expression example of estimating trajectory, landmarks and sensor-body-transform simultaneously

examples/Pose3SLAMExampleExpressions_BearinRangeWithTransform.cpp

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+/**
+ * @file    Pose3SLAMExampleExpressions_BearinRangeWithTransform.cpp
+ * @brief   A simultanious optimization of trajectory, landmarks and sensor-pose with respect to body-pose using bearing-range measurements done with Expressions
+ * @author  Thomas Horstink
+ * @date    January 4th, 2019
+ */
+
+#include <gtsam/inference/Symbol.h>
+#include <gtsam/geometry/BearingRange.h>
+#include <gtsam/slam/expressions.h>
+#include <gtsam/nonlinear/ExpressionFactorGraph.h>
+#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
+#include <gtsam/nonlinear/Values.h>
+
+using namespace gtsam;
+
+typedef BearingRange<Pose3, Point3> BearingRange3D;
+
+// These functions are very similar to those in the SFM example, except that it you can give it a fixed delta in between poses.
+/* ************************************************************************* */
+std::vector<Point3> createPoints() {
+
+  // Create the set of ground-truth landmarks
+  std::vector<Point3> points;
+  points.push_back(Point3(10.0,10.0,10.0));
+  points.push_back(Point3(-10.0,10.0,10.0));
+  points.push_back(Point3(-10.0,-10.0,10.0));
+  points.push_back(Point3(10.0,-10.0,10.0));
+  points.push_back(Point3(10.0,10.0,-10.0));
+  points.push_back(Point3(-10.0,10.0,-10.0));
+  points.push_back(Point3(-10.0,-10.0,-10.0));
+  points.push_back(Point3(10.0,-10.0,-10.0));
+
+  return points;
+}
+
+/* ************************************************************************* */
+std::vector<Pose3> createPoses(Pose3 delta, int steps) {
+
+  // Create the set of ground-truth poses
+  std::vector<Pose3> poses;
+  Pose3 pose = Pose3();
+  int i = 0;
+  for(; i < steps; ++i) {
+    poses.push_back(pose);
+    pose = pose.compose(delta);
+  }
+  poses.push_back(pose);
+
+  return poses;
+}
+
+/* ************************************************************************* */
+int main(int argc, char* argv[]) {
+  // Move around so the whole state (including the sensor tf) is observable
+  Pose3 delta_pose1 = Pose3(Rot3().Yaw(2*M_PI/8).Pitch(M_PI/8), Point3(1, 0, 0));
+  Pose3 delta_pose2 = Pose3(Rot3().Pitch(-M_PI/8), Point3(1, 0, 0));
+  Pose3 delta_pose3 = Pose3(Rot3().Yaw(-2*M_PI/8), Point3(1, 0, 0));
+
+  int steps = 4;
+  auto poses = createPoses(delta_pose1, steps);
+  auto poses2 = createPoses(delta_pose2, steps);
+  auto poses3 = createPoses(delta_pose3, steps);
+
+  // concatenate poses to create trajectory
+  poses.insert( poses.end(), poses2.begin(), poses2.end() );
+  poses.insert( poses.end(), poses3.begin(), poses3.end() );  // std::vector of Pose3
+  auto points = createPoints();                               // std::vector of Point3 
+
+  // (ground-truth) sensor pose in body frame, further an unknown variable
+  Pose3 body_T_sensor_gt(Rot3::RzRyRx(-M_PI_2, 0.0, -M_PI_2), Point3(0.25, -0.10, 1.0));
+  // a graph
+  ExpressionFactorGraph graph;
+  // Specify uncertainty on first pose prior and also for between factor (simplicity reasons)
+  auto poseNoise = noiseModel::Diagonal::Sigmas((Vector(6)<<0.3,0.3,0.3,0.1,0.1,0.1).finished());
+  // Uncertainty bearing range measurement;
+  auto bearingRangeNoise = noiseModel::Diagonal::Sigmas((Vector(3)<<0.01,0.03,0.05).finished());
+  // Expressions for body-frame at key 0 and sensor-tf
+  Pose3_ x_('x', 0);
+  Pose3_ body_T_sensor_('T', 0);
+  // add a prior on the body-pose and sensor-tf.
+  graph.addExpressionFactor(x_, poses[0], poseNoise); 
+  // Simulated measurements from pose, adding them to the factor graph
+  for (size_t i = 0; i < poses.size(); ++i) {
+    auto world_T_sensor = poses[i].compose(body_T_sensor_gt);
+    for (size_t j = 0; j < points.size(); ++j) {
+      // Create the expression
+      auto prediction = Expression<BearingRange3D>( BearingRange3D::Measure, Pose3_('x',i)*body_T_sensor_, Point3_('l',j));
+      // Create a *perfect* measurement
+      auto measurement = BearingRange3D(world_T_sensor.bearing(points[j]), world_T_sensor.range(points[j]));
+      graph.addExpressionFactor(prediction, measurement, bearingRangeNoise);
+    }
+    // and add a between factor 
+    if (i > 0)
+    {
+      // And also we have a nice measurement for the between factor.
+      graph.addExpressionFactor(between(Pose3_('x', i-1),Pose3_('x', i)), poses[i-1].between(poses[i]), poseNoise); 
+    }
+  }
+
+  // Create perturbed initial
+  Values initial;
+  Pose3 delta(Rot3::Rodrigues(-0.1, 0.2, 0.25), Point3(0.05, -0.10, 0.20));
+  for (size_t i = 0; i < poses.size(); ++i)
+    initial.insert(Symbol('x', i), poses[i].compose(delta)); 
+  for (size_t j = 0; j < points.size(); ++j)
+    initial.insert<Point3>(Symbol('l', j), points[j] + Point3(-0.25, 0.20, 0.15));
+  
+  // initialize body_T_sensor wrongly (because we do not know!)
+  initial.insert<Pose3>(Symbol('T',0), Pose3()); 
+
+  std::cout << "initial error: " << graph.error(initial) << std::endl;
+  Values result = LevenbergMarquardtOptimizer(graph, initial).optimize();
+  std::cout << "final error: " << graph.error(result) << std::endl;
+
+  initial.at<Pose3>(Symbol('T',0)).print("\nInitial estimate body_T_sensor\n"); /* initial sensor_P_body estimate */
+  result.at<Pose3>(Symbol('T',0)).print("\nFinal estimate body_T_sensor\n");    /* optimized sensor_P_body estimate */
+  body_T_sensor_gt.print("\nGround truth body_T_sensor\n");                     /* sensor_P_body ground truth */
+
+  return 0;
+}
+/* ************************************************************************* */