014 gtsam/examples/LocalizationExample.cpp

一、include files

/**
 * A simple 2D pose slam example with "GPS" measurements
 *  - The robot moves forward 2 meter each iteration
 *  - The robot initially faces along the X axis (horizontal, to the right in 2D)
 *  - We have full odometry between pose
 *  - We have "GPS-like" measurements implemented with a custom factor
 */

// We will use Pose2 variables (x, y, theta) to represent the robot positions
#include 

// We will use simple integer Keys to refer to the robot poses.
#include 

// As in OdometryExample.cpp, we use a BetweenFactor to model odometry measurements.
#include 

// We add all facors to a Nonlinear Factor Graph, as our factors are nonlinear.
#include 

// 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 

// 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 

// Once the optimized values have been calculated, we can also calculate the marginal covariance
// of desired variables
#include 

using namespace std;
using namespace gtsam;

// Before we begin the example, we must create a custom unary factor to implement a
// "GPS-like" functionality. Because standard GPS measurements provide information
// only on the position, and not on the orientation, we cannot use a simple prior to
// properly model this measurement.
//
// The factor will be a unary factor, affect only a single system variable. It will
// also use a standard Gaussian noise model. Hence, we will derive our new factor from
// the NoiseModelFactor1.
#include 
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GTSAM中的非线性求解器是迭代求解器，这意味着它们在初始线性化点周围线性化非线性函数，然后求解线性系统以更新线性化点。这会重复发生，直到解算器收敛到一组一致的变量值。这要求我们为保存在Values容器中的每个变量指定一个初始猜测。
　 给定一个起始的初值很重要
　
　
最后，一旦所有因子都添加到我们的因子图中，我们将需要对图进行求解/优化，以找到最佳（最大后验）变量值集。
GTSAM包括几个非线性优化器来执行此步骤。这里我们将使用标准的Levenberg-Marquardt解算器

二、一元因子

class UnaryFactor: public NoiseModelFactor1<Pose2> {
  // The factor will hold a measurement consisting of an (X,Y) location
  // We could this with a Point2 but here we just use two doubles
  double mx_, my_;

 public:
  /// shorthand for a smart pointer to a factor
  typedef boost::shared_ptr<UnaryFactor> shared_ptr;

  // The constructor requires the variable key, the (X, Y) measurement value, and the noise model
  UnaryFactor(Key j, double x, double y, const SharedNoiseModel& model):
    NoiseModelFactor1<Pose2>(model, j), mx_(x), my_(y) {}

  ~UnaryFactor() override {}

  // Using the NoiseModelFactor1 base class there are two functions that must be overridden.
  // The first is the 'evaluateError' function. This function implements the desired measurement
  // function, returning a vector of errors when evaluated at the provided variable value. It
  // must also calculate the Jacobians for this measurement function, if requested.
  Vector evaluateError(const Pose2& q, boost::optional<Matrix&> H = boost::none) const override {
    // The measurement function for a GPS-like measurement h(q) which predicts the measurement (m) is h(q) = q, q = [qx qy qtheta]
    // The error is then simply calculated as E(q) = h(q) - m:
    // error_x = q.x - mx
    // error_y = q.y - my
    // Node's orientation reflects in the Jacobian, in tangent space this is equal to the right-hand rule rotation matrix
    // H =  [ cos(q.theta)  -sin(q.theta) 0 ]
    //      [ sin(q.theta)   cos(q.theta) 0 ]
    const Rot2& R = q.rotation();
    if (H) (*H) = (gtsam::Matrix(2, 3) << R.c(), -R.s(), 0.0, R.s(), R.c(), 0.0).finished();
    return (Vector(2) << q.x() - mx_, q.y() - my_).finished();
  }

  // The second is a 'clone' function that allows the factor to be copied. Under most
  // circumstances, the following code that employs the default copy constructor should
  // work fine.
  gtsam::NonlinearFactor::shared_ptr clone() const override {
    return boost::static_pointer_cast<gtsam::NonlinearFactor>(
        gtsam::NonlinearFactor::shared_ptr(new UnaryFactor(*this))); }

  // Additionally, we encourage you the use of unit testing your custom factors,
  // (as all GTSAM factors are), in which you would need an equals and print, to satisfy the
  // GTSAM_CONCEPT_TESTABLE_INST(T) defined in Testable.h, but these are not needed below.
};  // UnaryFactor
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雅克比：
[ c o s ( q θ ) − s i n ( q θ ) 0 s i n ( q θ ) c o s ( q θ ) 0 ]

[cos(qθ​)sin(qθ​)​−sin(qθ​)cos(qθ​)​00​]

三、main function

构建因子图

  // 1. Create a factor graph container and add factors to it
  NonlinearFactorGraph graph;
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添加里程计因子

  // 2a. Add odometry factors
  // For simplicity, we will use the same noise model for each odometry factor
  auto odometryNoise = noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
  // Create odometry (Between) factors between consecutive poses
  graph.emplace_shared<BetweenFactor<Pose2> >(1, 2, Pose2(2.0, 0.0, 0.0), odometryNoise);
  graph.emplace_shared<BetweenFactor<Pose2> >(2, 3, Pose2(2.0, 0.0, 0.0), odometryNoise);
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添加自定义因子

  // 2b. Add "GPS-like" measurements
  // We will use our custom UnaryFactor for this.
  auto unaryNoise =
      noiseModel::Diagonal::Sigmas(Vector2(0.1, 0.1));  // 10cm std on x,y
  graph.emplace_shared<UnaryFactor>(1, 0.0, 0.0, unaryNoise);
  graph.emplace_shared<UnaryFactor>(2, 2.0, 0.0, unaryNoise);
  graph.emplace_shared<UnaryFactor>(3, 4.0, 0.0, unaryNoise);
  graph.print("\nFactor Graph:\n");  // print
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创造Values进行初值的存储

  // 3. Create the data structure to hold the initialEstimate estimate to the solution
  // For illustrative purposes, these have been deliberately set to incorrect values
  Values initialEstimate;
  initialEstimate.insert(1, Pose2(0.5, 0.0, 0.2));
  initialEstimate.insert(2, Pose2(2.3, 0.1, -0.2));
  initialEstimate.insert(3, Pose2(4.1, 0.1, 0.1));
  initialEstimate.print("\nInitial Estimate:\n");  // print
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进行优化
使用Levenberg-Marquardt优化进行优化。优化器接受一组可选的配置参数，控制收敛标准、要使用的线性系统解算器类型以及优化过程中显示的信息量。这里我们将使用默认的参数集。有关整套参数，请参见文档。

  // 4. Optimize using Levenberg-Marquardt optimization. The optimizer
  // accepts an optional set of configuration parameters, controlling
  // things like convergence criteria, the type of linear system solver
  // to use, and the amount of information displayed during optimization.
  // Here we will use the default set of parameters.  See the
  // documentation for the full set of parameters.
  LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
  Values result = optimizer.optimize();
  result.print("Final Result:\n");
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获取边际概率

  // 5. Calculate and print marginal covariances for all variables
  Marginals marginals(graph, result);
  cout << "x1 covariance:\n" << marginals.marginalCovariance(1) << endl;
  cout << "x2 covariance:\n" << marginals.marginalCovariance(2) << endl;
  cout << "x3 covariance:\n" << marginals.marginalCovariance(3) << endl;
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