frc971/vision/target_mapper.cc

#include "frc971/vision/target_mapper.h"

#include "absl/strings/str_format.h"

#include "frc971/control_loops/control_loop.h"
#include "frc971/vision/ceres/pose_graph_3d_error_term.h"
#include "frc971/vision/geometry.h"

DEFINE_uint64(max_num_iterations, 100,
              "Maximum number of iterations for the ceres solver");
DEFINE_double(distortion_noise_scalar, 1.0,
              "Scale the target pose distortion factor by this when computing "
              "the noise.");
DEFINE_int32(
    frozen_target_id, 1,
    "Freeze the pose of this target so the map can have one fixed point.");
DEFINE_int32(min_target_id, 1, "Minimum target id to solve for");
DEFINE_int32(max_target_id, 8, "Maximum target id to solve for");
DEFINE_bool(visualize_solver, false, "If true, visualize the solving process.");
// This does seem like a strict threshold for a constaint to be considered an
// outlier, but most inliers were very close together and this is what worked
// best for map solving.
DEFINE_double(outlier_std_devs, 1.0,
              "Number of standard deviations above average error needed for a "
              "constraint to be considered an outlier and get removed.");

namespace frc971::vision {
Eigen::Affine3d PoseUtils::Pose3dToAffine3d(
    const ceres::examples::Pose3d &pose3d) {
  Eigen::Affine3d H_world_pose =
      Eigen::Translation3d(pose3d.p(0), pose3d.p(1), pose3d.p(2)) * pose3d.q;
  return H_world_pose;
}

ceres::examples::Pose3d PoseUtils::Affine3dToPose3d(const Eigen::Affine3d &H) {
  return ceres::examples::Pose3d{.p = H.translation(),
                                 .q = Eigen::Quaterniond(H.rotation())};
}

ceres::examples::Pose3d PoseUtils::ComputeRelativePose(
    const ceres::examples::Pose3d &pose_1,
    const ceres::examples::Pose3d &pose_2) {
  Eigen::Affine3d H_world_1 = Pose3dToAffine3d(pose_1);
  Eigen::Affine3d H_world_2 = Pose3dToAffine3d(pose_2);

  // Get the location of 2 in the 1 frame
  Eigen::Affine3d H_1_2 = H_world_1.inverse() * H_world_2;
  return Affine3dToPose3d(H_1_2);
}

ceres::examples::Pose3d PoseUtils::ComputeOffsetPose(
    const ceres::examples::Pose3d &pose_1,
    const ceres::examples::Pose3d &pose_2_relative) {
  auto H_world_1 = Pose3dToAffine3d(pose_1);
  auto H_1_2 = Pose3dToAffine3d(pose_2_relative);
  auto H_world_2 = H_world_1 * H_1_2;

  return Affine3dToPose3d(H_world_2);
}

Eigen::Quaterniond PoseUtils::EulerAnglesToQuaternion(
    const Eigen::Vector3d &rpy) {
  Eigen::AngleAxisd roll_angle(rpy.x(), Eigen::Vector3d::UnitX());
  Eigen::AngleAxisd pitch_angle(rpy.y(), Eigen::Vector3d::UnitY());
  Eigen::AngleAxisd yaw_angle(rpy.z(), Eigen::Vector3d::UnitZ());

  return yaw_angle * pitch_angle * roll_angle;
}

Eigen::Vector3d PoseUtils::QuaternionToEulerAngles(
    const Eigen::Quaterniond &q) {
  return RotationMatrixToEulerAngles(q.toRotationMatrix());
}

Eigen::Vector3d PoseUtils::RotationMatrixToEulerAngles(
    const Eigen::Matrix3d &R) {
  double roll = aos::math::NormalizeAngle(std::atan2(R(2, 1), R(2, 2)));
  double pitch = aos::math::NormalizeAngle(-std::asin(R(2, 0)));
  double yaw = aos::math::NormalizeAngle(std::atan2(R(1, 0), R(0, 0)));

  return Eigen::Vector3d(roll, pitch, yaw);
}

flatbuffers::Offset<TargetPoseFbs> PoseUtils::TargetPoseToFbs(
    const TargetMapper::TargetPose &target_pose,
    flatbuffers::FlatBufferBuilder *fbb) {
  const auto position_offset =
      CreatePosition(*fbb, target_pose.pose.p(0), target_pose.pose.p(1),
                     target_pose.pose.p(2));
  const auto orientation_offset =
      CreateQuaternion(*fbb, target_pose.pose.q.w(), target_pose.pose.q.x(),
                       target_pose.pose.q.y(), target_pose.pose.q.z());
  return CreateTargetPoseFbs(*fbb, target_pose.id, position_offset,
                             orientation_offset);
}

TargetMapper::TargetPose PoseUtils::TargetPoseFromFbs(
    const TargetPoseFbs &target_pose_fbs) {
  return {.id = static_cast<TargetMapper::TargetId>(target_pose_fbs.id()),
          .pose = ceres::examples::Pose3d{
              Eigen::Vector3d(target_pose_fbs.position()->x(),
                              target_pose_fbs.position()->y(),
                              target_pose_fbs.position()->z()),
              Eigen::Quaterniond(target_pose_fbs.orientation()->w(),
                                 target_pose_fbs.orientation()->x(),
                                 target_pose_fbs.orientation()->y(),
                                 target_pose_fbs.orientation()->z())}};
}

ceres::examples::VectorOfConstraints DataAdapter::MatchTargetDetections(
    const std::vector<DataAdapter::TimestampedDetection>
        &timestamped_target_detections,
    aos::distributed_clock::duration max_dt) {
  CHECK_GE(timestamped_target_detections.size(), 2ul)
      << "Must have at least 2 detections";

  // Match consecutive detections
  ceres::examples::VectorOfConstraints target_constraints;
  for (auto detection = timestamped_target_detections.begin() + 1;
       detection < timestamped_target_detections.end(); detection++) {
    auto last_detection = detection - 1;

    // Skip two consecutive detections of the same target, because the solver
    // doesn't allow this
    if (detection->id == last_detection->id) {
      continue;
    }

    // Don't take into account constraints too far apart in time, because the
    // recording device could have moved too much
    if ((detection->time - last_detection->time) > max_dt) {
      continue;
    }

    auto confidence = ComputeConfidence(*last_detection, *detection);
    target_constraints.emplace_back(
        ComputeTargetConstraint(*last_detection, *detection, confidence));
  }

  return target_constraints;
}

TargetMapper::ConfidenceMatrix DataAdapter::ComputeConfidence(
    const TimestampedDetection &detection_start,
    const TimestampedDetection &detection_end) {
  constexpr size_t kX = 0;
  constexpr size_t kY = 1;
  constexpr size_t kZ = 2;
  constexpr size_t kOrientation1 = 3;
  constexpr size_t kOrientation2 = 4;
  constexpr size_t kOrientation3 = 5;

  // Uncertainty matrix between start and end
  TargetMapper::ConfidenceMatrix P = TargetMapper::ConfidenceMatrix::Zero();

  {
    // Noise for odometry-based robot position measurements
    TargetMapper::ConfidenceMatrix Q_odometry =
        TargetMapper::ConfidenceMatrix::Zero();
    Q_odometry(kX, kX) = std::pow(0.045, 2);
    Q_odometry(kY, kY) = std::pow(0.045, 2);
    Q_odometry(kZ, kZ) = std::pow(0.045, 2);
    Q_odometry(kOrientation1, kOrientation1) = std::pow(0.01, 2);
    Q_odometry(kOrientation2, kOrientation2) = std::pow(0.01, 2);
    Q_odometry(kOrientation3, kOrientation3) = std::pow(0.01, 2);

    // Add uncertainty for robot position measurements from start to end
    int iterations = (detection_end.time - detection_start.time) /
                     frc971::controls::kLoopFrequency;
    P += static_cast<double>(iterations) * Q_odometry;
  }

  {
    // Noise for vision-based target localizations. Multiplying this matrix by
    // the distance from camera to target squared results in the uncertainty
    // in that measurement
    TargetMapper::ConfidenceMatrix Q_vision =
        TargetMapper::ConfidenceMatrix::Zero();
    Q_vision(kX, kX) = std::pow(0.045, 2);
    Q_vision(kY, kY) = std::pow(0.045, 2);
    Q_vision(kZ, kZ) = std::pow(0.045, 2);
    Q_vision(kOrientation1, kOrientation1) = std::pow(0.02, 2);
    Q_vision(kOrientation2, kOrientation2) = std::pow(0.02, 2);
    Q_vision(kOrientation3, kOrientation3) = std::pow(0.02, 2);

    // Add uncertainty for the 2 vision measurements (1 at start and 1 at end)
    P += Q_vision * std::pow(detection_start.distance_from_camera *
                                 (1.0 + FLAGS_distortion_noise_scalar *
                                            detection_start.distortion_factor),
                             2);
    P += Q_vision * std::pow(detection_end.distance_from_camera *
                                 (1.0 + FLAGS_distortion_noise_scalar *
                                            detection_end.distortion_factor),
                             2);
  }

  return P.inverse();
}

ceres::examples::Constraint3d DataAdapter::ComputeTargetConstraint(
    const TimestampedDetection &target_detection_start,
    const TimestampedDetection &target_detection_end,
    const TargetMapper::ConfidenceMatrix &confidence) {
  // Compute the relative pose (constraint) between the two targets
  Eigen::Affine3d H_targetstart_targetend =
      target_detection_start.H_robot_target.inverse() *
      target_detection_end.H_robot_target;
  ceres::examples::Pose3d target_constraint =
      PoseUtils::Affine3dToPose3d(H_targetstart_targetend);

  const auto constraint_3d =
      ceres::examples::Constraint3d{target_detection_start.id,
                                    target_detection_end.id,
                                    {target_constraint.p, target_constraint.q},
                                    confidence};

  VLOG(2) << "Computed constraint: " << constraint_3d;
  return constraint_3d;
}

TargetMapper::TargetMapper(
    std::string_view target_poses_path,
    const ceres::examples::VectorOfConstraints &target_constraints)
    : target_constraints_(target_constraints),
      T_frozen_actual_(Eigen::Vector3d::Zero()),
      R_frozen_actual_(Eigen::Quaterniond::Identity()),
      vis_robot_(cv::Size(kImageWidth_, kImageHeight_)) {
  aos::FlatbufferDetachedBuffer<TargetMap> target_map =
      aos::JsonFileToFlatbuffer<TargetMap>(target_poses_path);
  for (const auto *target_pose_fbs : *target_map.message().target_poses()) {
    ideal_target_poses_[target_pose_fbs->id()] =
        PoseUtils::TargetPoseFromFbs(*target_pose_fbs).pose;
  }
  target_poses_ = ideal_target_poses_;
  CountConstraints();
}

TargetMapper::TargetMapper(
    const ceres::examples::MapOfPoses &target_poses,
    const ceres::examples::VectorOfConstraints &target_constraints)
    : ideal_target_poses_(target_poses),
      target_poses_(ideal_target_poses_),
      target_constraints_(target_constraints),
      T_frozen_actual_(Eigen::Vector3d::Zero()),
      R_frozen_actual_(Eigen::Quaterniond::Identity()),
      vis_robot_(cv::Size(kImageWidth_, kImageHeight_)) {
  CountConstraints();
}

namespace {
std::pair<TargetMapper::TargetId, TargetMapper::TargetId> MakeIdPair(
    const ceres::examples::Constraint3d &constraint) {
  auto min_id = std::min(constraint.id_begin, constraint.id_end);
  auto max_id = std::max(constraint.id_begin, constraint.id_end);
  return std::make_pair(min_id, max_id);
}
}  // namespace

void TargetMapper::CountConstraints() {
  for (const auto &constraint : target_constraints_) {
    auto id_pair = MakeIdPair(constraint);
    if (constraint_counts_.count(id_pair) == 0) {
      constraint_counts_[id_pair] = 0;
    }
    constraint_counts_[id_pair]++;
  }
}

std::optional<TargetMapper::TargetPose> TargetMapper::GetTargetPoseById(
    std::vector<TargetMapper::TargetPose> target_poses, TargetId target_id) {
  for (auto target_pose : target_poses) {
    if (target_pose.id == target_id) {
      return target_pose;
    }
  }

  return std::nullopt;
}

std::optional<TargetMapper::TargetPose> TargetMapper::GetTargetPoseById(
    TargetId target_id) const {
  if (target_poses_.count(target_id) > 0) {
    return TargetMapper::TargetPose{target_id, target_poses_.at(target_id)};
  }

  return std::nullopt;
}

// Taken from ceres/examples/slam/pose_graph_3d/pose_graph_3d.cc
// Constructs the nonlinear least squares optimization problem from the pose
// graph constraints.
void TargetMapper::BuildTargetPoseOptimizationProblem(
    const ceres::examples::VectorOfConstraints &constraints,
    ceres::examples::MapOfPoses *poses, ceres::Problem *problem) {
  CHECK(poses != nullptr);
  CHECK(problem != nullptr);
  if (constraints.empty()) {
    LOG(INFO) << "No constraints, no problem to optimize.";
    return;
  }

  ceres::LossFunction *loss_function = new ceres::HuberLoss(2.0);
  ceres::LocalParameterization *quaternion_local_parameterization =
      new ceres::EigenQuaternionParameterization;

  for (ceres::examples::VectorOfConstraints::const_iterator constraints_iter =
           constraints.begin();
       constraints_iter != constraints.end(); ++constraints_iter) {
    const ceres::examples::Constraint3d &constraint = *constraints_iter;

    ceres::examples::MapOfPoses::iterator pose_begin_iter =
        poses->find(constraint.id_begin);
    CHECK(pose_begin_iter != poses->end())
        << "Pose with ID: " << constraint.id_begin << " not found.";
    ceres::examples::MapOfPoses::iterator pose_end_iter =
        poses->find(constraint.id_end);
    CHECK(pose_end_iter != poses->end())
        << "Pose with ID: " << constraint.id_end << " not found.";

    const Eigen::Matrix<double, 6, 6> sqrt_information =
        constraint.information.llt().matrixL();

    auto id_pair = MakeIdPair(constraint);
    CHECK_GT(constraint_counts_.count(id_pair), 0ul)
        << "Should have counted constraints for " << id_pair.first << "->"
        << id_pair.second;

    // Normalize constraint cost by occurances
    size_t constraint_count = constraint_counts_[id_pair];
    // Scale all costs so the total cost comes out to more reasonable numbers
    constexpr double kGlobalWeight = 1000.0;
    double constraint_weight =
        kGlobalWeight / static_cast<double>(constraint_count);

    // Ceres will take ownership of the pointer.
    ceres::CostFunction *cost_function =
        ceres::examples::PoseGraph3dErrorTerm::Create(
            constraint.t_be, sqrt_information, constraint_weight);

    problem->AddResidualBlock(cost_function, loss_function,
                              pose_begin_iter->second.p.data(),
                              pose_begin_iter->second.q.coeffs().data(),
                              pose_end_iter->second.p.data(),
                              pose_end_iter->second.q.coeffs().data());

    problem->SetParameterization(pose_begin_iter->second.q.coeffs().data(),
                                 quaternion_local_parameterization);
    problem->SetParameterization(pose_end_iter->second.q.coeffs().data(),
                                 quaternion_local_parameterization);
  }

  // The pose graph optimization problem has six DOFs that are not fully
  // constrained. This is typically referred to as gauge freedom. You can
  // apply a rigid body transformation to all the nodes and the optimization
  // problem will still have the exact same cost. The Levenberg-Marquardt
  // algorithm has internal damping which mitigates this issue, but it is
  // better to properly constrain the gauge freedom. This can be done by
  // setting one of the poses as constant so the optimizer cannot change it.
  CHECK_NE(poses->count(FLAGS_frozen_target_id), 0ul)
      << "Got no poses for frozen target id " << FLAGS_frozen_target_id;
  ceres::examples::MapOfPoses::iterator pose_start_iter =
      poses->find(FLAGS_frozen_target_id);
  CHECK(pose_start_iter != poses->end()) << "There are no poses.";
  problem->SetParameterBlockConstant(pose_start_iter->second.p.data());
  problem->SetParameterBlockConstant(pose_start_iter->second.q.coeffs().data());
}

std::unique_ptr<ceres::CostFunction>
TargetMapper::BuildMapFittingOptimizationProblem(ceres::Problem *problem) {
  // Set up robot visualization.
  vis_robot_.ClearImage();
  // Compute focal length so that image shows field with viewpoint at 10m above
  // it (default for viewer)
  const double kFocalLength = kImageWidth_ * 10.0 / kFieldWidth_;
  vis_robot_.SetDefaultViewpoint(kImageWidth_, kFocalLength);

  const size_t num_targets = FLAGS_max_target_id - FLAGS_min_target_id;
  // Translation and rotation error for each target
  const size_t num_residuals = num_targets * 6;
  // Set up the only cost function (also known as residual). This uses
  // auto-differentiation to obtain the derivative (jacobian).
  std::unique_ptr<ceres::CostFunction> cost_function = std::make_unique<
      ceres::AutoDiffCostFunction<TargetMapper, ceres::DYNAMIC, 3, 4>>(
      this, num_residuals, ceres::DO_NOT_TAKE_OWNERSHIP);

  ceres::LossFunction *loss_function = new ceres::HuberLoss(2.0);
  ceres::LocalParameterization *quaternion_local_parameterization =
      new ceres::EigenQuaternionParameterization;

  problem->AddResidualBlock(cost_function.get(), loss_function,
                            T_frozen_actual_.vector().data(),
                            R_frozen_actual_.coeffs().data());
  problem->SetParameterization(R_frozen_actual_.coeffs().data(),
                               quaternion_local_parameterization);
  return cost_function;
}

// Taken from ceres/examples/slam/pose_graph_3d/pose_graph_3d.cc
bool TargetMapper::SolveOptimizationProblem(ceres::Problem *problem) {
  CHECK_NOTNULL(problem);

  ceres::Solver::Options options;
  options.max_num_iterations = FLAGS_max_num_iterations;
  options.linear_solver_type = ceres::SPARSE_NORMAL_CHOLESKY;
  options.minimizer_progress_to_stdout = false;

  ceres::Solver::Summary summary;
  ceres::Solve(options, problem, &summary);

  LOG(INFO) << summary.FullReport() << '\n';

  return summary.IsSolutionUsable();
}

void TargetMapper::Solve(std::string_view field_name,
                         std::optional<std::string_view> output_dir) {
  ceres::Problem target_pose_problem_1;
  BuildTargetPoseOptimizationProblem(target_constraints_, &target_poses_,
                                     &target_pose_problem_1);
  CHECK(SolveOptimizationProblem(&target_pose_problem_1))
      << "The target pose solve 1 was not successful, exiting.";

  RemoveOutlierConstraints();

  // Solve again once we've thrown out bad constraints
  ceres::Problem target_pose_problem_2;
  BuildTargetPoseOptimizationProblem(target_constraints_, &target_poses_,
                                     &target_pose_problem_2);
  CHECK(SolveOptimizationProblem(&target_pose_problem_2))
      << "The target pose solve 2 was not successful, exiting.";

  LOG(INFO) << "Solving the overall map's best alignment to the previous map";
  ceres::Problem map_fitting_problem(
      {.loss_function_ownership = ceres::DO_NOT_TAKE_OWNERSHIP});
  std::unique_ptr<ceres::CostFunction> map_fitting_cost_function =
      BuildMapFittingOptimizationProblem(&map_fitting_problem);
  CHECK(SolveOptimizationProblem(&map_fitting_problem))
      << "The map fitting solve was not successful, exiting.";
  map_fitting_cost_function.release();

  Eigen::Affine3d H_frozen_actual = T_frozen_actual_ * R_frozen_actual_;
  LOG(INFO) << "H_frozen_actual: "
            << PoseUtils::Affine3dToPose3d(H_frozen_actual);

  auto H_world_frozen =
      PoseUtils::Pose3dToAffine3d(target_poses_[FLAGS_frozen_target_id]);
  auto H_world_frozenactual = H_world_frozen * H_frozen_actual;

  // Offset the solved poses to become the actual ones
  for (auto &[id, pose] : target_poses_) {
    // Don't offset targets we didn't solve for
    if (id < FLAGS_min_target_id || id > FLAGS_max_target_id) {
      continue;
    }

    // Take the delta between the frozen target and the solved target, and put
    // that on top of the actual pose of the frozen target
    auto H_world_solved = PoseUtils::Pose3dToAffine3d(pose);
    auto H_frozen_solved = H_world_frozen.inverse() * H_world_solved;
    auto H_world_actual = H_world_frozenactual * H_frozen_solved;
    pose = PoseUtils::Affine3dToPose3d(H_world_actual);
  }

  auto map_json = MapToJson(field_name);
  VLOG(1) << "Solved target poses: " << map_json;

  if (output_dir.has_value()) {
    std::string output_path =
        absl::StrCat(output_dir.value(), "/", field_name, ".json");
    LOG(INFO) << "Writing map to file: " << output_path;
    aos::util::WriteStringToFileOrDie(output_path, map_json);
  }

  for (TargetId id_start = FLAGS_min_target_id; id_start < FLAGS_max_target_id;
       id_start++) {
    for (TargetId id_end = id_start + 1; id_end <= FLAGS_max_target_id;
         id_end++) {
      auto H_start_end =
          PoseUtils::Pose3dToAffine3d(target_poses_.at(id_start)).inverse() *
          PoseUtils::Pose3dToAffine3d(target_poses_.at(id_end));
      auto constraint = PoseUtils::Affine3dToPose3d(H_start_end);
      LOG(INFO) << id_start << "->" << id_end << ": " << constraint.p.norm()
                << " meters";
    }
  }
}

std::string TargetMapper::MapToJson(std::string_view field_name) const {
  flatbuffers::FlatBufferBuilder fbb;

  // Convert poses to flatbuffers
  std::vector<flatbuffers::Offset<TargetPoseFbs>> target_poses_fbs;
  for (const auto &[id, pose] : target_poses_) {
    target_poses_fbs.emplace_back(
        PoseUtils::TargetPoseToFbs(TargetPose{.id = id, .pose = pose}, &fbb));
  }

  const auto field_name_offset = fbb.CreateString(field_name);
  flatbuffers::Offset<TargetMap> target_map_offset = CreateTargetMap(
      fbb, fbb.CreateVector(target_poses_fbs), field_name_offset);

  return aos::FlatbufferToJson(
      flatbuffers::GetMutableTemporaryPointer(fbb, target_map_offset),
      {.multi_line = true});
}

namespace {
// Hacks to extract a double from a scalar, which is either a ceres jet or a
// double. Only used for debugging and displaying.
template <typename S>
double ScalarToDouble(S s) {
  const double *ptr = reinterpret_cast<double *>(&s);
  return *ptr;
}

template <typename S>
Eigen::Affine3d ScalarAffineToDouble(Eigen::Transform<S, 3, Eigen::Affine> H) {
  Eigen::Affine3d H_double;
  for (size_t i = 0; i < H.rows(); i++) {
    for (size_t j = 0; j < H.cols(); j++) {
      H_double(i, j) = ScalarToDouble(H(i, j));
    }
  }
  return H_double;
}

}  // namespace

template <typename S>
bool TargetMapper::operator()(const S *const translation,
                              const S *const rotation, S *residual) const {
  using Affine3s = Eigen::Transform<S, 3, Eigen::Affine>;
  Eigen::Quaternion<S> R_frozen_actual(rotation[3], rotation[1], rotation[2],
                                       rotation[0]);
  Eigen::Translation<S, 3> T_frozen_actual(translation[0], translation[1],
                                           translation[2]);
  // Actual target pose in the frame of the fixed pose.
  Affine3s H_frozen_actual = T_frozen_actual * R_frozen_actual;
  VLOG(2) << "H_frozen_actual: "
          << PoseUtils::Affine3dToPose3d(ScalarAffineToDouble(H_frozen_actual));

  Affine3s H_world_frozen =
      PoseUtils::Pose3dToAffine3d(target_poses_.at(FLAGS_frozen_target_id))
          .cast<S>();
  Affine3s H_world_frozenactual = H_world_frozen * H_frozen_actual;

  size_t residual_index = 0;
  if (FLAGS_visualize_solver) {
    vis_robot_.ClearImage();
  }

  for (const auto &[id, solved_pose] : target_poses_) {
    if (id < FLAGS_min_target_id || id > FLAGS_max_target_id) {
      continue;
    }

    Affine3s H_world_ideal =
        PoseUtils::Pose3dToAffine3d(ideal_target_poses_.at(id)).cast<S>();
    Affine3s H_world_solved =
        PoseUtils::Pose3dToAffine3d(solved_pose).cast<S>();
    // Take the delta between the frozen target and the solved target, and put
    // that on top of the actual pose of the frozen target
    auto H_frozen_solved = H_world_frozen.inverse() * H_world_solved;
    auto H_world_actual = H_world_frozenactual * H_frozen_solved;
    VLOG(2) << id << ": " << H_world_actual.translation();
    Affine3s H_ideal_actual = H_world_ideal.inverse() * H_world_actual;
    auto T_ideal_actual = H_ideal_actual.translation();
    VLOG(2) << "T_ideal_actual: " << T_ideal_actual;
    VLOG(2);
    auto R_ideal_actual = Eigen::AngleAxis<S>(H_ideal_actual.rotation());

    // Weight translation errors higher than rotation.
    // 1 m in position error = 0.01 radian (or ~0.573 degrees)
    constexpr double kTranslationScalar = 1000.0;
    constexpr double kRotationScalar = 100.0;

    // Penalize based on how much our actual poses matches the ideal
    // ones. We've already solved for the relative poses, now figure out
    // where all of them fit in the world.
    residual[residual_index++] = kTranslationScalar * T_ideal_actual(0);
    residual[residual_index++] = kTranslationScalar * T_ideal_actual(1);
    residual[residual_index++] = kTranslationScalar * T_ideal_actual(2);
    residual[residual_index++] =
        kRotationScalar * R_ideal_actual.angle() * R_ideal_actual.axis().x();
    residual[residual_index++] =
        kRotationScalar * R_ideal_actual.angle() * R_ideal_actual.axis().y();
    residual[residual_index++] =
        kRotationScalar * R_ideal_actual.angle() * R_ideal_actual.axis().z();

    if (FLAGS_visualize_solver) {
      LOG(INFO) << std::to_string(id) + std::string("-est") << " at "
                << ScalarAffineToDouble(H_world_actual).matrix();
      vis_robot_.DrawFrameAxes(ScalarAffineToDouble(H_world_actual),
                               std::to_string(id) + std::string("-est"),
                               cv::Scalar(0, 255, 0));
      vis_robot_.DrawFrameAxes(ScalarAffineToDouble(H_world_ideal),
                               std::to_string(id), cv::Scalar(255, 255, 255));
    }
  }
  if (FLAGS_visualize_solver) {
    cv::imshow("Target maps", vis_robot_.image_);
    cv::waitKey(0);
  }

  // Ceres can't handle residual values of exactly zero
  for (size_t i = 0; i < residual_index; i++) {
    if (residual[i] == S(0)) {
      residual[i] = S(1e-9);
    }
  }

  return true;
}

TargetMapper::PoseError TargetMapper::ComputeError(
    const ceres::examples::Constraint3d &constraint) const {
  // Compute the difference between the map-based transform of the end target
  // in the start target frame, to the one from this constraint
  auto H_start_end_map =
      PoseUtils::Pose3dToAffine3d(target_poses_.at(constraint.id_begin))
          .inverse() *
      PoseUtils::Pose3dToAffine3d(target_poses_.at(constraint.id_end));
  auto H_start_end_constraint = PoseUtils::Pose3dToAffine3d(constraint.t_be);
  ceres::examples::Pose3d delta_pose = PoseUtils::Affine3dToPose3d(
      H_start_end_map.inverse() * H_start_end_constraint);
  double distance = delta_pose.p.norm();
  Eigen::AngleAxisd err_angle(delta_pose.q);
  double angle = std::abs(err_angle.angle());
  return {.angle = angle, .distance = distance};
}

TargetMapper::Stats TargetMapper::ComputeStats() const {
  Stats stats{.avg_err = {.angle = 0.0, .distance = 0.0},
              .std_dev = {.angle = 0.0, .distance = 0.0},
              .max_err = {.angle = 0.0, .distance = 0.0}};

  for (const auto &constraint : target_constraints_) {
    PoseError err = ComputeError(constraint);

    // Update our statistics
    stats.avg_err.distance += err.distance;
    if (err.distance > stats.max_err.distance) {
      stats.max_err.distance = err.distance;
    }

    stats.avg_err.angle += err.angle;
    if (err.angle > stats.max_err.angle) {
      stats.max_err.angle = err.angle;
    }
  }

  stats.avg_err.distance /= static_cast<double>(target_constraints_.size());
  stats.avg_err.angle /= static_cast<double>(target_constraints_.size());

  for (const auto &constraint : target_constraints_) {
    PoseError err = ComputeError(constraint);

    // Update our statistics
    stats.std_dev.distance +=
        std::pow(err.distance - stats.avg_err.distance, 2);

    stats.std_dev.angle += std::pow(err.angle - stats.avg_err.angle, 2);
  }

  stats.std_dev.distance = std::sqrt(
      stats.std_dev.distance / static_cast<double>(target_constraints_.size()));
  stats.std_dev.angle = std::sqrt(
      stats.std_dev.angle / static_cast<double>(target_constraints_.size()));

  return stats;
}

void TargetMapper::RemoveOutlierConstraints() {
  stats_with_outliers_ = ComputeStats();
  size_t original_size = target_constraints_.size();
  target_constraints_.erase(
      std::remove_if(
          target_constraints_.begin(), target_constraints_.end(),
          [&](const auto &constraint) {
            PoseError err = ComputeError(constraint);
            // Remove constraints with errors significantly above
            // the average
            if (err.distance > stats_with_outliers_.avg_err.distance +
                                   FLAGS_outlier_std_devs *
                                       stats_with_outliers_.std_dev.distance) {
              return true;
            }
            if (err.angle > stats_with_outliers_.avg_err.angle +
                                FLAGS_outlier_std_devs *
                                    stats_with_outliers_.std_dev.angle) {
              return true;
            }
            return false;
          }),
      target_constraints_.end());

  LOG(INFO) << "Removed " << (original_size - target_constraints_.size())
            << " outlier constraints out of " << original_size << " total";
}

void TargetMapper::DumpStats(std::string_view path) const {
  LOG(INFO) << "Dumping mapping stats to " << path;
  Stats stats = ComputeStats();
  std::ofstream fout(path.data());
  fout << "Stats after outlier rejection: " << std::endl;
  fout << "Average error - angle: " << stats.avg_err.angle
       << ", distance: " << stats.avg_err.distance << std::endl
       << std::endl;
  fout << "Standard deviation - angle: " << stats.std_dev.angle
       << ", distance: " << stats.std_dev.distance << std::endl
       << std::endl;
  fout << "Max error - angle: " << stats.max_err.angle
       << ", distance: " << stats.max_err.distance << std::endl;

  fout << std::endl << "Stats before outlier rejection:" << std::endl;
  fout << "Average error - angle: " << stats_with_outliers_.avg_err.angle
       << ", distance: " << stats_with_outliers_.avg_err.distance << std::endl
       << std::endl;
  fout << "Standard deviation - angle: " << stats_with_outliers_.std_dev.angle
       << ", distance: " << stats_with_outliers_.std_dev.distance << std::endl
       << std::endl;
  fout << "Max error - angle: " << stats_with_outliers_.max_err.angle
       << ", distance: " << stats_with_outliers_.max_err.distance << std::endl;

  fout.flush();
  fout.close();
}

void TargetMapper::DumpConstraints(std::string_view path) const {
  LOG(INFO) << "Dumping target constraints to " << path;
  std::ofstream fout(path.data());
  for (const auto &constraint : target_constraints_) {
    fout << constraint << std::endl;
  }
  fout.flush();
  fout.close();
}

}  // namespace frc971::vision

std::ostream &operator<<(std::ostream &os, ceres::examples::Pose3d pose) {
  auto rpy = frc971::vision::PoseUtils::QuaternionToEulerAngles(pose.q);
  os << absl::StrFormat(
      "{x: %.3f, y: %.3f, z: %.3f, roll: %.3f, pitch: "
      "%.3f, yaw: %.3f}",
      pose.p(0), pose.p(1), pose.p(2), rpy(0), rpy(1), rpy(2));
  return os;
}

std::ostream &operator<<(std::ostream &os,
                         ceres::examples::Constraint3d constraint) {
  os << absl::StrFormat("{id_begin: %d, id_end: %d, pose: ",
                        constraint.id_begin, constraint.id_end)
     << constraint.t_be << "}";
  return os;
}