == 0: + return None + if idx_poses[1] == len(control_points) - 1: + return None + + # Get the four control points that bound the timestamp + pose_1 = control_points[idx_poses[0]] + pose_2 = control_points[idx_poses[1]] + pose_0 = control_points[idx_poses[0] - 1] + pose_3 = control_points[idx_poses[1] + 1] + return [pose_0, pose_1, pose_2, pose_3] + + @staticmethod + def _find_bounding_poses( + stamp: float, + poses: typing.List[SE3State], + ) -> typing.List[int]: + """Finds the bounding poses for a given timestamp. + + Returns None if there are no bounding poses, otherwise returns the + indices in the pose list that bound the timestamp. + """ + # Check if the timestamp if outside the range of the poses + if stamp < poses[0].stamp or stamp > poses[-1].stamp: + return None + + # Find the poses that bound the timestamp + for i in range(1, len(poses)): + if poses[i].stamp > stamp: + return [i - 1, i] + + @staticmethod + def _compute_basis_functions(u) -> typing.List[float]: + b0 = (1.0 / 6.0) * (5.0 + 3.0 * u - 3.0 * u * u + u * u * u) + b1 = (1.0 / 6.0) * (1.0 + 3.0 * u + 3.0 * u * u - 2.0 * u * u * u) + b2 = (1.0 / 6.0) * (u * u * u) + return [b0, b1, b2] + + @staticmethod + def _compute_basis_functions_dot(u: float, dt: float) -> typing.List[float]: + b0dot = 1.0 / (6.0 * dt) * (3.0 - 6.0 * u + 3.0 * u * u) + b1dot = 1.0 / (6.0 * dt) * (3.0 + 6.0 * u - 6.0 * u * u) + b2dot = 1.0 / (6.0 * dt) * (3.0 * u * u) + return [b0dot, b1dot, b2dot] + + @staticmethod + def _compute_basis_functions_ddot( + u: float, dt: float + ) -> typing.List[float]: + b0ddot = 1.0 / (6.0 * dt * dt) * (-6.0 + 6.0 * u) + b1ddot = 1.0 / (6.0 * dt * dt) * (6.0 - 12.0 * u) + b2ddot = 1.0 / (6.0 * dt * dt) * (6.0 * u) + return [b0ddot, b1ddot, b2ddot] diff --git a/navlie/utils/common.py b/navlie/utils/common.py index 1bbc3943..50344600 100644 --- a/navlie/utils/common.py +++ b/navlie/utils/common.py @@ -7,11 +7,41 @@ from navlie.types import State, StateWithCovariance from navlie.lib.states import MixtureState from navlie.utils.mixture import gaussian_mixing +from navlie.lib.states import SE3State +from pymlg import SO3, SE3 + import numpy as np from scipy.interpolate import interp1d from scipy.linalg import block_diag, expm from scipy.stats.distributions import chi2 +def load_tum_trajectory(fpath: str) -> List[SE3State]: + """Loads a TUM trajectory file into a list of SE3State objects. + + Each row in the file should have 8 entries separated by spaces with the + following format: + timestamp px py pz qx qy qz qw + + where px, py, and pz are the position components of the robot pose, + and qx, qy, qz, and qw are the quaternion components of the robot pose + corresponding to the DCM C_ab. + """ + txt_file = np.loadtxt(fpath, delimiter=" ", comments="#") + + if txt_file.shape[1] != 8: + raise ValueError("TUM trajectory file must have 8 columns") + + pose_list: List[SE3State] = [] + for i in range(txt_file.shape[0]): + data_row = txt_file[i, :] + position = data_row[1:4] + quat = data_row[4:] + C_ab = SO3.from_quat(quat, order="xyzw") + pose_list.append(SE3State( + value=SE3.from_components(C_ab, position), + stamp=data_row[0])) + return pose_list + def state_interp( query_stamps: Union[float, List[float], Any], state_list: List[State], diff --git a/tests/unit/test_bspline.py b/tests/unit/test_bspline.py new file mode 100644 index 00000000..1b52f217 --- /dev/null +++ b/tests/unit/test_bspline.py @@ -0,0 +1,61 @@ +import os +import numpy as np +import typing +from tqdm import tqdm + +from pymlg import SE3 +from navlie.lib.states import SE3State +from navlie.bspline import SE3Bspline +from navlie.lib.models import BodyFrameVelocity, VectorInput + +import matplotlib.pyplot as plt + +cur_dir = os.path.dirname(os.path.realpath(__file__)) + + +def test_bspline(): + """Tests the B-Spline class by fitting a B-Spline to a + constant velocity trajectory and ensuring that the velocities computed + from the B-Spline match the true velocities . + """ + + # Constant velocity input + vel_input = VectorInput( + value=np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6]), + stamp=0.0, + ) + + # Propagate an initial pose forward with the constant velocity input + dt = 0.01 + init_pose = SE3State( + value=np.eye(4), + stamp=0.0, + ) + gt_poses = [init_pose.copy()] + process_model = BodyFrameVelocity(Q=np.identity(6)) + for i in range(1000): + next_pose = process_model.evaluate(gt_poses[-1], vel_input, dt) + next_pose.stamp += dt + gt_poses.append(next_pose) + + # Fit a B-Spline to the trajectory + bspline = SE3Bspline(gt_poses, verbose=True) + + # Query the B-Spline to get the poses and velocities at a set of times + query_stamps = [x.stamp for x in gt_poses] + for stamp in query_stamps: + pose_spline = bspline.get_pose(stamp) + omega_b_ba, vel_a_spline = bspline.get_velocity(stamp) + alpha_spline, accel_a_spline = bspline.get_acceleration(stamp) + + if pose_spline is not None and vel_a_spline is not None: + vel_b = pose_spline.attitude.T @ vel_a_spline + # Check that the spline velocities match the inputs + assert np.allclose(omega_b_ba.ravel(), vel_input.value[:3]) + assert np.allclose(vel_b.ravel(), vel_input.value[3:6]) + # Check angular acceleration is zero + assert np.allclose(alpha_spline.ravel(), np.zeros(3)) + + +if __name__ == "__main__": + test_bspline() From 355221fc2df5054011da6ca74d39814bc0cd2cb1 Mon Sep 17 00:00:00 2001 From: Mitchell Date: Mon, 10 Feb 2025 10:37:35 -0500 Subject: [PATCH 2/2] Update documentation --- data/README.md | 4 ++- navlie/bspline.py | 66 ++++++++++++++++++++++++++++++++++++++--------- 2 files changed, 57 insertions(+), 13 deletions(-) diff --git a/data/README.md b/data/README.md index 192bb96e..d6d820d1 100644 --- a/data/README.md +++ b/data/README.md @@ -11,4 +11,6 @@ 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 translation \ No newline at end of file +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`. \ No newline at end of file diff --git a/navlie/bspline.py b/navlie/bspline.py index a47df874..be7689b7 100644 --- a/navlie/bspline.py +++ b/navlie/bspline.py @@ -34,6 +34,21 @@ def __init__( verbose: bool = False, max_dt: float = 0.1, ): + """ + Creates a B-Spline on SE(3) from a list of SE3State poses. + + Will interopolate the poses at uniform intervals to create the control points. + + Parameters + ---------- + traj_points : List[SE3State] + List of SE3State poses to use to generate the B-Spline + verbose : bool, optional + Whether to print out debug information, by default False + max_dt : float, optional + Maximum time interval between control points, by default 0.1 + """ + self.traj_points = traj_points # self.verbose = verbose @@ -83,7 +98,18 @@ def __init__( print(f"Trajectory end time: {self.end_time:.3f}") def get_pose(self, stamp: float) -> SE3State: - """Query the B-Spline to get the pose at a given timestamp.""" + """Query the B-Spline to get the pose at a given timestamp. + + Parameters + ---------- + stamp : float + Query timestamp + + Returns + ------- + SE3State + The pose at the given timestamp + """ # Get the bounding control points control_points = self._find_bounding_control_points( stamp, self.control_points @@ -111,13 +137,21 @@ def get_pose(self, stamp: float) -> SE3State: ) return pose_interp - def get_velocity(self, stamp) -> typing.Tuple[np.ndarray, np.ndarray]: + def get_velocity(self, stamp: float) -> typing.Tuple[np.ndarray, np.ndarray]: """Gets the angular and translational velocity at a given timestamp. - The returned quantity is a tuple of numpy arrays, where the first - quantity is the angular velocity :math:`\mathbf{\omega}_b^{ba}`, - resolved in the body frame. The second quantity is the translational - velocity resolved in the inertial frame :math:`\mathbf{v}_a^{ba}`. + The the angular velocity is resolved in the body frame, :math:`\mathbf{\omega}_b^{ba}`, + whereas the translational velocity resolved in the inertial frame :math:`\mathbf{v}_a^{ba}`. + + Parameters + ---------- + stamp : float + Query timestamp + + Returns + ------- + Tuple[np.ndarray, np.ndarray] + Angular and translational velocity. """ control_points = self._find_bounding_control_points( @@ -160,14 +194,22 @@ def get_velocity(self, stamp) -> typing.Tuple[np.ndarray, np.ndarray]: vel_a_ba = vel_interp_mat[0:3, 3].reshape((-1, 1)) return omega_b_ba, vel_a_ba - def get_acceleration(self, stamp) -> typing.Tuple[np.ndarray, np.ndarray]: + def get_acceleration(self, stamp: float) -> typing.Tuple[np.ndarray, np.ndarray]: """Computes the angular and translational acceleration at a given timestamp. - - The returned quantity is a tuple of numpy array with dimension [6 x 1], - where the first entry is the angular acceleration :math:`\alpha_b^{ba}`, - and the second entry is the translational acceleration resolved in the - global frame, :math:`\mathbf{a}_a^{ba}`. + + Returns the angular acceleration resolved in the body frame, :math:`\mathbf{\\alpha}_b^{ba}`, + and the translational acceleration resolved in the global frame, :math:`\mathbf{a}_a^{ba}`. + + Parameters + ---------- + stamp : float + Query timestamp + + Returns + ------- + Tuple[np.ndarray, np.ndarray] + Angular and translational acceleration. """ control_points = self._find_bounding_control_points( stamp, self.control_points