241 lines
7.3 KiB
C++
241 lines
7.3 KiB
C++
/**
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* @file Pose3.cpp
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* @brief 3D Pose
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*/
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#include <iostream>
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#include <gtsam/geometry/Pose3.h>
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#include <gtsam/base/Lie-inl.h>
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using namespace std;
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using namespace boost::numeric::ublas;
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namespace gtsam {
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/** Explicit instantiation of base class to export members */
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INSTANTIATE_LIE(Pose3);
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static const Matrix I3 = eye(3), _I3=-I3, I6 = eye(6), Z3 = zeros(3, 3);
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/* ************************************************************************* */
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// Calculate Adjoint map
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// Ad_pose is 6*6 matrix that when applied to twist xi, returns Ad_pose(xi)
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// Experimental - unit tests of derivatives based on it do not check out yet
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Matrix Pose3::AdjointMap() const {
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const Matrix R = R_.matrix();
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const Vector t = t_.vector();
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Matrix A = skewSymmetric(t)*R;
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Matrix DR = collect(2, &R, &Z3);
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Matrix Dt = collect(2, &A, &R);
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return gtsam::stack(2, &DR, &Dt);
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}
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/* ************************************************************************* */
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void Pose3::print(const string& s) const {
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R_.print(s + ".R");
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t_.print(s + ".t");
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}
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/* ************************************************************************* */
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bool Pose3::equals(const Pose3& pose, double tol) const {
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return R_.equals(pose.R_,tol) && t_.equals(pose.t_,tol);
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}
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/* ************************************************************************* */
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#ifdef CORRECT_POSE3_EXMAP
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/** Modified from Murray94book version (which assumes w and v normalized?) */
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template<> Pose3 expmap(const Vector& xi) {
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// get angular velocity omega and translational velocity v from twist xi
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Point3 w(xi(0),xi(1),xi(2)), v(xi(3),xi(4),xi(5));
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double theta = w.norm();
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if (theta < 1e-5) {
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static const Rot3 I;
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return Pose3(I, v);
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}
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else {
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Point3 n(w/theta); // axis unit vector
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Rot3 R = Rot3::rodriguez(n.vector(),theta);
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double vn = n.dot(v); // translation parallel to n
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Point3 n_cross_v = n.cross(v); // points towards axis
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Point3 t = (n_cross_v - R*n_cross_v)/theta + vn*n;
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return Pose3(R, t);
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}
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}
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Vector logmap(const Pose3& p) {
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Vector w = logmap(p.rotation()), T = p.translation().vector();
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double t = norm_2(w);
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if (t < 1e-5)
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return concatVectors(2, &w, &T);
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else {
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Matrix W = skewSymmetric(w/t);
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Matrix Ainv = I3 - (0.5*t)*W + ((2*sin(t)-t*(1+cos(t)))/(2*sin(t))) * (W * W);
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Vector u = Ainv*T;
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return concatVectors(2, &w, &u);
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}
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}
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Pose3 expmap(const Pose3& T, const Vector& d) {
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return compose(T,Pose3::Expmap(d));
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}
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Vector logmap(const Pose3& T1, const Pose3& T2) {
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return Pose3::logmap(between(T1,T2));
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}
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#else
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/* ************************************************************************* */
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/* incorrect versions for which we know how to compute derivatives */
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Pose3 Pose3::Expmap(const Vector& d) {
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Vector w = sub(d, 0,3);
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Vector u = sub(d, 3,6);
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return Pose3(Rot3::Expmap(w), Point3::Expmap(u));
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}
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/* ************************************************************************* */
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// Log map at identity - return the translation and canonical rotation
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// coordinates of a pose.
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Vector Pose3::Logmap(const Pose3& p) {
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const Vector w = Rot3::Logmap(p.rotation()), u = Point3::Logmap(p.translation());
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return concatVectors(2, &w, &u);
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}
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/** These are the "old-style" expmap and logmap about the specified
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* pose. Increments the offset and rotation independently given a translation and
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* canonical rotation coordinates. Created to match ML derivatives, but
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* superseded by the correct exponential map story in .cpp */
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Pose3 Pose3::expmap(const Vector& d) const {
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return Pose3(R_.expmap(sub(d, 0, 3)),
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t_.expmap(sub(d, 3, 6)));
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}
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/** Independently computes the logmap of the translation and rotation. */
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Vector Pose3::logmap(const Pose3& pp) const {
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const Vector r(R_.logmap(pp.rotation())),
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t(t_.logmap(pp.translation()));
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return concatVectors(2, &r, &t);
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}
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#endif
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/* ************************************************************************* */
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Matrix Pose3::matrix() const {
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const Matrix R = R_.matrix(), T = Matrix_(3,1, t_.vector());
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const Matrix A34 = collect(2, &R, &T);
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const Matrix A14 = Matrix_(1,4, 0.0, 0.0, 0.0, 1.0);
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return gtsam::stack(2, &A34, &A14);
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}
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/* ************************************************************************* */
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Pose3 Pose3::transform_to(const Pose3& pose) const {
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Rot3 cRv = R_ * Rot3(pose.R_.inverse());
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Point3 t = pose.transform_to(t_);
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return Pose3(cRv, t);
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}
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/* ************************************************************************* */
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Point3 Pose3::transform_from(const Point3& p,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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if (H1) {
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#ifdef CORRECT_POSE3_EXMAP
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const Matrix R = R_.matrix();
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Matrix DR = R*skewSymmetric(-p.x(), -p.y(), -p.z());
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*H1 = collect(2,&DR,&R);
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#else
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Matrix DR;
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R_.rotate(p, DR, boost::none);
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*H1 = collect(2,&DR,&I3);
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#endif
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}
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if (H2) *H2 = R_.matrix();
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return R_ * p + t_;
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}
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/* ************************************************************************* */
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Point3 Pose3::transform_to(const Point3& p,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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const Point3 result = R_.unrotate(p - t_);
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if (H1) { // *H1 = Dtransform_to1(pose, p);
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const Point3& q = result;
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Matrix DR = skewSymmetric(q.x(), q.y(), q.z());
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#ifdef CORRECT_POSE3_EXMAP
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*H1 = collect(2, &DR, &_I3);
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#else
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Matrix DT = - R_.transpose(); // negative because of sub
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*H1 = collect(2,&DR,&DT);
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#endif
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}
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if (H2) *H2 = R_.transpose();
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return result;
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}
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/* ************************************************************************* */
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Pose3 Pose3::compose(const Pose3& p2,
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boost::optional<Matrix&> H1, boost::optional<Matrix&> H2) const {
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if (H1) {
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#ifdef CORRECT_POSE3_EXMAP
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*H1 = AdjointMap(inverse(p2));
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#else
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const Rot3& R2 = p2.rotation();
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const Point3& t2 = p2.translation();
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Matrix DR_R1 = R2.transpose(), DR_t1 = Z3;
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Matrix DR = collect(2, &DR_R1, &DR_t1);
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Matrix Dt;
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transform_from(t2, Dt, boost::none);
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*H1 = gtsam::stack(2, &DR, &Dt);
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#endif
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}
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if (H2) {
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#ifdef CORRECT_POSE3_EXMAP
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*H2 = I6;
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#else
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Matrix R1 = rotation().matrix();
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Matrix DR = collect(2, &I3, &Z3);
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Matrix Dt = collect(2, &Z3, &R1);
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*H2 = gtsam::stack(2, &DR, &Dt);
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#endif
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}
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return (*this) * p2;
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}
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/* ************************************************************************* */
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Pose3 Pose3::inverse(boost::optional<Matrix&> H1) const {
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if (H1)
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#ifdef CORRECT_POSE3_EXMAP
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{ *H1 = - AdjointMap(p); }
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#else
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{
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Matrix Rt = R_.transpose();
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Matrix DR_R1 = -R_.matrix(), DR_t1 = Z3;
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Matrix Dt_R1 = -skewSymmetric(R_.unrotate(t_).vector()), Dt_t1 = -Rt;
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Matrix DR = collect(2, &DR_R1, &DR_t1);
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Matrix Dt = collect(2, &Dt_R1, &Dt_t1);
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*H1 = gtsam::stack(2, &DR, &Dt);
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}
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#endif
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Rot3 Rt = R_.inverse();
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return Pose3(Rt, Rt*(-t_));
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}
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/* ************************************************************************* */
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// between = compose(p2,inverse(p1));
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Pose3 Pose3::between(const Pose3& p2, boost::optional<Matrix&> H1,
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boost::optional<Matrix&> H2) const {
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Matrix invH;
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Pose3 invp1 = inverse(invH);
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Matrix composeH1;
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Pose3 result = invp1.compose(p2, composeH1, H2);
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if (H1) *H1 = composeH1 * invH;
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return result;
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}
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/* ************************************************************************* */
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} // namespace gtsam
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