gtsam/gtsam_unstable/dynamics/tests/testSimpleHelicopter.cpp

/**
 * @file testPendulumExplicitEuler.cpp
 * @author Duy-Nguyen Ta
 */

#include <CppUnitLite/TestHarness.h>
#include <gtsam/base/numericalDerivative.h>
#include <gtsam/inference/Symbol.h>
#include <gtsam_unstable/dynamics/SimpleHelicopter.h>

/* ************************************************************************* */
using namespace gtsam;
using namespace gtsam::symbol_shorthand;

const double tol=1e-5;
const double h = 0.01;
const double deg2rad = M_PI/180.0;

//Pose3 g1(Rot3::ypr(deg2rad*10.0, deg2rad*20.0, deg2rad*30.0), Point3(100.0, 200.0, 300.0));
Pose3 g1(Rot3(), Point3(100.0, 0.0, 300.0));
//LieVector v1((Vec(6) << 0.1, 0.05, 0.02, 10.0, 20.0, 30.0));
LieVector V1_w((Vec(6) << 0.0, 0.0, M_PI/3, 0.0, 0.0, 30.0));
LieVector V1_g1 = g1.inverse().Adjoint(V1_w);
Pose3 g2(g1.retract(h*V1_g1, Pose3::EXPMAP));
//LieVector v2 = Pose3::Logmap(g1.between(g2));

double mass = 100.0;
Vector gamma2 = (Vec(2) << 0.0, 0.0);  // no shape
Vector u2 = (Vec(2) << 0.0, 0.0); // no control at time 2
double distT = 1.0; // distance from the body-centered x axis to the big top motor
double distR = 5.0; // distance from the body-centered z axis to the small motor
Matrix Mass = diag((Vec(3) << mass, mass, mass));
Matrix Inertia = diag((Vec(6) << 2.0/5.0*mass*distR*distR, 2.0/5.0*mass*distR*distR, 2.0/5.0*mass*distR*distR, mass, mass, mass));

Vector computeFu(const Vector& gamma, const Vector& control) {
  double gamma_r = gamma(0), gamma_p = gamma(1);

  Matrix F = (Mat(6, 2) << distT*sin(gamma_r), 0.0,
                           distT*sin(gamma_p*cos(gamma_r)), 0.0,
                           0.0, distR,
                           sin(gamma_p)*cos(gamma_r), 0.0,
                          -sin(gamma_r), -1.0,
                           cos(gamma_p)*sin(gamma_r), 0.0
                            );
  return F*control;
}

/* ************************************************************************* */
Vector testExpmapDeriv(const LieVector& v) {
  return Pose3::Logmap(Pose3::Expmap(-h*V1_g1)*Pose3::Expmap(h*V1_g1+v));
}

TEST(Reconstruction, ExpmapInvDeriv) {
  Matrix numericalExpmap = numericalDerivative11(
      boost::function<Vector(const LieVector&)>(
          boost::bind(testExpmapDeriv,  _1)
          ),
      LieVector(Vector::Zero(6)), 1e-5
      );
  Matrix dExpInv = Pose3::dExpInv_exp(h*V1_g1);
  EXPECT(assert_equal(numericalExpmap, dExpInv, 1e-2));
}

/* ************************************************************************* */
TEST( Reconstruction, evaluateError) {
  // hard constraints don't need a noise model
  Reconstruction constraint(G(2), G(1), V(1), h);

  // verify error function
  Matrix H1, H2, H3;
  EXPECT(assert_equal(zero(6), constraint.evaluateError(g2, g1, V1_g1, H1, H2, H3), tol));


  Matrix numericalH1 = numericalDerivative31(
      boost::function<Vector(const Pose3&, const Pose3&, const LieVector&)>(
          boost::bind(&Reconstruction::evaluateError, constraint, _1, _2, _3, boost::none, boost::none, boost::none)
          ),
      g2, g1, V1_g1, 1e-5
      );

  Matrix numericalH2 = numericalDerivative32(
      boost::function<Vector(const Pose3&, const Pose3&, const LieVector&)>(
          boost::bind(&Reconstruction::evaluateError, constraint, _1, _2, _3, boost::none, boost::none, boost::none)
          ),
      g2, g1, V1_g1, 1e-5
      );

  Matrix numericalH3 = numericalDerivative33(
      boost::function<Vector(const Pose3&, const Pose3&, const LieVector&)>(
          boost::bind(&Reconstruction::evaluateError, constraint, _1, _2, _3, boost::none, boost::none, boost::none)
          ),
      g2, g1, V1_g1, 1e-5
      );

  EXPECT(assert_equal(numericalH1,H1,1e-5));
  EXPECT(assert_equal(numericalH2,H2,1e-5));
  EXPECT(assert_equal(numericalH3,H3,1e-5));
}

/* ************************************************************************* */
// Implement Newton-Euler equation for rigid body dynamics
Vector newtonEuler(const Vector& Vb, const Vector& Fb, const Matrix& Inertia) {
  Matrix W = Pose3::adjointMap((Vec(6) << Vb(0), Vb(1), Vb(2), 0., 0., 0.));
  Vector dV = Inertia.inverse()*(Fb - W*Inertia*Vb);
  return dV;
}

TEST( DiscreteEulerPoincareHelicopter, evaluateError) {
  Vector Fu = computeFu(gamma2, u2);
  Vector fGravity_g1 = zero(6);  subInsert(fGravity_g1, g1.rotation().unrotate(Point3(0.0, 0.0, -mass*9.81)).vector(), 3); // gravity force in g1 frame
  Vector Fb = Fu+fGravity_g1;

  Vector dV = newtonEuler(V1_g1, Fb, Inertia);
  Vector V2_g1 = dV*h + V1_g1;
  Pose3 g21 = g2.between(g1);
  Vector V2_g2 = g21.Adjoint(V2_g1);  // convert the new velocity to g2's frame

  LieVector expectedv2(V2_g2);

  // hard constraints don't need a noise model
  DiscreteEulerPoincareHelicopter constraint(V(2), V(1), G(2), h,
      Inertia, Fu, mass);

  // verify error function
  Matrix H1, H2, H3;
  EXPECT(assert_equal(zero(6), constraint.evaluateError(expectedv2, V1_g1, g2, H1, H2, H3), 1e0));

  Matrix numericalH1 = numericalDerivative31(
      boost::function<Vector(const LieVector&, const LieVector&, const Pose3&)>(
          boost::bind(&DiscreteEulerPoincareHelicopter::evaluateError, constraint, _1, _2, _3, boost::none, boost::none, boost::none)
          ),
          expectedv2, V1_g1, g2, 1e-5
      );

  Matrix numericalH2 = numericalDerivative32(
      boost::function<Vector(const LieVector&, const LieVector&, const Pose3&)>(
          boost::bind(&DiscreteEulerPoincareHelicopter::evaluateError, constraint, _1, _2, _3, boost::none, boost::none, boost::none)
          ),
          expectedv2, V1_g1, g2, 1e-5
      );

  Matrix numericalH3 = numericalDerivative33(
      boost::function<Vector(const LieVector&, const LieVector&, const Pose3&)>(
          boost::bind(&DiscreteEulerPoincareHelicopter::evaluateError, constraint, _1, _2, _3, boost::none, boost::none, boost::none)
          ),
          expectedv2, V1_g1, g2, 1e-5
      );

  EXPECT(assert_equal(numericalH1,H1,1e-5));
  EXPECT(assert_equal(numericalH2,H2,1e-5));
  EXPECT(assert_equal(numericalH3,H3,5e-5));
}

/* ************************************************************************* */
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
/* ************************************************************************* */