459 lines
15 KiB
C++
459 lines
15 KiB
C++
/**
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* @file testPose3.cpp
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* @brief Unit tests for Pose3 class
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*/
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#include <math.h>
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#include <gtsam/CppUnitLite/TestHarness.h>
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#include <gtsam/base/numericalDerivative.h>
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#include <gtsam/base/lieProxies.h>
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#include <gtsam/geometry/Pose3.h>
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using namespace std;
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using namespace gtsam;
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static Point3 P(0.2,0.7,-2);
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static Rot3 R = Rot3::rodriguez(0.3,0,0);
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static Pose3 T(R,Point3(3.5,-8.2,4.2));
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static Pose3 T2(Rot3::rodriguez(0.3,0.2,0.1),Point3(3.5,-8.2,4.2));
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static Pose3 T3(Rot3::rodriguez(-90, 0, 0), Point3(1, 2, 3));
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/* ************************************************************************* */
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TEST( Pose3, equals)
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{
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Pose3 pose2 = T3;
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CHECK(T3.equals(pose2));
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Pose3 origin;
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CHECK(!T3.equals(origin));
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}
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/* ************************************************************************* */
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TEST( Pose3, expmap_a)
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{
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Pose3 id;
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Vector v(6);
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fill(v.begin(), v.end(), 0);
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v(0) = 0.3;
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CHECK(assert_equal(id.expmap(v), Pose3(R, Point3())));
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#ifdef CORRECT_POSE3_EXMAP
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v(3)=0.2;v(4)=0.394742;v(5)=-2.08998;
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#else
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v(3)=0.2;v(4)=0.7;v(5)=-2;
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#endif
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CHECK(assert_equal(Pose3(R, P),id.expmap(v),1e-5));
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}
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/* ************************************************************************* */
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TEST(Pose3, expmap_b)
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{
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Pose3 p1(Rot3(), Point3(100, 0, 0));
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Pose3 p2 = p1.expmap(Vector_(6,0.0, 0.0, 0.1, 0.0, 0.0, 0.0));
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Pose3 expected(Rot3::rodriguez(0.0, 0.0, 0.1), Point3(100.0, 0.0, 0.0));
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CHECK(assert_equal(expected, p2));
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}
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#ifdef CORRECT_POSE3_EXMAP
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/* ************************************************************************* */
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// test case for screw motion in the plane
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namespace screw {
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double a=0.3, c=cos(a), s=sin(a), w=0.3;
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Vector xi = Vector_(6, 0.0, 0.0, w, w, 0.0, 1.0);
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Rot3 expectedR(c, -s, 0, s, c, 0, 0, 0, 1);
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Point3 expectedT(0.29552, 0.0446635, 1);
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Pose3 expected(expectedR, expectedT);
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}
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TEST(Pose3, expmap_c)
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{
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CHECK(assert_equal(screw::expected, expm<Pose3>(screw::xi),1e-6));
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CHECK(assert_equal(screw::expected, Pose3::Expmap(screw::xi),1e-6));
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}
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/* ************************************************************************* */
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// assert that T*exp(xi)*T^-1 is equal to exp(Ad_T(xi))
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TEST(Pose3, Adjoint)
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{
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Pose3 expected = T * Pose3::Expmap(screw::xi) * inverse(T);
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Vector xiprime = Adjoint(T, screw::xi);
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CHECK(assert_equal(expected, Pose3::Expmap(xiprime), 1e-6));
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Pose3 expected2 = T2 * Pose3::Expmap(screw::xi) * inverse(T2);
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Vector xiprime2 = Adjoint(T2, screw::xi);
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CHECK(assert_equal(expected2, Pose3::Expmap(xiprime2), 1e-6));
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Pose3 expected3 = T3 * Pose3::Expmap(screw::xi) * inverse(T3);
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Vector xiprime3 = Adjoint(T3, screw::xi);
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CHECK(assert_equal(expected3, Pose3::Expmap(xiprime3), 1e-6));
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}
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/* ************************************************************************* */
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/** Agrawal06iros version */
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using namespace boost::numeric::ublas;
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Pose3 Agrawal06iros(const Vector& xi) {
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Vector w = vector_range<const Vector>(xi, range(0,3));
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Vector v = vector_range<const Vector>(xi, range(3,6));
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double t = norm_2(w);
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if (t < 1e-5)
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return Pose3(Rot3(), expmap<Point3> (v));
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else {
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Matrix W = skewSymmetric(w/t);
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Matrix A = eye(3) + ((1 - cos(t)) / t) * W + ((t - sin(t)) / t) * (W * W);
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return Pose3(Rot3::Expmap (w), expmap<Point3> (A * v));
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}
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}
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/* ************************************************************************* */
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TEST(Pose3, expmaps_galore)
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{
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Vector xi; Pose3 actual;
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xi = Vector_(6,0.1,0.2,0.3,0.4,0.5,0.6);
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actual = Pose3::Expmap(xi);
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CHECK(assert_equal(expm<Pose3>(xi), actual,1e-6));
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CHECK(assert_equal(Agrawal06iros(xi), actual,1e-6));
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CHECK(assert_equal(xi, logmap(actual),1e-6));
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xi = Vector_(6,0.1,-0.2,0.3,-0.4,0.5,-0.6);
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for (double theta=1.0;0.3*theta<=M_PI;theta*=2) {
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Vector txi = xi*theta;
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actual = Pose3::Expmap(txi);
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CHECK(assert_equal(expm<Pose3>(txi,30), actual,1e-6));
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CHECK(assert_equal(Agrawal06iros(txi), actual,1e-6));
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Vector log = logmap(actual);
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CHECK(assert_equal(actual, Pose3::Expmap(log),1e-6));
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CHECK(assert_equal(txi,log,1e-6)); // not true once wraps
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}
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// Works with large v as well, but expm needs 10 iterations!
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xi = Vector_(6,0.2,0.3,-0.8,100.0,120.0,-60.0);
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actual = Pose3::Expmap(xi);
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CHECK(assert_equal(expm<Pose3>(xi,10), actual,1e-5));
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CHECK(assert_equal(Agrawal06iros(xi), actual,1e-6));
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CHECK(assert_equal(xi, logmap(actual),1e-6));
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}
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/* ************************************************************************* */
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TEST(Pose3, Adjoint_compose)
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{
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// To debug derivatives of compose, assert that
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// T1*T2*exp(Adjoint(inv(T2),x) = T1*exp(x)*T2
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const Pose3& T1 = T;
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Vector x = Vector_(6,0.1,0.1,0.1,0.4,0.2,0.8);
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Pose3 expected = T1 * Pose3::Expmap(x) * T2;
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Vector y = Adjoint(inverse(T2), x);
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Pose3 actual = T1 * T2 * Pose3::Expmap(y);
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CHECK(assert_equal(expected, actual, 1e-6));
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}
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#endif // SLOW_BUT_CORRECT_EXMAP
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/* ************************************************************************* */
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TEST( Pose3, compose )
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{
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Matrix actual = (T2*T2).matrix();
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Matrix expected = T2.matrix()*T2.matrix();
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CHECK(assert_equal(actual,expected,1e-8));
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Matrix actualDcompose1, actualDcompose2;
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T2.compose(T2, actualDcompose1, actualDcompose2);
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Matrix numericalH1 = numericalDerivative21(testing::compose<Pose3>, T2, T2, 1e-5);
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CHECK(assert_equal(numericalH1,actualDcompose1,5e-5));
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Matrix numericalH2 = numericalDerivative22(testing::compose<Pose3>, T2, T2, 1e-5);
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CHECK(assert_equal(numericalH2,actualDcompose2));
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}
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/* ************************************************************************* */
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TEST( Pose3, compose2 )
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{
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const Pose3& T1 = T;
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Matrix actual = (T1*T2).matrix();
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Matrix expected = T1.matrix()*T2.matrix();
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CHECK(assert_equal(actual,expected,1e-8));
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Matrix actualDcompose1, actualDcompose2;
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T1.compose(T2, actualDcompose1, actualDcompose2);
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Matrix numericalH1 = numericalDerivative21(testing::compose<Pose3>, T1, T2, 1e-5);
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CHECK(assert_equal(numericalH1,actualDcompose1,5e-5));
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Matrix numericalH2 = numericalDerivative22(testing::compose<Pose3>, T1, T2, 1e-5);
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CHECK(assert_equal(numericalH2,actualDcompose2));
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}
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/* ************************************************************************* */
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TEST( Pose3, inverse)
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{
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Matrix actualDinverse;
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Matrix actual = T.inverse(actualDinverse).matrix();
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Matrix expected = inverse(T.matrix());
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CHECK(assert_equal(actual,expected,1e-8));
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Matrix numericalH = numericalDerivative11(testing::inverse<Pose3>, T, 1e-5);
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CHECK(assert_equal(numericalH,actualDinverse));
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}
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/* ************************************************************************* */
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TEST( Pose3, inverseDerivatives2)
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{
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Rot3 R = Rot3::rodriguez(0.3,0.4,-0.5);
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Point3 t(3.5,-8.2,4.2);
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Pose3 T(R,t);
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Matrix numericalH = numericalDerivative11(testing::inverse<Pose3>, T, 1e-5);
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Matrix actualDinverse;
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T.inverse(actualDinverse);
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CHECK(assert_equal(numericalH,actualDinverse,5e-5));
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}
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/* ************************************************************************* */
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TEST( Pose3, compose_inverse)
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{
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Matrix actual = (T*T.inverse()).matrix();
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Matrix expected = eye(4,4);
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CHECK(assert_equal(actual,expected,1e-8));
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}
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/* ************************************************************************* */
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Point3 transform_from_(const Pose3& pose, const Point3& point) { return pose.transform_from(point); }
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TEST( Pose3, Dtransform_from1_a)
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{
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Matrix actualDtransform_from1;
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T.transform_from(P, actualDtransform_from1, boost::none);
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Matrix numerical = numericalDerivative21(transform_from_,T,P);
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CHECK(assert_equal(numerical,actualDtransform_from1,1e-8));
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}
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TEST( Pose3, Dtransform_from1_b)
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{
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Pose3 origin;
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Matrix actualDtransform_from1;
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origin.transform_from(P, actualDtransform_from1, boost::none);
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Matrix numerical = numericalDerivative21(transform_from_,origin,P);
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CHECK(assert_equal(numerical,actualDtransform_from1,1e-8));
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}
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TEST( Pose3, Dtransform_from1_c)
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{
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Point3 origin;
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Pose3 T0(R,origin);
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Matrix actualDtransform_from1;
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T0.transform_from(P, actualDtransform_from1, boost::none);
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Matrix numerical = numericalDerivative21(transform_from_,T0,P);
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CHECK(assert_equal(numerical,actualDtransform_from1,1e-8));
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}
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TEST( Pose3, Dtransform_from1_d)
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{
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Rot3 I;
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Point3 t0(100,0,0);
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Pose3 T0(I,t0);
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Matrix actualDtransform_from1;
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T0.transform_from(P, actualDtransform_from1, boost::none);
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//print(computed, "Dtransform_from1_d computed:");
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Matrix numerical = numericalDerivative21(transform_from_,T0,P);
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//print(numerical, "Dtransform_from1_d numerical:");
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CHECK(assert_equal(numerical,actualDtransform_from1,1e-8));
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}
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/* ************************************************************************* */
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TEST( Pose3, Dtransform_from2)
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{
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Matrix actualDtransform_from2;
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T.transform_from(P, boost::none, actualDtransform_from2);
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Matrix numerical = numericalDerivative22(transform_from_,T,P);
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CHECK(assert_equal(numerical,actualDtransform_from2,1e-8));
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}
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/* ************************************************************************* */
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Point3 transform_to_(const Pose3& pose, const Point3& point) { return pose.transform_to(point); }
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TEST( Pose3, Dtransform_to1)
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{
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Matrix computed;
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T.transform_to(P, computed, boost::none);
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Matrix numerical = numericalDerivative21(transform_to_,T,P);
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CHECK(assert_equal(numerical,computed,1e-8));
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}
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/* ************************************************************************* */
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TEST( Pose3, Dtransform_to2)
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{
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Matrix computed;
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T.transform_to(P, boost::none, computed);
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Matrix numerical = numericalDerivative22(transform_to_,T,P);
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CHECK(assert_equal(numerical,computed,1e-8));
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}
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/* ************************************************************************* */
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TEST( Pose3, transform_to_with_derivatives)
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{
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Matrix actH1, actH2;
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T.transform_to(P,actH1,actH2);
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Matrix expH1 = numericalDerivative21(transform_to_, T,P),
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expH2 = numericalDerivative22(transform_to_, T,P);
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CHECK(assert_equal(expH1, actH1, 1e-8));
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CHECK(assert_equal(expH2, actH2, 1e-8));
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}
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/* ************************************************************************* */
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TEST( Pose3, transform_from_with_derivatives)
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{
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Matrix actH1, actH2;
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T.transform_from(P,actH1,actH2);
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Matrix expH1 = numericalDerivative21(transform_from_, T,P),
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expH2 = numericalDerivative22(transform_from_, T,P);
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CHECK(assert_equal(expH1, actH1, 1e-8));
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CHECK(assert_equal(expH2, actH2, 1e-8));
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}
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/* ************************************************************************* */
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TEST( Pose3, transform_to_translate)
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{
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Point3 actual = Pose3(Rot3(), Point3(1, 2, 3)).transform_to(Point3(10.,20.,30.));
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Point3 expected(9.,18.,27.);
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CHECK(assert_equal(expected, actual));
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}
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/* ************************************************************************* */
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TEST( Pose3, transform_to_rotate)
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{
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Pose3 transform(Rot3::rodriguez(0,0,-1.570796), Point3());
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Point3 actual = transform.transform_to(Point3(2,1,10));
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Point3 expected(-1,2,10);
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CHECK(assert_equal(expected, actual, 0.001));
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}
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/* ************************************************************************* */
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TEST( Pose3, transform_to)
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{
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Pose3 transform(Rot3::rodriguez(0,0,-1.570796), Point3(2,4, 0));
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Point3 actual = transform.transform_to(Point3(3,2,10));
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Point3 expected(2,1,10);
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CHECK(assert_equal(expected, actual, 0.001));
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}
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/* ************************************************************************* */
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TEST( Pose3, transform_from)
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{
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Point3 actual = T3.transform_from(Point3());
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Point3 expected = Point3(1.,2.,3.);
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CHECK(assert_equal(expected, actual));
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}
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/* ************************************************************************* */
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TEST( Pose3, transform_roundtrip)
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{
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Point3 actual = T3.transform_from(T3.transform_to(Point3(12., -0.11,7.0)));
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Point3 expected(12., -0.11,7.0);
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CHECK(assert_equal(expected, actual));
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}
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/* ************************************************************************* */
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TEST( Pose3, transformPose_to_origin)
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{
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// transform to origin
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Pose3 actual = T3.transform_to(Pose3());
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CHECK(assert_equal(T3, actual, 1e-8));
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}
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/* ************************************************************************* */
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TEST( Pose3, transformPose_to_itself)
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{
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// transform to itself
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Pose3 actual = T3.transform_to(T3);
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CHECK(assert_equal(Pose3(), actual, 1e-8));
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}
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/* ************************************************************************* */
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TEST( Pose3, transformPose_to_translation)
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{
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// transform translation only
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Rot3 r = Rot3::rodriguez(-1.570796,0,0);
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Pose3 pose2(r, Point3(21.,32.,13.));
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Pose3 actual = pose2.transform_to(Pose3(Rot3(), Point3(1,2,3)));
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Pose3 expected(r, Point3(20.,30.,10.));
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CHECK(assert_equal(expected, actual, 1e-8));
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}
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/* ************************************************************************* */
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TEST( Pose3, transformPose_to_simple_rotate)
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{
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// transform translation only
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Rot3 r = Rot3::rodriguez(0,0,-1.570796);
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Pose3 pose2(r, Point3(21.,32.,13.));
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Pose3 transform(r, Point3(1,2,3));
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Pose3 actual = pose2.transform_to(transform);
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Pose3 expected(Rot3(), Point3(-30.,20.,10.));
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CHECK(assert_equal(expected, actual, 0.001));
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}
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/* ************************************************************************* */
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TEST( Pose3, transformPose_to)
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{
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// transform to
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Rot3 r = Rot3::rodriguez(0,0,-1.570796); //-90 degree yaw
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Rot3 r2 = Rot3::rodriguez(0,0,0.698131701); //40 degree yaw
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Pose3 pose2(r2, Point3(21.,32.,13.));
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Pose3 transform(r, Point3(1,2,3));
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Pose3 actual = pose2.transform_to(transform);
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Pose3 expected(Rot3::rodriguez(0,0,2.26892803), Point3(-30.,20.,10.));
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CHECK(assert_equal(expected, actual, 0.001));
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}
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/* ************************************************************************* */
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TEST(Pose3, manifold)
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{
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//cout << "manifold" << endl;
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Pose3 t1 = T;
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Pose3 t2 = T3;
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Pose3 origin;
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Vector d12 = t1.logmap(t2);
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CHECK(assert_equal(t2, t1.expmap(d12)));
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// todo: richard - commented out because this tests for "compose-style" (new) expmap
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// CHECK(assert_equal(t2, expmap(origin,d12)*t1));
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Vector d21 = t2.logmap(t1);
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CHECK(assert_equal(t1, t2.expmap(d21)));
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// todo: richard - commented out because this tests for "compose-style" (new) expmap
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// CHECK(assert_equal(t1, expmap(origin,d21)*t2));
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// Check that log(t1,t2)=-log(t2,t1) - this holds even for incorrect expmap :-)
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CHECK(assert_equal(d12,-d21));
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#ifdef CORRECT_POSE3_EXMAP
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// todo: Frank - Below only works for correct "Agrawal06iros style expmap
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// lines in canonical coordinates correspond to Abelian subgroups in SE(3)
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Vector d = Vector_(6,0.1,0.2,0.3,0.4,0.5,0.6);
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// exp(-d)=inverse(exp(d))
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CHECK(assert_equal(Pose3::Expmap(-d),inverse(Pose3::Expmap(d))));
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// exp(5d)=exp(2*d+3*d)=exp(2*d)exp(3*d)=exp(3*d)exp(2*d)
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Pose3 T2 = Pose3::Expmap(2*d);
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Pose3 T3 = Pose3::Expmap(3*d);
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Pose3 T5 = Pose3::Expmap(5*d);
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CHECK(assert_equal(T5,T2*T3));
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CHECK(assert_equal(T5,T3*T2));
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#endif
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}
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/* ************************************************************************* */
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TEST( Pose3, between )
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{
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Pose3 expected = T2.inverse() * T3;
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Matrix actualDBetween1,actualDBetween2;
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Pose3 actual = T2.between(T3, actualDBetween1,actualDBetween2);
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CHECK(assert_equal(expected,actual));
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|
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Matrix numericalH1 = numericalDerivative21(testing::between<Pose3> , T2, T3, 1e-5);
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CHECK(assert_equal(numericalH1,actualDBetween1,5e-5));
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|
|
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Matrix numericalH2 = numericalDerivative22(testing::between<Pose3> , T2, T3, 1e-5);
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CHECK(assert_equal(numericalH2,actualDBetween2));
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}
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|
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/* ************************************************************************* */
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int main(){ TestResult tr; return TestRegistry::runAllTests(tr);}
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/* ************************************************************************* */
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