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 SimpleRotation.cpp
14 * @brief This is a super-simple example of optimizing a single rotation according to a single prior
15 * @date Jul 1, 2010
16 * @author Frank Dellaert
17 * @author Alex Cunningham
18 */
19
20 /**
21 * This example will perform a relatively trivial optimization on
22 * a single variable with a single factor.
23 */
24
25// In this example, a 2D rotation will be used as the variable of interest
26#include <gtsam/geometry/Rot2.h>
27
28// Each variable in the system (poses) must be identified with a unique key.
29// We can either use simple integer keys (1, 2, 3, ...) or symbols (X1, X2, L1).
30// Here we will use symbols
31#include <gtsam/inference/Symbol.h>
32
33// In GTSAM, measurement functions are represented as 'factors'. Several common factors
34// have been provided with the library for solving robotics/SLAM/Bundle Adjustment problems.
35// We will apply a simple prior on the rotation. We do so via the `addPrior` convenience
36// method in NonlinearFactorGraph.
37
38// When the factors are created, we will add them to a Factor Graph. As the factors we are using
39// are nonlinear factors, we will need a Nonlinear Factor Graph.
40#include <gtsam/nonlinear/NonlinearFactorGraph.h>
41
42// The nonlinear solvers within GTSAM are iterative solvers, meaning they linearize the
43// nonlinear functions around an initial linearization point, then solve the linear system
44// to update the linearization point. This happens repeatedly until the solver converges
45// to a consistent set of variable values. This requires us to specify an initial guess
46// for each variable, held in a Values container.
47#include <gtsam/nonlinear/Values.h>
48
49// Finally, once all of the factors have been added to our factor graph, we will want to
50// solve/optimize to graph to find the best (Maximum A Posteriori) set of variable values.
51// GTSAM includes several nonlinear optimizers to perform this step. Here we will use the
52// standard Levenberg-Marquardt solver
53#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
54
55
56using namespace std;
57using namespace gtsam;
58
59const double degree = M_PI / 180;
60
61int main() {
62 /**
63 * Step 1: Create a factor to express a unary constraint
64 * The "prior" in this case is the measurement from a sensor,
65 * with a model of the noise on the measurement.
66 *
67 * The "Key" created here is a label used to associate parts of the
68 * state (stored in "RotValues") with particular factors. They require
69 * an index to allow for lookup, and should be unique.
70 *
71 * In general, creating a factor requires:
72 * - A key or set of keys labeling the variables that are acted upon
73 * - A measurement value
74 * - A measurement model with the correct dimensionality for the factor
75 */
76 Rot2 prior = Rot2::fromAngle(theta: 30 * degree);
77 prior.print(s: "goal angle");
78 auto model = noiseModel::Isotropic::Sigma(dim: 1, sigma: 1 * degree);
79 Symbol key('x', 1);
80
81 /**
82 * Step 2: Create a graph container and add the factor to it
83 * Before optimizing, all factors need to be added to a Graph container,
84 * which provides the necessary top-level functionality for defining a
85 * system of constraints.
86 *
87 * In this case, there is only one factor, but in a practical scenario,
88 * many more factors would be added.
89 */
90 NonlinearFactorGraph graph;
91 graph.addPrior(key, prior, model);
92 graph.print(str: "full graph");
93
94 /**
95 * Step 3: Create an initial estimate
96 * An initial estimate of the solution for the system is necessary to
97 * start optimization. This system state is the "RotValues" structure,
98 * which is similar in structure to a STL map, in that it maps
99 * keys (the label created in step 1) to specific values.
100 *
101 * The initial estimate provided to optimization will be used as
102 * a linearization point for optimization, so it is important that
103 * all of the variables in the graph have a corresponding value in
104 * this structure.
105 *
106 * The interface to all RotValues types is the same, it only depends
107 * on the type of key used to find the appropriate value map if there
108 * are multiple types of variables.
109 */
110 Values initial;
111 initial.insert(j: key, val: Rot2::fromAngle(theta: 20 * degree));
112 initial.print(str: "initial estimate");
113
114 /**
115 * Step 4: Optimize
116 * After formulating the problem with a graph of constraints
117 * and an initial estimate, executing optimization is as simple
118 * as calling a general optimization function with the graph and
119 * initial estimate. This will yield a new RotValues structure
120 * with the final state of the optimization.
121 */
122 Values result = LevenbergMarquardtOptimizer(graph, initial).optimize();
123 result.print(str: "final result");
124
125 return 0;
126}
127