1/* ----------------------------------------------------------------------------
2
3 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
4 * Atlanta, Georgia 30332-0415
5 * All Rights Reserved
6 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
7
8 * See LICENSE for the license information
9
10 * -------------------------------------------------------------------------- */
11
12/**
13 * @file PlanarSLAMExample.cpp
14 * @brief Simple robotics example using odometry measurements and bearing-range (laser) measurements
15 * @author Alex Cunningham
16 */
17
18/**
19 * A simple 2D planar slam example with landmarks
20 * - The robot and landmarks are on a 2 meter grid
21 * - Robot poses are facing along the X axis (horizontal, to the right in 2D)
22 * - The robot moves 2 meters each step
23 * - We have full odometry between poses
24 * - We have bearing and range information for measurements
25 * - Landmarks are 2 meters away from the robot trajectory
26 */
27
28// As this is a planar SLAM example, we will use Pose2 variables (x, y, theta) to represent
29// the robot positions and Point2 variables (x, y) to represent the landmark coordinates.
30#include <gtsam/geometry/Pose2.h>
31#include <gtsam/geometry/Point2.h>
32
33// Each variable in the system (poses and landmarks) must be identified with a unique key.
34// We can either use simple integer keys (1, 2, 3, ...) or symbols (X1, X2, L1).
35// Here we will use Symbols
36#include <gtsam/inference/Symbol.h>
37
38// In GTSAM, measurement functions are represented as 'factors'. Several common factors
39// have been provided with the library for solving robotics/SLAM/Bundle Adjustment problems.
40// Here we will use a RangeBearing factor for the range-bearing measurements to identified
41// landmarks, and Between factors for the relative motion described by odometry measurements.
42// Also, we will initialize the robot at the origin using a Prior factor.
43#include <gtsam/slam/BetweenFactor.h>
44#include <gtsam/sam/BearingRangeFactor.h>
45
46// When the factors are created, we will add them to a Factor Graph. As the factors we are using
47// are nonlinear factors, we will need a Nonlinear Factor Graph.
48#include <gtsam/nonlinear/NonlinearFactorGraph.h>
49
50// Finally, once all of the factors have been added to our factor graph, we will want to
51// solve/optimize to graph to find the best (Maximum A Posteriori) set of variable values.
52// GTSAM includes several nonlinear optimizers to perform this step. Here we will use the
53// common Levenberg-Marquardt solver
54#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
55
56// Once the optimized values have been calculated, we can also calculate the marginal covariance
57// of desired variables
58#include <gtsam/nonlinear/Marginals.h>
59
60// The nonlinear solvers within GTSAM are iterative solvers, meaning they linearize the
61// nonlinear functions around an initial linearization point, then solve the linear system
62// to update the linearization point. This happens repeatedly until the solver converges
63// to a consistent set of variable values. This requires us to specify an initial guess
64// for each variable, held in a Values container.
65#include <gtsam/nonlinear/Values.h>
66
67
68using namespace std;
69using namespace gtsam;
70
71int main(int argc, char** argv) {
72 // Create a factor graph
73 NonlinearFactorGraph graph;
74
75 // Create the keys we need for this simple example
76 static Symbol x1('x', 1), x2('x', 2), x3('x', 3);
77 static Symbol l1('l', 1), l2('l', 2);
78
79 // Add a prior on pose x1 at the origin. A prior factor consists of a mean and
80 // a noise model (covariance matrix)
81 Pose2 prior(0.0, 0.0, 0.0); // prior mean is at origin
82 auto priorNoise = noiseModel::Diagonal::Sigmas(
83 sigmas: Vector3(0.3, 0.3, 0.1)); // 30cm std on x,y, 0.1 rad on theta
84 graph.addPrior(key: x1, prior, model: priorNoise); // add directly to graph
85
86 // Add two odometry factors
87 Pose2 odometry(2.0, 0.0, 0.0);
88 // create a measurement for both factors (the same in this case)
89 auto odometryNoise = noiseModel::Diagonal::Sigmas(
90 sigmas: Vector3(0.2, 0.2, 0.1)); // 20cm std on x,y, 0.1 rad on theta
91 graph.emplace_shared<BetweenFactor<Pose2> >(args&: x1, args&: x2, args&: odometry, args&: odometryNoise);
92 graph.emplace_shared<BetweenFactor<Pose2> >(args&: x2, args&: x3, args&: odometry, args&: odometryNoise);
93
94 // Add Range-Bearing measurements to two different landmarks
95 // create a noise model for the landmark measurements
96 auto measurementNoise = noiseModel::Diagonal::Sigmas(
97 sigmas: Vector2(0.1, 0.2)); // 0.1 rad std on bearing, 20cm on range
98 // create the measurement values - indices are (pose id, landmark id)
99 Rot2 bearing11 = Rot2::fromDegrees(theta: 45), bearing21 = Rot2::fromDegrees(theta: 90),
100 bearing32 = Rot2::fromDegrees(theta: 90);
101 double range11 = std::sqrt(x: 4.0 + 4.0), range21 = 2.0, range32 = 2.0;
102
103 // Add Bearing-Range factors
104 graph.emplace_shared<BearingRangeFactor<Pose2, Point2> >(args&: x1, args&: l1, args&: bearing11, args&: range11, args&: measurementNoise);
105 graph.emplace_shared<BearingRangeFactor<Pose2, Point2> >(args&: x2, args&: l1, args&: bearing21, args&: range21, args&: measurementNoise);
106 graph.emplace_shared<BearingRangeFactor<Pose2, Point2> >(args&: x3, args&: l2, args&: bearing32, args&: range32, args&: measurementNoise);
107
108 // Print
109 graph.print(str: "Factor Graph:\n");
110
111 // Create (deliberately inaccurate) initial estimate
112 Values initialEstimate;
113 initialEstimate.insert(j: x1, val: Pose2(0.5, 0.0, 0.2));
114 initialEstimate.insert(j: x2, val: Pose2(2.3, 0.1, -0.2));
115 initialEstimate.insert(j: x3, val: Pose2(4.1, 0.1, 0.1));
116 initialEstimate.insert(j: l1, val: Point2(1.8, 2.1));
117 initialEstimate.insert(j: l2, val: Point2(4.1, 1.8));
118
119 // Print
120 initialEstimate.print(str: "Initial Estimate:\n");
121
122 // Optimize using Levenberg-Marquardt optimization. The optimizer
123 // accepts an optional set of configuration parameters, controlling
124 // things like convergence criteria, the type of linear system solver
125 // to use, and the amount of information displayed during optimization.
126 // Here we will use the default set of parameters. See the
127 // documentation for the full set of parameters.
128 LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
129 Values result = optimizer.optimize();
130 result.print(str: "Final Result:\n");
131
132 // Calculate and print marginal covariances for all variables
133 Marginals marginals(graph, result);
134 print(A: marginals.marginalCovariance(variable: x1), s: "x1 covariance");
135 print(A: marginals.marginalCovariance(variable: x2), s: "x2 covariance");
136 print(A: marginals.marginalCovariance(variable: x3), s: "x3 covariance");
137 print(A: marginals.marginalCovariance(variable: l1), s: "l1 covariance");
138 print(A: marginals.marginalCovariance(variable: l2), s: "l2 covariance");
139
140 return 0;
141}
142