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/* ----------------------------------------------------------------------------
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
* Atlanta, Georgia 30332-0415
* All Rights Reserved
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
* See LICENSE for the license information
* -------------------------------------------------------------------------- */
/**
* @file SimpleRotation.cpp
* @brief This is a super-simple example of optimizing a single rotation according to a single prior
* @date Jul 1, 2010
* @author Frank Dellaert
* @author Alex Cunningham
*/
/**
* This example will perform a relatively trivial optimization on
* a single variable with a single factor.
*/
// In this example, a 2D rotation will be used as the variable of interest
#include <gtsam/geometry/Rot2.h>
// Each variable in the system (poses) must be identified with a unique key.
// We can either use simple integer keys (1, 2, 3, ...) or symbols (X1, X2, L1).
// Here we will use symbols
#include <gtsam/inference/Symbol.h>
// In GTSAM, measurement functions are represented as 'factors'. Several common factors
// have been provided with the library for solving robotics/SLAM/Bundle Adjustment problems.
// We will apply a simple prior on the rotation. We do so via the `addPrior` convenience
// method in NonlinearFactorGraph.
// When the factors are created, we will add them to a Factor Graph. As the factors we are using
// are nonlinear factors, we will need a Nonlinear Factor Graph.
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
// The nonlinear solvers within GTSAM are iterative solvers, meaning they linearize the
// nonlinear functions around an initial linearization point, then solve the linear system
// to update the linearization point. This happens repeatedly until the solver converges
// to a consistent set of variable values. This requires us to specify an initial guess
// for each variable, held in a Values container.
#include <gtsam/nonlinear/Values.h>
// Finally, once all of the factors have been added to our factor graph, we will want to
// solve/optimize to graph to find the best (Maximum A Posteriori) set of variable values.
// GTSAM includes several nonlinear optimizers to perform this step. Here we will use the
// standard Levenberg-Marquardt solver
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
using namespace std;
using namespace gtsam;
const double degree = M_PI / 180;
int main() {
/**
* Step 1: Create a factor to express a unary constraint
* The "prior" in this case is the measurement from a sensor,
* with a model of the noise on the measurement.
*
* The "Key" created here is a label used to associate parts of the
* state (stored in "RotValues") with particular factors. They require
* an index to allow for lookup, and should be unique.
*
* In general, creating a factor requires:
* - A key or set of keys labeling the variables that are acted upon
* - A measurement value
* - A measurement model with the correct dimensionality for the factor
*/
Rot2 prior = Rot2::fromAngle(30 * degree);
prior.print("goal angle");
auto model = noiseModel::Isotropic::Sigma(1, 1 * degree);
Symbol key('x', 1);
/**
* Step 2: Create a graph container and add the factor to it
* Before optimizing, all factors need to be added to a Graph container,
* which provides the necessary top-level functionality for defining a
* system of constraints.
*
* In this case, there is only one factor, but in a practical scenario,
* many more factors would be added.
*/
NonlinearFactorGraph graph;
graph.addPrior(key, prior, model);
graph.print("full graph");
/**
* Step 3: Create an initial estimate
* An initial estimate of the solution for the system is necessary to
* start optimization. This system state is the "RotValues" structure,
* which is similar in structure to a STL map, in that it maps
* keys (the label created in step 1) to specific values.
*
* The initial estimate provided to optimization will be used as
* a linearization point for optimization, so it is important that
* all of the variables in the graph have a corresponding value in
* this structure.
*
* The interface to all RotValues types is the same, it only depends
* on the type of key used to find the appropriate value map if there
* are multiple types of variables.
*/
Values initial;
initial.insert(key, Rot2::fromAngle(20 * degree));
initial.print("initial estimate");
/**
* Step 4: Optimize
* After formulating the problem with a graph of constraints
* and an initial estimate, executing optimization is as simple
* as calling a general optimization function with the graph and
* initial estimate. This will yield a new RotValues structure
* with the final state of the optimization.
*/
Values result = LevenbergMarquardtOptimizer(graph, initial).optimize();
result.print("final result");
return 0;
}
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