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 Pose2SLAMExample.cpp
14 * @brief A 2D Pose SLAM example
15 * @date Oct 21, 2010
16 * @author Yong Dian Jian
17 */
18
19/**
20 * A simple 2D pose slam example
21 * - The robot moves in a 2 meter square
22 * - The robot moves 2 meters each step, turning 90 degrees after each step
23 * - The robot initially faces along the X axis (horizontal, to the right in 2D)
24 * - We have full odometry between pose
25 * - We have a loop closure constraint when the robot returns to the first position
26 */
27
28// In planar SLAM example we use Pose2 variables (x, y, theta) to represent the robot poses
29#include <gtsam/geometry/Pose2.h>
30
31// We will use simple integer Keys to refer to the robot poses.
32#include <gtsam/inference/Key.h>
33
34// In GTSAM, measurement functions are represented as 'factors'. Several common factors
35// have been provided with the library for solving robotics/SLAM/Bundle Adjustment problems.
36// Here we will use Between factors for the relative motion described by odometry measurements.
37// We will also use a Between Factor to encode the loop closure constraint
38// Also, we will initialize the robot at the origin using a Prior factor.
39#include <gtsam/slam/BetweenFactor.h>
40
41// When the factors are created, we will add them to a Factor Graph. As the factors we are using
42// are nonlinear factors, we will need a Nonlinear Factor Graph.
43#include <gtsam/nonlinear/NonlinearFactorGraph.h>
44
45// Finally, once all of the factors have been added to our factor graph, we will want to
46// solve/optimize to graph to find the best (Maximum A Posteriori) set of variable values.
47// GTSAM includes several nonlinear optimizers to perform this step. Here we will use the
48// a Gauss-Newton solver
49#include <gtsam/nonlinear/GaussNewtonOptimizer.h>
50
51// Once the optimized values have been calculated, we can also calculate the marginal covariance
52// of desired variables
53#include <gtsam/nonlinear/Marginals.h>
54
55// The nonlinear solvers within GTSAM are iterative solvers, meaning they linearize the
56// nonlinear functions around an initial linearization point, then solve the linear system
57// to update the linearization point. This happens repeatedly until the solver converges
58// to a consistent set of variable values. This requires us to specify an initial guess
59// for each variable, held in a Values container.
60#include <gtsam/nonlinear/Values.h>
61
62
63using namespace std;
64using namespace gtsam;
65
66int main(int argc, char** argv) {
67 // 1. Create a factor graph container and add factors to it
68 NonlinearFactorGraph graph;
69
70 // 2a. Add a prior on the first pose, setting it to the origin
71 // A prior factor consists of a mean and a noise model (covariance matrix)
72 auto priorNoise = noiseModel::Diagonal::Sigmas(sigmas: Vector3(0.3, 0.3, 0.1));
73 graph.addPrior(key: 1, prior: Pose2(0, 0, 0), model: priorNoise);
74
75 // For simplicity, we will use the same noise model for odometry and loop closures
76 auto model = noiseModel::Diagonal::Sigmas(sigmas: Vector3(0.2, 0.2, 0.1));
77
78 // 2b. Add odometry factors
79 // Create odometry (Between) factors between consecutive poses
80 graph.emplace_shared<BetweenFactor<Pose2> >(args: 1, args: 2, args: Pose2(2, 0, 0), args&: model);
81 graph.emplace_shared<BetweenFactor<Pose2> >(args: 2, args: 3, args: Pose2(2, 0, M_PI_2), args&: model);
82 graph.emplace_shared<BetweenFactor<Pose2> >(args: 3, args: 4, args: Pose2(2, 0, M_PI_2), args&: model);
83 graph.emplace_shared<BetweenFactor<Pose2> >(args: 4, args: 5, args: Pose2(2, 0, M_PI_2), args&: model);
84
85 // 2c. Add the loop closure constraint
86 // This factor encodes the fact that we have returned to the same pose. In real systems,
87 // these constraints may be identified in many ways, such as appearance-based techniques
88 // with camera images. We will use another Between Factor to enforce this constraint:
89 graph.emplace_shared<BetweenFactor<Pose2> >(args: 5, args: 2, args: Pose2(2, 0, M_PI_2), args&: model);
90 graph.print(str: "\nFactor Graph:\n"); // print
91
92 // 3. Create the data structure to hold the initialEstimate estimate to the solution
93 // For illustrative purposes, these have been deliberately set to incorrect values
94 Values initialEstimate;
95 initialEstimate.insert(j: 1, val: Pose2(0.5, 0.0, 0.2));
96 initialEstimate.insert(j: 2, val: Pose2(2.3, 0.1, -0.2));
97 initialEstimate.insert(j: 3, val: Pose2(4.1, 0.1, M_PI_2));
98 initialEstimate.insert(j: 4, val: Pose2(4.0, 2.0, M_PI));
99 initialEstimate.insert(j: 5, val: Pose2(2.1, 2.1, -M_PI_2));
100 initialEstimate.print(str: "\nInitial Estimate:\n"); // print
101
102 // 4. Optimize the initial values using a Gauss-Newton nonlinear optimizer
103 // The optimizer accepts an optional set of configuration parameters,
104 // controlling things like convergence criteria, the type of linear
105 // system solver to use, and the amount of information displayed during
106 // optimization. We will set a few parameters as a demonstration.
107 GaussNewtonParams parameters;
108 // Stop iterating once the change in error between steps is less than this value
109 parameters.relativeErrorTol = 1e-5;
110 // Do not perform more than N iteration steps
111 parameters.maxIterations = 100;
112 // Create the optimizer ...
113 GaussNewtonOptimizer optimizer(graph, initialEstimate, parameters);
114 // ... and optimize
115 Values result = optimizer.optimize();
116 result.print(str: "Final Result:\n");
117
118 // 5. Calculate and print marginal covariances for all variables
119 cout.precision(prec: 3);
120 Marginals marginals(graph, result);
121 cout << "x1 covariance:\n" << marginals.marginalCovariance(variable: 1) << endl;
122 cout << "x2 covariance:\n" << marginals.marginalCovariance(variable: 2) << endl;
123 cout << "x3 covariance:\n" << marginals.marginalCovariance(variable: 3) << endl;
124 cout << "x4 covariance:\n" << marginals.marginalCovariance(variable: 4) << endl;
125 cout << "x5 covariance:\n" << marginals.marginalCovariance(variable: 5) << endl;
126
127 return 0;
128}
129