added new Python examples using iSAM2
jerredchen
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"""
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GTSAM Copyright 2010-2018, Georgia Tech Research Corporation,
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Atlanta, Georgia 30332-0415
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All Rights Reserved
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Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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See LICENSE for the license information
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Pose SLAM example using iSAM2 in the 2D plane.
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Author: Jerred Chen, Yusuf Ali
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Modelled after:
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- VisualISAM2Example by: Duy-Nguyen Ta (C++), Frank Dellaert (Python)
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- Pose2SLAMExample by: Alex Cunningham (C++), Kevin Deng & Frank Dellaert (Python)
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"""
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from __future__ import print_function
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import math
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import numpy as np
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from numpy.random import multivariate_normal as mult_gauss
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import gtsam
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import matplotlib.pyplot as plt
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import gtsam.utils.plot as gtsam_plot
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def Pose2SLAM_ISAM2_plot(graph, current_estimate):
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"""
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Plots incremental state of the robot for 2D Pose SLAM using iSAM2
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Author: Jerred Chen
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Based on version by:
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- Ellon Paiva (Python),
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- Duy Nguyen Ta and Frank Dellaert (MATLAB)
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"""
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marginals = gtsam.Marginals(graph, current_estimate)
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fig = plt.figure(0)
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axes = fig.gca()
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plt.cla()
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i = 1
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while current_estimate.exists(i):
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gtsam_plot.plot_pose2(0, current_estimate.atPose2(i), 0.5, marginals.marginalCovariance(i))
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i += 1
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plt.axis('equal')
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axes.set_xlim(-1, 5)
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axes.set_ylim(-1, 3)
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plt.pause(1)
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return marginals
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def Pose2SLAM_ISAM2_example():
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plt.ion()
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def vector3(x, y, z):
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"""Create 3d double numpy array."""
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return np.array([x, y, z], dtype=float)
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# Although this example only uses linear measurements and Gaussian noise models, it is important
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# to note that iSAM2 can be utilized to its full potential during nonlinear optimization. This example
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# simply showcases how iSAM2 may be applied to a Pose2 SLAM problem.
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PRIOR_NOISE = gtsam.noiseModel.Diagonal.Sigmas(vector3(0.3, 0.3, 0.1))
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ODOMETRY_NOISE = gtsam.noiseModel.Diagonal.Sigmas(vector3(0.2, 0.2, 0.1))
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# Create a Nonlinear factor graph as well as the data structure to hold state estimates.
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graph = gtsam.NonlinearFactorGraph()
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initial_estimate = gtsam.Values()
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# iSAM2 parameters which can adjust the threshold necessary to force relinearization and how many
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# update calls are required to perform the relinearization.
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parameters = gtsam.ISAM2Params()
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parameters.setRelinearizeThreshold(0.1)
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parameters.setRelinearizeSkip(1)
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isam = gtsam.ISAM2(parameters)
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# The ground truth odometry measurements (without noise) of the robot during the trajectory.
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odom_arr = [(2, 0, 0),
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(2, 0, math.pi/2),
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(2, 0, math.pi/2),
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(2, 0, math.pi/2),
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(2, 0, math.pi/2)]
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# The initial estimates for robot poses 2-5. Pose 1 is initialized by the prior.
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# To demonstrate iSAM2 incremental optimization, poor initializations were intentionally inserted.
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pose_est = [gtsam.Pose2(2.3, 0.1, -0.2),
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gtsam.Pose2(4.1, 0.1, math.pi/2),
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gtsam.Pose2(4.0, 2.0, math.pi),
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gtsam.Pose2(2.1, 2.1, -math.pi/2),
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gtsam.Pose2(1.9, -0.2, 0.2)]
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graph.push_back(gtsam.PriorFactorPose2(1, gtsam.Pose2(0, 0, 0), PRIOR_NOISE))
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initial_estimate.insert(1, gtsam.Pose2(0.5, 0.0, 0.2))
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def determine_loop_closure(odom, current_estimate, xy_tol=0.6, theta_tol=0.3):
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"""
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Simple brute force approach which iterates through previous states
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and checks for loop closure.
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### Parameters:
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odom: (numpy.ndarray) 1x3 vector representing noisy odometry (x, y, theta)
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measurement in the body frame.
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current_estimate: (gtsam.Values) The current estimates computed by iSAM2.
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xy_tol: (double) Optional argument for the x-y measurement tolerance.
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theta_tol: (double) Optional argument for the theta measurement tolerance.
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### Returns:
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k: (int) The key of the state which is helping add the loop closure constraint.
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If loop closure is not found, then None is returned.
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"""
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if current_estimate:
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prev_est = current_estimate.atPose2(i+1)
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rotated_odom = prev_est.rotation().matrix() @ odom[:2]
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curr_xy = np.array([prev_est.x() + rotated_odom[0],
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prev_est.y() + rotated_odom[1]])
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curr_theta = prev_est.theta() + odom[2]
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for k in range(1, i+1):
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pose_xy = np.array([current_estimate.atPose2(k).x(),
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current_estimate.atPose2(k).y()])
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pose_theta = current_estimate.atPose2(k).theta()
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if (abs(pose_xy - curr_xy) <= xy_tol).all() and \
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(abs(pose_theta - curr_theta) <= theta_tol):
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return k
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current_estimate = None
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for i in range(len(odom_arr)):
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odom_x, odom_y, odom_theta = odom_arr[i]
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# Odometry measurement that is received by the robot and corrupted by gaussian noise
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odom = mult_gauss(odom_arr[i], ODOMETRY_NOISE.covariance())
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# Determine if there is loop closure based on the odometry measurement and the previous estimate of the state
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loop = determine_loop_closure(odom, current_estimate)
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if loop:
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graph.push_back(gtsam.BetweenFactorPose2(i + 1, loop, gtsam.Pose2(odom_x, odom_y, odom_theta), ODOMETRY_NOISE))
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else:
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graph.push_back(gtsam.BetweenFactorPose2(i + 1, i + 2, gtsam.Pose2(odom_x, odom_y, odom_theta), ODOMETRY_NOISE))
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initial_estimate.insert(i + 2, pose_est[i])
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# Incremental update to iSAM2's internal Baye's tree, which only optimizes upon the added variables
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# as well as any affected variables
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isam.update(graph, initial_estimate)
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# Another iSAM2 update can be performed for additional optimization
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isam.update()
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current_estimate = isam.calculateEstimate()
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print("*"*50)
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print(f"Inference after State {i+1}:")
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print(current_estimate)
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marginals = Pose2SLAM_ISAM2_plot(graph, current_estimate)
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initial_estimate.clear()
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for i in range(1, len(odom_arr)+1):
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print(f"X{i} covariance:\n{marginals.marginalCovariance(i)}\n")
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plt.ioff()
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plt.show()
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if __name__ == "__main__":
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Pose2SLAM_ISAM2_example()
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@ -0,0 +1,165 @@
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"""
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GTSAM Copyright 2010-2018, Georgia Tech Research Corporation,
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Atlanta, Georgia 30332-0415
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All Rights Reserved
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Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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See LICENSE for the license information
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Pose SLAM example using iSAM2 in 3D space.
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Author: Jerred Chen
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Modelled after version by:
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- VisualISAM2Example by: Duy-Nguyen Ta (C++), Frank Dellaert (Python)
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"""
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from __future__ import print_function
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import gtsam
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from gtsam import Pose3, Rot3
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from gtsam.symbol_shorthand import X
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import gtsam.utils.plot as gtsam_plot
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import numpy as np
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from numpy import cos, sin, pi
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from numpy.random import multivariate_normal as mult_gauss
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import matplotlib.pyplot as plt
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def Pose3SLAM_ISAM2_plot(graph, current_estimate):
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"""
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Plots incremental state of the robot for 3D Pose SLAM using iSAM2
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Author: Jerred Chen
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Based on version by:
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- Ellon Paiva (Python),
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- Duy Nguyen Ta and Frank Dellaert (MATLAB)
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"""
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marginals = gtsam.Marginals(graph, current_estimate)
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fig = plt.figure(0)
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axes = fig.gca(projection='3d')
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plt.cla()
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i = 0
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while current_estimate.exists(X(i)):
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gtsam_plot.plot_pose3(0, current_estimate.atPose3(X(i)), 10,
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marginals.marginalCovariance(X(i)))
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i += 1
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axes.set_xlim3d(-30, 45)
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axes.set_ylim3d(-30, 45)
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axes.set_zlim3d(-30, 45)
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plt.pause(1)
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return marginals
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def createPoses():
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"""
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Creates ground truth poses of the robot.
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"""
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P0 = np.array([[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]])
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P1 = np.array([[0, -1, 0, 15],
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[1, 0, 0, 15],
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[0, 0, 1, 20],
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[0, 0, 0, 1]])
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P2 = np.array([[cos(pi/4), 0, sin(pi/4), 30],
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[0, 1, 0, 30],
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[-sin(pi/4), 0, cos(pi/4), 30],
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[0, 0, 0, 1]])
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P3 = np.array([[0, 1, 0, 30],
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[0, 0, -1, 0],
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[-1, 0, 0, -15],
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[0, 0, 0, 1]])
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P4 = np.array([[-1, 0, 0, 0],
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[0, -1, 0, -10],
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[0, 0, 1, -10],
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[0, 0, 0, 1]])
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P5 = P0[:]
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return [Pose3(P0), Pose3(P1), Pose3(P2), Pose3(P3), Pose3(P4), Pose3(P5)]
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def Pose3_ISAM2_example():
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"""
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"""
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plt.ion()
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def vector6(x, y, z, a, b, c):
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"""Create 6d double numpy array."""
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return np.array([x, y, z, a, b, c], dtype=float)
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PRIOR_NOISE = gtsam.noiseModel.Diagonal.Sigmas(vector6(0.1, 0.1, 0.1, 0.3, 0.3, 0.3))
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ODOMETRY_NOISE = gtsam.noiseModel.Diagonal.Sigmas(vector6(0.1, 0.1, 0.1, 0.2, 0.2, 0.2))
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poses = createPoses()
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parameters = gtsam.ISAM2Params()
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parameters.setRelinearizeThreshold(0.1)
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parameters.setRelinearizeSkip(1)
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isam = gtsam.ISAM2(parameters)
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graph = gtsam.NonlinearFactorGraph()
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initial_estimate = gtsam.Values()
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# Add prior factor to the first pose
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graph.push_back(gtsam.PriorFactorPose3(X(0), poses[0], PRIOR_NOISE))
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initial_estimate.insert(X(0), poses[0].compose(gtsam.Pose3(
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gtsam.Rot3.Rodrigues(-0.1, 0.2, 0.25), gtsam.Point3(0.05, -0.10, 0.20))))
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def determine_loop_closure(odom, current_estimate, xyz_tol=0.6, rot_tol=0.3):
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"""
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Simple brute force approach which iterates through previous states
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and checks for loop closure.
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### Parameters:
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odom: (numpy.ndarray) 1x6 vector representing noisy odometry transformation
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measurement in the body frame, [roll, pitch, yaw, x, y, z]
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current_estimate: (gtsam.Values) The current estimates computed by iSAM2.
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xyz_tol: (double) Optional argument for the translational tolerance.
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rot_tol: (double) Optional argument for the rotational tolerance.
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### Returns:
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k: (int) The key of the state which is helping add the loop closure constraint.
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If loop closure is not found, then None is returned.
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"""
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if current_estimate:
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rot = Rot3.RzRyRx(odom[:3])
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odom_tf = Pose3(rot, odom[3:6].reshape(-1,1))
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prev_est = current_estimate.atPose3(X(i-1))
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curr_est = prev_est.transformPoseFrom(odom_tf)
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for k in range(i):
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pose = current_estimate.atPose3(X(k))
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if (abs(pose.matrix()[:3,:3] - curr_est.matrix()[:3,:3]) <= rot_tol).all() and \
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(abs(pose.matrix()[:3,3] - curr_est.matrix()[:3,3]) <= xyz_tol).all():
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return k
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current_estimate = None
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for i in range(1, len(poses)):
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# The odometry "ground truth" measurement between poses
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odom_tf = poses[i-1].transformPoseTo(poses[i])
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odom_xyz = odom_tf.x(), odom_tf.y(), odom_tf.z()
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odom_rpy = odom_tf.rotation().rpy()
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# Odometry measurement that is received by the robot and corrupted by gaussian noise
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measurement = mult_gauss(np.hstack((odom_rpy,odom_xyz)), ODOMETRY_NOISE.covariance())
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loop = determine_loop_closure(measurement, current_estimate)
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if loop is not None:
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graph.push_back(gtsam.BetweenFactorPose3(X(i-1), X(loop), gtsam.Pose3(odom_tf), ODOMETRY_NOISE))
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else:
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graph.push_back(gtsam.BetweenFactorPose3(X(i-1), X(i), gtsam.Pose3(odom_tf), ODOMETRY_NOISE))
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# Intentionally insert poor initializations
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initial_estimate.insert(X(i), poses[i].compose(gtsam.Pose3(
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gtsam.Rot3.Rodrigues(-0.1, 0.2, 0.25), gtsam.Point3(0.05, -0.10, 0.20))))
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isam.update(graph, initial_estimate)
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isam.update()
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current_estimate = isam.calculateEstimate()
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print("*"*50)
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print(f"Inference after State {i}:")
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print(current_estimate)
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marginals = Pose3SLAM_ISAM2_plot(graph, current_estimate)
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initial_estimate.clear()
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i = 0
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while current_estimate.exists(X(i)):
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print(f"X{i} covariance:\n{marginals.marginalCovariance(X(i))}\n")
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i += 1
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plt.ioff()
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plt.show()
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if __name__ == '__main__':
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Pose3_ISAM2_example()
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