Quadrotor

/*************************************************************

  Generalized-ICP Copyright (c) 2009 Aleksandr Segal.

  All rights reserved.

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  or without modification, are permitted provided that the 

  following conditions are met:

* Redistributions of source code must retain the above 

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  following disclaimer.

* Redistributions in binary form must reproduce the above

  copyright notice, this list of conditions and the 

  following disclaimer in the documentation and/or other

  materials provided with the distribution.

* The names of the contributors may not be used to endorse

  or promote products derived from this software

  without specific prior written permission.

  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND

  CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED

  WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED

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  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,

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*************************************************************/

#include "optimize.h"

#include <iostream>

#include <assert.h>

#include <fstream>

#include <sstream>

using namespace std;

namespace dgc {

  namespace gicp {

    GICPOptimizer::GICPOptimizer() :

      T_min(gsl_multimin_fdfminimizer_vector_bfgs2)

    {

      max_iter = 20;

      iter = -1;

      status = GSL_CONTINUE;

      gsl_minimizer = gsl_multimin_fdfminimizer_alloc(T_min, N);

      if(gsl_minimizer == NULL) {

        //TODO: handle

      }

      x = gsl_vector_alloc(N);

      if(x == NULL) {

        //TODO: handle

      }

      debug = false;

    }

    GICPOptimizer::~GICPOptimizer() {

      if(gsl_minimizer != NULL) {

        gsl_multimin_fdfminimizer_free(gsl_minimizer);

      }

      if(x != NULL) {

        gsl_vector_free(x);

      }

    }

    // this method outputs data files containing the value of the error function on a 2d grid.

    // a seperate file and grid is constructed for each pair of coordinates

    // this is used to verify convergence of the numerical minimization

    void GICPOptimizer::PlotError(dgc_transform_t t, GICPOptData &opt_data, const char* filename) {

      double resolution = .005;

      double min = -.1;

      double max = .1;

      // initialize the starting point

      double tx, ty, tz, rx, ry, rz;

      dgc_transform_get_translation(t, &tx, &ty, &tz);

      dgc_transform_get_rotation(t, &rx, &ry, &rz);

      gsl_vector_set(x, 0, tx);

      gsl_vector_set(x, 1, ty);

      gsl_vector_set(x, 2, tz);

      gsl_vector_set(x, 3, rx);

      gsl_vector_set(x, 4, ry);

      gsl_vector_set(x, 5, rz);

      dgc_transform_t temp;

      int N = (max-min)/resolution;

      for(int n1 = 0; n1 < 6; n1++) {

        for(int n2 = 0; n2 < n1; n2++) {

          // set up the filename for this pair of coordinates

          ostringstream full_filename;

          full_filename << filename << "_" << n1 << "vs" << n2 << ".dat";

          // open the file

          ofstream fout(full_filename.str().c_str());

          if(!fout) {

            cout << "Could not open file for writing." << endl;

            return;

          }

          // loop through pairs of values for these two coordinates while keeping others fixed

          double val1_0 = gsl_vector_get(x, n1);

          for(int k1 = 0; k1 < N; k1++) {    

            gsl_vector_set(x, n1, val1_0 + min + resolution*k1);

            double val2_0 = gsl_vector_get(x, n2);

            for(int k2 = 0; k2 < N; k2++) {

              gsl_vector_set(x, n2, val2_0 + min + resolution*k2);

              dgc_transform_copy(temp, opt_data.base_t);

              apply_state(temp, x);

              double error = f(x, &opt_data);

              fout << error << "\t";                              

            }

            gsl_vector_set(x, n2, val2_0); // restore to old value

            fout << endl;

          }

          gsl_vector_set(x, n1, val1_0); // restore to old value

          // close the file for this pair of coordinates

          fout.close();

        }

      }

    }

    bool GICPOptimizer::Optimize(dgc_transform_t t, GICPOptData & opt_data) {

      double line_search_tol = .01;

      double gradient_tol = 1e-2;

      double step_size = 1.;

      // set up the gsl function_fdf struct

      gsl_multimin_function_fdf func;

      func.f = f;

      func.df = df;

      func.fdf = fdf;

      func.n = N;

      func.params = &opt_data;

      // initialize the starting point

      double tx, ty, tz, rx, ry, rz;

      dgc_transform_get_translation(t, &tx, &ty, &tz);

      dgc_transform_get_rotation(t, &rx, &ry, &rz);

      gsl_vector_set(x, 0, tx);

      gsl_vector_set(x, 1, ty);

      gsl_vector_set(x, 2, tz);

      gsl_vector_set(x, 3, rx);

      gsl_vector_set(x, 4, ry);

      gsl_vector_set(x, 5, rz);

      // initialize the minimizer

      gsl_multimin_fdfminimizer_set(gsl_minimizer, &func, x, step_size, line_search_tol);

      //iterate the minimization algorithm using gsl primatives

      status = GSL_CONTINUE;

      iter = 0;

      if(debug) {

        cout << "iter\t\tf-value\t\tstatus" << endl;

        cout << iter << "\t\t" << gsl_minimizer->f << "\t\t" << Status() << endl;

      }

      while(status == GSL_CONTINUE && iter < max_iter) {

        iter++;

        status = gsl_multimin_fdfminimizer_iterate(gsl_minimizer);

        if(debug) {

          cout << iter << "\t\t" << gsl_minimizer->f << "\t\t" << Status() <<endl;

        }

        if(status) {

          break;

        }

        status = gsl_multimin_test_gradient (gsl_minimizer->gradient, gradient_tol);

      }

      if(status == GSL_SUCCESS || iter == max_iter) {

        //set t to the converged solution

        dgc_transform_identity(t);

        // apply the current state to the base

        apply_state(t, gsl_minimizer->x);

        //dgc_transform_print(t, "converged to:");        

        return true;

      }

      else {

        // the algorithm failed to converge

        return false;

      }

    }

    double GICPOptimizer::mat_inner_prod(gsl_matrix const* mat1, gsl_matrix const* mat2) {

      double r = 0.;

      int n = mat1->size1;

      for(int i = 0; i < n; i++) {

        for(int j = 0; j < n; j++) { // tr(mat1^t.mat2)

          r += gsl_matrix_get(mat1, j, i)*gsl_matrix_get(mat2, i, j);

        }

      }

      return r;

    }

    void GICPOptimizer::apply_state(dgc_transform_t t, gsl_vector const* x) {

      double tx, ty, tz, rx, ry, rz;

      tx = gsl_vector_get(x, 0);

      ty = gsl_vector_get(x, 1);

      tz = gsl_vector_get(x, 2);

      rx = gsl_vector_get(x, 3);

      ry = gsl_vector_get(x, 4);

      rz = gsl_vector_get(x, 5);

      dgc_transform_rotate_x(t, rx);

      dgc_transform_rotate_y(t, ry);

      dgc_transform_rotate_z(t, rz);      

      dgc_transform_translate(t, tx, ty, tz);

    }

    void GICPOptimizer::compute_dr(gsl_vector const* x, gsl_matrix const* gsl_temp_mat_r, gsl_vector *g) {

      double dR_dPhi[3][3];

      double dR_dTheta[3][3];

      double dR_dPsi[3][3];

      gsl_matrix_view gsl_d_rx = gsl_matrix_view_array(&dR_dPhi[0][0],3, 3);

      gsl_matrix_view gsl_d_ry = gsl_matrix_view_array(&dR_dTheta[0][0],3, 3);

      gsl_matrix_view gsl_d_rz = gsl_matrix_view_array(&dR_dPsi[0][0],3, 3);

      double phi = gsl_vector_get(x ,3);

      double theta = gsl_vector_get(x ,4);

      double psi = gsl_vector_get(x ,5);  

      double cphi = cos(phi), sphi = sin(phi);

      double ctheta = cos(theta), stheta = sin(theta);

      double cpsi = cos(psi), spsi = sin(psi);

      dR_dPhi[0][0] = 0.;

      dR_dPhi[1][0] = 0.;

      dR_dPhi[2][0] = 0.;

      dR_dPhi[0][1] = sphi*spsi + cphi*cpsi*stheta;

      dR_dPhi[1][1] = -cpsi*sphi + cphi*spsi*stheta;

      dR_dPhi[2][1] = cphi*ctheta;

      dR_dPhi[0][2] = cphi*spsi - cpsi*sphi*stheta;

      dR_dPhi[1][2] = -cphi*cpsi - sphi*spsi*stheta;

      dR_dPhi[2][2] = -ctheta*sphi;

      dR_dTheta[0][0] = -cpsi*stheta;

      dR_dTheta[1][0] = -spsi*stheta;

      dR_dTheta[2][0] = -ctheta;

      dR_dTheta[0][1] = cpsi*ctheta*sphi;

      dR_dTheta[1][1] = ctheta*sphi*spsi;

      dR_dTheta[2][1] = -sphi*stheta;

      dR_dTheta[0][2] = cphi*cpsi*ctheta;

      dR_dTheta[1][2] = cphi*ctheta*spsi;

      dR_dTheta[2][2] = -cphi*stheta;

      dR_dPsi[0][0] = -ctheta*spsi;

      dR_dPsi[1][0] = cpsi*ctheta;

      dR_dPsi[2][0] = 0.;

      dR_dPsi[0][1] = -cphi*cpsi - sphi*spsi*stheta;

      dR_dPsi[1][1] = -cphi*spsi + cpsi*sphi*stheta;

      dR_dPsi[2][1] = 0.;

      dR_dPsi[0][2] = cpsi*sphi - cphi*spsi*stheta;

      dR_dPsi[1][2] = sphi*spsi + cphi*cpsi*stheta;

      dR_dPsi[2][2] = 0.;

      // set d/d_rx = tr(dR_dPhi'*gsl_temp_mat_r) [= <dR_dPhi, gsl_temp_mat_r>]

      gsl_vector_set(g, 3, mat_inner_prod(&gsl_d_rx.matrix, gsl_temp_mat_r));

      // set d/d_ry = tr(dR_dTheta'*gsl_temp_mat_r) = [<dR_dTheta, gsl_temp_mat_r>]

      gsl_vector_set(g, 4, mat_inner_prod(&gsl_d_ry.matrix, gsl_temp_mat_r));

      // set d/d_rz = tr(dR_dPsi'*gsl_temp_mat_r) = [<dR_dPsi, gsl_temp_mat_r>]

      gsl_vector_set(g, 5, mat_inner_prod(&gsl_d_rz.matrix, gsl_temp_mat_r));      

    }

  }

}