125 lines
5.1 KiB
Python
125 lines
5.1 KiB
Python
"""
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GTSAM Copyright 2010, 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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A structure-from-motion problem on a simulated dataset
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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import gtsam
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from gtsam import symbol_shorthand
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L = symbol_shorthand.L
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X = symbol_shorthand.X
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from gtsam.examples import SFMdata
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from gtsam.utils import plot
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from gtsam import (Cal3_S2, DoglegOptimizer, GenericProjectionFactorCal3_S2,
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Marginals, NonlinearFactorGraph, PinholeCameraCal3_S2,
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PriorFactorPoint3, PriorFactorPose3, Values)
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def main():
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"""
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Camera observations of landmarks (i.e. pixel coordinates) will be stored as Point2 (x, y).
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Each variable in the system (poses and landmarks) must be identified with a unique key.
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We can either use simple integer keys (1, 2, 3, ...) or symbols (X1, X2, L1).
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Here we will use Symbols
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In GTSAM, measurement functions are represented as 'factors'. Several common factors
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have been provided with the library for solving robotics/SLAM/Bundle Adjustment problems.
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Here we will use Projection factors to model the camera's landmark observations.
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Also, we will initialize the robot at some location using a Prior factor.
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When the factors are created, we will add them to a Factor Graph. As the factors we are using
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are nonlinear factors, we will need a Nonlinear Factor Graph.
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Finally, once all of the factors have been added to our factor graph, we will want to
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solve/optimize to graph to find the best (Maximum A Posteriori) set of variable values.
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GTSAM includes several nonlinear optimizers to perform this step. Here we will use a
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trust-region method known as Powell's Dogleg
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The nonlinear solvers within GTSAM are iterative solvers, meaning they linearize the
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nonlinear functions around an initial linearization point, then solve the linear system
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to update the linearization point. This happens repeatedly until the solver converges
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to a consistent set of variable values. This requires us to specify an initial guess
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for each variable, held in a Values container.
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"""
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# Define the camera calibration parameters
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K = Cal3_S2(50.0, 50.0, 0.0, 50.0, 50.0)
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# Define the camera observation noise model
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measurement_noise = gtsam.noiseModel.Isotropic.Sigma(2, 1.0) # one pixel in u and v
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# Create the set of ground-truth landmarks
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points = SFMdata.createPoints()
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# Create the set of ground-truth poses
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poses = SFMdata.createPoses()
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# Create a factor graph
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graph = NonlinearFactorGraph()
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# Add a prior on pose x1. This indirectly specifies where the origin is.
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# 0.3 rad std on roll,pitch,yaw and 0.1m on x,y,z
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pose_noise = gtsam.noiseModel.Diagonal.Sigmas(np.array([0.3, 0.3, 0.3, 0.1, 0.1, 0.1]))
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factor = PriorFactorPose3(X(0), poses[0], pose_noise)
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graph.push_back(factor)
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# Simulated measurements from each camera pose, adding them to the factor graph
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for i, pose in enumerate(poses):
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camera = PinholeCameraCal3_S2(pose, K)
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for j, point in enumerate(points):
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measurement = camera.project(point)
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factor = GenericProjectionFactorCal3_S2(measurement, measurement_noise, X(i), L(j), K)
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graph.push_back(factor)
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# Because the structure-from-motion problem has a scale ambiguity, the problem is still under-constrained
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# Here we add a prior on the position of the first landmark. This fixes the scale by indicating the distance
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# between the first camera and the first landmark. All other landmark positions are interpreted using this scale.
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point_noise = gtsam.noiseModel.Isotropic.Sigma(3, 0.1)
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factor = PriorFactorPoint3(L(0), points[0], point_noise)
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graph.push_back(factor)
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graph.print("Factor Graph:\n")
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# Create the data structure to hold the initial estimate to the solution
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# Intentionally initialize the variables off from the ground truth
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initial_estimate = Values()
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rng = np.random.default_rng()
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for i, pose in enumerate(poses):
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transformed_pose = pose.retract(0.1 * rng.standard_normal(6).reshape(6, 1))
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initial_estimate.insert(X(i), transformed_pose)
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for j, point in enumerate(points):
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transformed_point = point + 0.1 * rng.standard_normal(3)
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initial_estimate.insert(L(j), transformed_point)
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initial_estimate.print("Initial Estimates:\n")
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# Optimize the graph and print results
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params = gtsam.DoglegParams()
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params.setVerbosity("TERMINATION")
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optimizer = DoglegOptimizer(graph, initial_estimate, params)
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print("Optimizing:")
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result = optimizer.optimize()
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result.print("Final results:\n")
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print("initial error = {}".format(graph.error(initial_estimate)))
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print("final error = {}".format(graph.error(result)))
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marginals = Marginals(graph, result)
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plot.plot_3d_points(1, result, marginals=marginals)
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plot.plot_trajectory(1, result, marginals=marginals, scale=8)
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plot.set_axes_equal(1)
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plt.show()
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if __name__ == "__main__":
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main()
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