Merge pull request #1934 from truher/team100_frc_factors

projection and SFM for 2d poses

gtsam/geometry/Pose3.cpp

@@ -43,6 +43,20 @@ Pose3 Pose3::Create(const Rot3& R, const Point3& t, OptionalJacobian<6, 3> HR,
   return Pose3(R, t);
 }
 
+// Pose2 constructor Jacobian is always the same.
+static const Matrix63 Hpose2 = (Matrix63() << //
+    0., 0., 0., //
+    0., 0., 0.,//
+    0., 0., 1.,//
+    1., 0., 0.,//
+    0., 1., 0.,//
+    0., 0., 0.).finished();
+
+Pose3 Pose3::FromPose2(const Pose2& p, OptionalJacobian<6, 3> H) {
+  if (H) *H << Hpose2;
+  return Pose3(p);
+}
+
 /* ************************************************************************* */
 Pose3 Pose3::inverse() const {
   Rot3 Rt = R_.inverse();

gtsam/geometry/Pose3.h

@@ -78,6 +78,9 @@ public:
                       OptionalJacobian<6, 3> HR = {},
                       OptionalJacobian<6, 3> Ht = {});
 
+  /** Construct from Pose2 in the xy plane, with derivative. */
+  static Pose3 FromPose2(const Pose2& p, OptionalJacobian<6,3> H = {});
+
   /**
    *  Create Pose3 by aligning two point pairs
    *  A pose aTb is estimated between pairs (a_point, b_point) such that a_point = aTb * b_point

gtsam/slam/PlanarProjectionFactor.h

@@ -0,0 +1,298 @@
+/**
+ * ProjectionFactor, but with pose2 (robot on the floor)
+ *
+ * This factor is useful for high-school robotics competitions,
+ * which run robots on the floor, with use fixed maps and fiducial
+ * markers.
+ *
+ * @see https://www.firstinspires.org/
+ *
+ * @file PlanarProjectionFactor.h
+ * @brief for planar smoothing
+ * @date Dec 2, 2024
+ * @author joel@truher.org
+ */
+#pragma once
+
+#include <gtsam/base/Testable.h>
+#include <gtsam/base/Lie.h>
+
+#include <gtsam/geometry/Cal3DS2.h>
+#include <gtsam/geometry/PinholeCamera.h>
+#include <gtsam/geometry/Point3.h>
+#include <gtsam/geometry/Pose2.h>
+#include <gtsam/geometry/Pose3.h>
+#include <gtsam/geometry/Rot3.h>
+#include <gtsam/nonlinear/NonlinearFactor.h>
+#include <gtsam/base/numericalDerivative.h>
+
+
+namespace gtsam {
+
+    /**
+     * @class PlanarProjectionFactorBase
+     * @brief Camera projection for robot on the floor.  Measurement is camera pixels.
+     */
+    class PlanarProjectionFactorBase {
+    protected:
+        PlanarProjectionFactorBase() {}
+
+        /**
+         * @param measured pixels in the camera frame
+         */
+        PlanarProjectionFactorBase(const Point2& measured) : measured_(measured) {}
+
+        /**
+         * Predict the projection of the landmark in camera pixels.
+         *
+         * @param landmark point3 of the target
+         * @param wTb "world to body": planar pose2 of vehicle body frame in world frame
+         * @param bTc "body to camera": camera pose in body frame, oriented parallel to pose2 zero i.e. +x
+         * @param calib camera calibration with distortion
+         * @param Hlandmark jacobian
+         * @param HwTb jacobian
+         * @param HbTc jacobian
+         * @param Hcalib jacobian
+         */
+        Point2 predict(
+            const Point3& landmark,
+            const Pose2& wTb,
+            const Pose3& bTc,
+            const Cal3DS2& calib,
+            OptionalJacobian<2, 3> Hlandmark = {}, // (x, y, z)
+            OptionalJacobian<2, 3> HwTb = {}, // (x, y, theta)
+            OptionalJacobian<2, 6> HbTc = {}, // (rx, ry, rz, x, y, theta)
+            OptionalJacobian<2, 9> Hcalib = {}
+        ) const {
+#ifndef GTSAM_THROW_CHEIRALITY_EXCEPTION
+            try {
+#endif
+                Matrix63 Hp; // 6x3
+                Matrix66 H0; // 6x6
+                Pose3 wTc = Pose3::FromPose2(wTb, HwTb ? &Hp : nullptr).compose(bTc, HwTb ? &H0 : nullptr);
+                PinholeCamera<Cal3DS2> camera = PinholeCamera<Cal3DS2>(wTc, calib);
+                if (HwTb || HbTc) {
+                    // Dpose is for pose3 (R,t)
+                    Matrix26 Dpose;
+                    Point2 result = camera.project(landmark, Dpose, Hlandmark, Hcalib);
+                    if (HbTc)
+                        *HbTc = Dpose;
+                    if (HwTb)
+                        *HwTb = Dpose * H0 * Hp;
+                    return result;
+                } else {
+                    return camera.project(landmark, {}, {}, {});
+                }
+#ifndef GTSAM_THROW_CHEIRALITY_EXCEPTION
+            } catch (CheiralityException& e) {
+                std::cout << "****** CHIRALITY EXCEPTION ******\n";
+                if (Hlandmark) Hlandmark->setZero();
+                if (HwTb) HwTb->setZero();
+                if (HbTc) HbTc->setZero();
+                if (Hcalib) Hcalib->setZero();
+                // return a large error
+                return Matrix::Constant(2, 1, 2.0 * calib.fx());
+            }
+#endif
+        }
+
+        Point2 measured_; // pixel measurement
+    };
+
+
+    /**
+     * @class PlanarProjectionFactor1
+     * @brief One variable: the pose.
+     * Landmark, camera offset, camera calibration are constant.
+     * This is intended for localization within a known map.
+     */
+    class PlanarProjectionFactor1
+        : public PlanarProjectionFactorBase, public NoiseModelFactorN<Pose2> {
+    public:
+        typedef NoiseModelFactorN<Pose2> Base;
+        using Base::evaluateError;
+        PlanarProjectionFactor1() {}
+
+        ~PlanarProjectionFactor1() override {}
+
+        /// @return a deep copy of this factor
+        NonlinearFactor::shared_ptr clone() const override {
+            return std::static_pointer_cast<NonlinearFactor>(
+                NonlinearFactor::shared_ptr(new PlanarProjectionFactor1(*this)));
+        }
+
+
+        /**
+         * @brief constructor for known landmark, offset, and calibration
+         * @param poseKey index of the robot pose2 in the z=0 plane
+         * @param landmark point3 in the world
+         * @param measured corresponding point2 in the camera frame
+         * @param bTc "body to camera": constant camera offset from pose
+         * @param calib constant camera calibration
+         * @param model stddev of the measurements, ~one pixel?
+         */
+        PlanarProjectionFactor1(
+            Key poseKey,
+            const Point3& landmark,
+            const Point2& measured,
+            const Pose3& bTc,
+            const Cal3DS2& calib,
+            const SharedNoiseModel& model = {})
+            : PlanarProjectionFactorBase(measured),
+            NoiseModelFactorN(model, poseKey),
+            landmark_(landmark),
+            bTc_(bTc),
+            calib_(calib) {}
+
+        /**
+         * @param wTb "world to body": estimated pose2
+         * @param HwTb jacobian
+         */
+        Vector evaluateError(const Pose2& wTb, OptionalMatrixType HwTb) const override {
+            return predict(landmark_, wTb, bTc_, calib_, {}, HwTb, {}, {}) - measured_;
+        }
+
+    private:
+        Point3 landmark_; // landmark
+        Pose3 bTc_; // "body to camera": camera offset to robot pose
+        Cal3DS2 calib_; // camera calibration
+    };
+
+    template<>
+    struct traits<PlanarProjectionFactor1> :
+        public Testable<PlanarProjectionFactor1> {};
+
+    /**
+     * @class PlanarProjectionFactor2
+     * @brief Two unknowns: the pose and the landmark.
+     * Camera offset and calibration are constant.
+     * This is similar to GeneralSFMFactor, used for SLAM.
+    */
+    class PlanarProjectionFactor2
+        : public PlanarProjectionFactorBase, public NoiseModelFactorN<Pose2, Point3> {
+    public:
+        typedef NoiseModelFactorN<Pose2, Point3> Base;
+        using Base::evaluateError;
+
+        PlanarProjectionFactor2() {}
+
+        ~PlanarProjectionFactor2() override {}
+
+        /// @return a deep copy of this factor
+        NonlinearFactor::shared_ptr clone() const override {
+            return std::static_pointer_cast<NonlinearFactor>(
+                NonlinearFactor::shared_ptr(new PlanarProjectionFactor2(*this)));
+        }
+
+        /**
+         * @brief constructor for variable landmark, known offset and calibration
+         * @param poseKey index of the robot pose2 in the z=0 plane
+         * @param landmarkKey index of the landmark point3
+         * @param measured corresponding point in the camera frame
+         * @param bTc "body to camera": constant camera offset from pose
+         * @param calib constant camera calibration
+         * @param model stddev of the measurements, ~one pixel?
+         */
+        PlanarProjectionFactor2(
+            Key poseKey,
+            Key landmarkKey,
+            const Point2& measured,
+            const Pose3& bTc,
+            const Cal3DS2& calib,
+            const SharedNoiseModel& model = {})
+            : PlanarProjectionFactorBase(measured),
+            NoiseModelFactorN(model, landmarkKey, poseKey),
+            bTc_(bTc),
+            calib_(calib) {}
+
+        /**
+         * @param wTb "world to body": estimated pose2
+         * @param landmark estimated landmark
+         * @param HwTb jacobian
+         * @param Hlandmark jacobian
+         */
+        Vector evaluateError(
+            const Pose2& wTb,
+            const Point3& landmark,
+            OptionalMatrixType HwTb,
+            OptionalMatrixType Hlandmark) const override {
+            return predict(landmark, wTb, bTc_, calib_, Hlandmark, HwTb, {}, {}) - measured_;
+        }
+
+    private:
+        Pose3 bTc_; // "body to camera": camera offset to robot pose
+        Cal3DS2 calib_; // camera calibration
+    };
+
+    template<>
+    struct traits<PlanarProjectionFactor2> :
+        public Testable<PlanarProjectionFactor2> {};
+
+    /**
+     * @class PlanarProjectionFactor3
+     * @brief Three unknowns: the pose, the camera offset, and the camera calibration.
+     * Landmark is constant.
+     * This is intended to be used for camera calibration.
+    */
+    class PlanarProjectionFactor3 : public PlanarProjectionFactorBase, public NoiseModelFactorN<Pose2, Pose3, Cal3DS2> {
+    public:
+        typedef NoiseModelFactorN<Pose2, Pose3, Cal3DS2> Base;
+        using Base::evaluateError;
+
+        PlanarProjectionFactor3() {}
+
+        ~PlanarProjectionFactor3() override {}
+
+        /// @return a deep copy of this factor
+        NonlinearFactor::shared_ptr clone() const override {
+            return std::static_pointer_cast<NonlinearFactor>(
+                NonlinearFactor::shared_ptr(new PlanarProjectionFactor3(*this)));
+        }
+
+        /**
+         * @brief constructor for variable pose, offset, and calibration, known landmark.
+         * @param poseKey index of the robot pose2 in the z=0 plane
+         * @param offsetKey index of camera offset from pose
+         * @param calibKey index of camera calibration
+         * @param landmark point3 in the world
+         * @param measured corresponding point2 in the camera frame
+         * @param model stddev of the measurements, ~one pixel?
+         */
+        PlanarProjectionFactor3(
+            Key poseKey,
+            Key offsetKey,
+            Key calibKey,
+            const Point3& landmark,
+            const Point2& measured,
+            const SharedNoiseModel& model = {})
+            : PlanarProjectionFactorBase(measured),
+            NoiseModelFactorN(model, poseKey, offsetKey, calibKey),
+            landmark_(landmark) {}
+
+        /**
+         * @param wTb "world to body": estimated pose2
+         * @param bTc "body to camera": pose3 offset from pose2 +x
+         * @param calib calibration
+         * @param HwTb pose jacobian
+         * @param HbTc offset jacobian
+         * @param Hcalib calibration jacobian
+         */
+        Vector evaluateError(
+            const Pose2& wTb,
+            const Pose3& bTc,
+            const Cal3DS2& calib,
+            OptionalMatrixType HwTb,
+            OptionalMatrixType HbTc,
+            OptionalMatrixType Hcalib) const override {
+            return predict(landmark_, wTb, bTc, calib, {}, HwTb, HbTc, Hcalib) - measured_;
+        }
+
+    private:
+        Point3 landmark_; // landmark
+    };
+
+    template<>
+    struct traits<PlanarProjectionFactor3> :
+        public Testable<PlanarProjectionFactor3> {};
+
+} // namespace gtsam

gtsam/slam/slam.i

@@ -24,6 +24,38 @@ virtual class BetweenFactor : gtsam::NoiseModelFactor {
   void serialize() const;
 };
 
+#include <gtsam/slam/PlanarProjectionFactor.h>
+virtual class PlanarProjectionFactor1 : gtsam::NoiseModelFactor {
+  PlanarProjectionFactor1(
+    size_t poseKey,
+    const gtsam::Point3& landmark,
+    const gtsam::Point2& measured,
+    const gtsam::Pose3& bTc,
+    const gtsam::Cal3DS2& calib,
+    const gtsam::noiseModel::Base* model);
+  void serialize() const;
+};
+virtual class PlanarProjectionFactor2 : gtsam::NoiseModelFactor {
+  PlanarProjectionFactor2(
+    size_t poseKey,
+    size_t landmarkKey,
+    const gtsam::Point2& measured,
+    const gtsam::Pose3& bTc,
+    const gtsam::Cal3DS2& calib,
+    const gtsam::noiseModel::Base* model);
+  void serialize() const;
+};
+virtual class PlanarProjectionFactor3 : gtsam::NoiseModelFactor {
+  PlanarProjectionFactor3(
+    size_t poseKey,
+    size_t offsetKey,
+    size_t calibKey,
+    const gtsam::Point3& landmark,
+    const gtsam::Point2& measured,
+    const gtsam::noiseModel::Base* model);
+  void serialize() const;
+};
+
 #include <gtsam/slam/ProjectionFactor.h>
 template <POSE, LANDMARK, CALIBRATION>
 virtual class GenericProjectionFactor : gtsam::NoiseModelFactor {

gtsam/slam/tests/testPlanarProjectionFactor.cpp

@@ -0,0 +1,437 @@
+/**
+ * @file testPlanarProjectionFactor.cpp
+ * @date Dec 3, 2024
+ * @author joel@truher.org
+ * @brief unit tests for PlanarProjectionFactor
+ */
+
+#include <random>
+
+#include <gtsam/base/Testable.h>
+#include <gtsam/base/numericalDerivative.h>
+#include <gtsam/geometry/Cal3DS2.h>
+#include <gtsam/geometry/Point3.h>
+#include <gtsam/geometry/Pose2.h>
+#include <gtsam/geometry/Pose3.h>
+#include <gtsam/geometry/Rot2.h>
+#include <gtsam/geometry/Rot3.h>
+#include <gtsam/inference/Symbol.h>
+#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
+#include <gtsam/nonlinear/Marginals.h>
+#include <gtsam/nonlinear/NonlinearFactorGraph.h>
+#include <gtsam/nonlinear/PriorFactor.h>
+#include <gtsam/nonlinear/Values.h>
+#include <gtsam/slam/PlanarProjectionFactor.h>
+
+#include <CppUnitLite/TestHarness.h>
+
+using namespace std;
+using namespace gtsam;
+using symbol_shorthand::X;
+using symbol_shorthand::C;
+using symbol_shorthand::K;
+using symbol_shorthand::L;
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor1, Error1) {
+    // Example: center projection and Jacobian
+    Point3 landmark(1, 0, 0);
+    Point2 measured(200, 200);
+    Pose3 offset(
+        Rot3(0, 0, 1,//
+            -1, 0, 0, //
+            0, -1, 0),
+        Vector3(0, 0, 0)
+    );
+    Cal3DS2 calib(200, 200, 0, 200, 200, 0, 0);
+    SharedNoiseModel model = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    PlanarProjectionFactor1 factor(X(0), landmark, measured, offset, calib, model);
+    Pose2 pose(0, 0, 0);
+    Matrix H;
+    CHECK(assert_equal(Vector2(0, 0), factor.evaluateError(pose, H), 1e-6));
+    CHECK(assert_equal((Matrix23() << //
+        0, 200, 200, //
+        0, 0, 0).finished(), H, 1e-6));
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor1, Error2) {
+    // Example: upper left corner projection and Jacobian
+    Point3 landmark(1, 1, 1);
+    Point2 measured(0, 0);
+    Pose3 offset(
+        Rot3(0, 0, 1,//
+            -1, 0, 0, //
+            0, -1, 0),
+        Vector3(0, 0, 0)
+    );
+    Cal3DS2 calib(200, 200, 0, 200, 200, 0, 0);
+    SharedNoiseModel model = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    PlanarProjectionFactor1 factor(X(0), landmark, measured, offset, calib, model);
+    Pose2 pose(0, 0, 0);
+    Matrix H;
+    CHECK(assert_equal(Vector2(0, 0), factor.evaluateError(pose, H), 1e-6));
+    CHECK(assert_equal((Matrix23() << //
+        -200, 200, 400, //
+        -200, 0, 200).finished(), H, 1e-6));
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor1, Error3) {
+    // Example: upper left corner projection and Jacobian with distortion
+    Point3 landmark(1, 1, 1);
+    Point2 measured(0, 0);
+    Pose3 offset(
+        Rot3(0, 0, 1,//
+            -1, 0, 0, //
+            0, -1, 0),
+        Vector3(0, 0, 0)
+    );
+    Cal3DS2 calib(200, 200, 0, 200, 200, -0.2, 0.1); // note distortion
+    SharedNoiseModel model = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    PlanarProjectionFactor1 factor(X(0), landmark, measured, offset, calib, model);
+    Pose2 pose(0, 0, 0);
+    Matrix H;
+    CHECK(assert_equal(Vector2(0, 0), factor.evaluateError(pose, H), 1e-6));
+    CHECK(assert_equal((Matrix23() << //
+        -360, 280, 640, //
+        -360, 80, 440).finished(), H, 1e-6));
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor1, Jacobian) {
+    // Verify Jacobians with numeric derivative
+    std::default_random_engine rng(42);
+    std::uniform_real_distribution<double> dist(-0.3, 0.3);
+    SharedNoiseModel model = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    // center of the random camera poses
+    Pose3 centerOffset(
+        Rot3(0, 0, 1,//
+            -1, 0, 0, //
+            0, -1, 0),
+        Vector3(0, 0, 0)
+    );
+
+    for (int i = 0; i < 1000; ++i) {
+        Point3 landmark(2 + dist(rng), dist(rng), dist(rng));
+        Point2 measured(200 + 100 * dist(rng), 200 + 100 * dist(rng));
+        Pose3 offset = centerOffset.compose(
+            Pose3(
+                Rot3::Ypr(dist(rng), dist(rng), dist(rng)),
+                Point3(dist(rng), dist(rng), dist(rng))));
+        Cal3DS2 calib(200, 200, 0, 200, 200, -0.2, 0.1);
+        PlanarProjectionFactor1 factor(X(0), landmark, measured, offset, calib, model);
+        Pose2 pose(dist(rng), dist(rng), dist(rng));
+        Matrix H1;
+        factor.evaluateError(pose, H1);
+        auto expectedH1 = numericalDerivative11<Vector, Pose2>(
+            [&factor](const Pose2& p) {
+                return factor.evaluateError(p, {});},
+                pose);
+        CHECK(assert_equal(expectedH1, H1, 5e-6));
+    }
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor1, Solve) {
+    // Example localization
+
+    SharedNoiseModel pxModel = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    // pose model is wide, so the solver finds the right answer.
+    SharedNoiseModel xNoise = noiseModel::Diagonal::Sigmas(Vector3(10, 10, 10));
+
+    // landmarks
+    Point3 l0(1, 0.1, 1);
+    Point3 l1(1, -0.1, 1);
+
+    // camera pixels
+    Point2 p0(180, 0);
+    Point2 p1(220, 0);
+
+    // body
+    Pose2 x0(0, 0, 0);
+
+    // camera z looking at +x with (xy) antiparallel to (yz)
+    Pose3 c0(
+        Rot3(0, 0, 1, //
+            -1, 0, 0, //
+            0, -1, 0), //
+        Vector3(0, 0, 0));
+    Cal3DS2 calib(200, 200, 0, 200, 200, 0, 0);
+
+    NonlinearFactorGraph graph;
+    graph.add(PlanarProjectionFactor1(X(0), l0, p0, c0, calib, pxModel));
+    graph.add(PlanarProjectionFactor1(X(0), l1, p1, c0, calib, pxModel));
+    graph.add(PriorFactor<Pose2>(X(0), x0, xNoise));
+
+    Values initialEstimate;
+    initialEstimate.insert(X(0), x0);
+
+    // run the optimizer
+    LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
+    Values result = optimizer.optimize();
+
+    // verify that the optimizer found the right pose.
+    CHECK(assert_equal(x0, result.at<Pose2>(X(0)), 2e-3));
+
+    // covariance
+    Marginals marginals(graph, result);
+    Matrix cov = marginals.marginalCovariance(X(0));
+    CHECK(assert_equal((Matrix33() << //
+        0.000012, 0.000000, 0.000000, //
+        0.000000, 0.001287, -.001262, //
+        0.000000, -.001262, 0.001250).finished(), cov, 3e-6));
+
+    // pose stddev
+    Vector3 sigma = cov.diagonal().cwiseSqrt();
+    CHECK(assert_equal((Vector3() << //
+        0.0035,
+        0.0359,
+        0.0354
+        ).finished(), sigma, 1e-4));
+
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor3, Error1) {
+    // Example: center projection and Jacobian
+    Point3 landmark(1, 0, 0);
+    Point2 measured(200, 200);
+    SharedNoiseModel model = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    PlanarProjectionFactor3 factor(X(0), C(0), K(0), landmark, measured, model);
+    Pose2 pose(0, 0, 0);
+    Pose3 offset(
+        Rot3(0, 0, 1,//
+            -1, 0, 0, //
+            0, -1, 0),
+        Vector3(0, 0, 0)
+    );
+    Cal3DS2 calib(200, 200, 0, 200, 200, 0, 0);
+    Matrix H1;
+    Matrix H2;
+    Matrix H3;
+    CHECK(assert_equal(Vector2(0, 0), factor.evaluateError(pose, offset, calib, H1, H2, H3), 1e-6));
+    CHECK(assert_equal((Matrix23() <<//
+        0, 200, 200,//
+        0, 0, 0).finished(), H1, 1e-6));
+    CHECK(assert_equal((Matrix26() <<//
+        0, -200, 0, -200, 0, 0,//
+        200, -0, 0, 0, -200, 0).finished(), H2, 1e-6));
+    CHECK(assert_equal((Matrix29() <<//
+        0, 0, 0, 1, 0, 0, 0, 0, 0,//
+        0, 0, 0, 0, 1, 0, 0, 0, 0).finished(), H3, 1e-6));
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor3, Error2) {
+    Point3 landmark(1, 1, 1);
+    Point2 measured(0, 0);
+    SharedNoiseModel model = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    PlanarProjectionFactor3 factor(X(0), C(0), K(0), landmark, measured, model);
+    Pose2 pose(0, 0, 0);
+    Pose3 offset(
+        Rot3(0, 0, 1,//
+            -1, 0, 0, //
+            0, -1, 0),
+        Vector3(0, 0, 0)
+    );
+    Cal3DS2 calib(200, 200, 0, 200, 200, 0, 0);
+    Matrix H1;
+    Matrix H2;
+    Matrix H3;
+    gtsam::Vector actual = factor.evaluateError(pose, offset, calib, H1, H2, H3);
+    CHECK(assert_equal(Vector2(0, 0), actual));
+    CHECK(assert_equal((Matrix23() <<//
+        -200, 200, 400,//
+        -200, 0, 200).finished(), H1, 1e-6));
+    CHECK(assert_equal((Matrix26() <<//
+        200, -400, -200, -200, 0, -200,//
+        400, -200, 200, 0, -200, -200).finished(), H2, 1e-6));
+    CHECK(assert_equal((Matrix29() <<//
+        -1, 0, -1, 1, 0, -400, -800, 400, 800,//
+        0, -1, 0, 0, 1, -400, -800, 800, 400).finished(), H3, 1e-6));
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor3, Error3) {
+    Point3 landmark(1, 1, 1);
+    Point2 measured(0, 0);
+    SharedNoiseModel model = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    PlanarProjectionFactor3 factor(X(0), C(0), K(0), landmark, measured, model);
+    Pose2 pose(0, 0, 0);
+    Pose3 offset(
+        Rot3(0, 0, 1,//
+            -1, 0, 0, //
+            0, -1, 0),
+        Vector3(0, 0, 0)
+    );
+    Cal3DS2 calib(200, 200, 0, 200, 200, -0.2, 0.1);
+    Matrix H1;
+    Matrix H2;
+    Matrix H3;
+    CHECK(assert_equal(Vector2(0, 0), factor.evaluateError(pose, offset, calib, H1, H2, H3), 1e-6));
+    CHECK(assert_equal((Matrix23() <<//
+        -360, 280, 640,//
+        -360, 80, 440).finished(), H1, 1e-6));
+    CHECK(assert_equal((Matrix26() <<//
+        440, -640, -200, -280, -80, -360,//
+        640, -440, 200, -80, -280, -360).finished(), H2, 1e-6));
+    CHECK(assert_equal((Matrix29() <<//
+        -1, 0, -1, 1, 0, -400, -800, 400, 800,//
+        0, -1, 0, 0, 1, -400, -800, 800, 400).finished(), H3, 1e-6));
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor3, Jacobian) {
+    // Verify Jacobians with numeric derivative
+
+    std::default_random_engine rng(42);
+    std::uniform_real_distribution<double> dist(-0.3, 0.3);
+    SharedNoiseModel model = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    // center of the random camera poses
+    Pose3 centerOffset(
+        Rot3(0, 0, 1,//
+            -1, 0, 0, //
+            0, -1, 0),
+        Vector3(0, 0, 0)
+    );
+
+    for (int i = 0; i < 1000; ++i) {
+        Point3 landmark(2 + dist(rng), dist(rng), dist(rng));
+        Point2 measured(200 + 100 * dist(rng), 200 + 100 * dist(rng));
+        Pose3 offset = centerOffset.compose(
+            Pose3(
+                Rot3::Ypr(dist(rng), dist(rng), dist(rng)),
+                Point3(dist(rng), dist(rng), dist(rng))));
+        Cal3DS2 calib(200, 200, 0, 200, 200, -0.2, 0.1);
+
+        PlanarProjectionFactor3 factor(X(0), C(0), K(0), landmark, measured, model);
+
+        Pose2 pose(dist(rng), dist(rng), dist(rng));
+
+        // actual H
+        Matrix H1, H2, H3;
+        factor.evaluateError(pose, offset, calib, H1, H2, H3);
+
+        Matrix expectedH1 = numericalDerivative31<Vector, Pose2, Pose3, Cal3DS2>(
+            [&factor](const Pose2& p, const Pose3& o, const Cal3DS2& c) {
+                return factor.evaluateError(p, o, c, {}, {}, {});},
+                pose, offset, calib);
+        Matrix expectedH2 = numericalDerivative32<Vector, Pose2, Pose3, Cal3DS2>(
+            [&factor](const Pose2& p, const Pose3& o, const Cal3DS2& c) {
+                return factor.evaluateError(p, o, c, {}, {}, {});},
+                pose, offset, calib);
+        Matrix expectedH3 = numericalDerivative33<Vector, Pose2, Pose3, Cal3DS2>(
+            [&factor](const Pose2& p, const Pose3& o, const Cal3DS2& c) {
+                return factor.evaluateError(p, o, c, {}, {}, {});},
+                pose, offset, calib);
+        CHECK(assert_equal(expectedH1, H1, 5e-6));
+        CHECK(assert_equal(expectedH2, H2, 5e-6));
+        CHECK(assert_equal(expectedH3, H3, 5e-6));
+    }
+}
+
+/* ************************************************************************* */
+TEST(PlanarProjectionFactor3, SolveOffset) {
+    // Example localization
+    SharedNoiseModel pxModel = noiseModel::Diagonal::Sigmas(Vector2(1, 1));
+    SharedNoiseModel xNoise = noiseModel::Diagonal::Sigmas(Vector3(0.01, 0.01, 0.01));
+    // offset model is wide, so the solver finds the right answer.
+    SharedNoiseModel cNoise = noiseModel::Diagonal::Sigmas(Vector6(10, 10, 10, 10, 10, 10));
+    SharedNoiseModel kNoise = noiseModel::Diagonal::Sigmas(Vector9(0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001));
+
+    // landmarks
+    Point3 l0(1, 0, 1);
+    Point3 l1(1, 0, 0);
+    Point3 l2(1, -1, 1);
+    Point3 l3(2, 2, 1);
+
+    // camera pixels
+    Point2 p0(200, 200);
+    Point2 p1(200, 400);
+    Point2 p2(400, 200);
+    Point2 p3(0, 200);
+
+    // body
+    Pose2 x0(0, 0, 0);
+
+    // camera z looking at +x with (xy) antiparallel to (yz)
+    Pose3 c0(
+        Rot3(0, 0, 1, //
+            -1, 0, 0, //
+            0, -1, 0), //
+        Vector3(0, 0, 1)); // note z offset
+    Cal3DS2 calib(200, 200, 0, 200, 200, 0, 0);
+
+    NonlinearFactorGraph graph;
+    graph.add(PlanarProjectionFactor3(X(0), C(0), K(0), l0, p0, pxModel));
+    graph.add(PlanarProjectionFactor3(X(0), C(0), K(0), l1, p1, pxModel));
+    graph.add(PlanarProjectionFactor3(X(0), C(0), K(0), l2, p2, pxModel));
+    graph.add(PlanarProjectionFactor3(X(0), C(0), K(0), l3, p3, pxModel));
+    graph.add(PriorFactor<Pose2>(X(0), x0, xNoise));
+    graph.add(PriorFactor<Pose3>(C(0), c0, cNoise));
+    graph.add(PriorFactor<Cal3DS2>(K(0), calib, kNoise));
+
+    Values initialEstimate;
+    initialEstimate.insert(X(0), x0);
+    initialEstimate.insert(C(0), c0);
+    initialEstimate.insert(K(0), calib);
+
+    // run the optimizer
+    LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
+    Values result = optimizer.optimize();
+
+    // verify that the optimizer found the right pose.
+    CHECK(assert_equal(x0, result.at<Pose2>(X(0)), 2e-3));
+
+    // verify the camera is pointing at +x
+    Pose3 cc0 = result.at<Pose3>(C(0));
+    CHECK(assert_equal(c0, cc0, 5e-3));
+
+    // verify the calibration
+    CHECK(assert_equal(calib, result.at<Cal3DS2>(K(0)), 2e-3));
+
+    Marginals marginals(graph, result);
+    Matrix x0cov = marginals.marginalCovariance(X(0));
+
+    // narrow prior => ~zero cov
+    CHECK(assert_equal(Matrix33::Zero(), x0cov, 1e-4));
+
+    Matrix c0cov = marginals.marginalCovariance(C(0));
+
+    // invert the camera offset to get covariance in body coordinates
+    Matrix66 HcTb = cc0.inverse().AdjointMap().inverse();
+    Matrix c0cov2 = HcTb * c0cov * HcTb.transpose();
+
+    // camera-frame stddev
+    Vector6 c0sigma = c0cov.diagonal().cwiseSqrt();
+    CHECK(assert_equal((Vector6() << //
+        0.009,
+        0.011,
+        0.004,
+        0.012,
+        0.012,
+        0.011
+        ).finished(), c0sigma, 1e-3));
+
+    // body frame stddev
+    Vector6 bTcSigma = c0cov2.diagonal().cwiseSqrt();
+    CHECK(assert_equal((Vector6() << //
+        0.004,
+        0.009,
+        0.011,
+        0.012,
+        0.012,
+        0.012
+        ).finished(), bTcSigma, 1e-3));
+
+    // narrow prior => ~zero cov
+    CHECK(assert_equal(Matrix99::Zero(), marginals.marginalCovariance(K(0)), 3e-3));
+}
+
+/* ************************************************************************* */
+int main() {
+    TestResult tr;
+    return TestRegistry::runAllTests(tr);
+}
+/* ************************************************************************* */