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pf.c
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/*
* Player - One Hell of a Robot Server
* Copyright (C) 2000 Brian Gerkey & Kasper Stoy
* gerkey@usc.edu kaspers@robotics.usc.edu
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
/**************************************************************************
* Desc: Simple particle filter for localization.
* Author: Andrew Howard
* Date: 10 Dec 2002
* CVS: $Id: pf.c 6345 2008-04-17 01:36:39Z gerkey $
*************************************************************************/
#include <assert.h>
#include <math.h>
#include <stdlib.h>
#include <time.h>
#include <stdio.h>
#include "amcl/pf/pf.h"
#include "amcl/pf/pf_pdf.h"
#include "amcl/pf/pf_kdtree.h"
#include "portable_utils.hpp"
#include <string.h>
// Compute the required number of samples, given that there are k bins
// with samples in them.
static int pf_resample_limit(pf_t *pf, int k);
// Create a new filter
pf_t *pf_alloc(int min_samples, int max_samples,
double alpha_slow, double alpha_fast,
pf_init_model_fn_t random_pose_fn, void *random_pose_data)
{
int i, j;
pf_t *pf;
pf_sample_set_t *set;
pf_sample_t *sample;
srand48(time(NULL));
pf = calloc(1, sizeof(pf_t));
pf->random_pose_fn = random_pose_fn;
pf->random_pose_data = random_pose_data;
pf->min_samples = min_samples;
pf->max_samples = max_samples;
// Control parameters for the population size calculation. [err] is
// the max error between the true distribution and the estimated
// distribution. [z] is the upper standard normal quantile for (1 -
// p), where p is the probability that the error on the estimated
// distrubition will be less than [err].
pf->pop_err = 0.01;
pf->pop_z = 3;
pf->dist_threshold = 0.5;
pf->current_set = 0;
for (j = 0; j < 2; j++)
{
set = pf->sets + j;
set->sample_count = max_samples;
set->samples = calloc(max_samples, sizeof(pf_sample_t));
for (i = 0; i < set->sample_count; i++)
{
sample = set->samples + i;
sample->pose.v[0] = 0.0;
sample->pose.v[1] = 0.0;
sample->pose.v[2] = 0.0;
sample->weight = 1.0 / max_samples;
}
// HACK: is 3 times max_samples enough?
set->kdtree = pf_kdtree_alloc(3 * max_samples);
set->cluster_count = 0;
set->cluster_max_count = max_samples;
set->clusters = calloc(set->cluster_max_count, sizeof(pf_cluster_t));
set->mean = pf_vector_zero();
set->cov = pf_matrix_zero();
}
pf->w_slow = 0.0;
pf->w_fast = 0.0;
pf->alpha_slow = alpha_slow;
pf->alpha_fast = alpha_fast;
//set converged to 0
pf_init_converged(pf);
return pf;
}
// Free an existing filter
void pf_free(pf_t *pf)
{
int i;
for (i = 0; i < 2; i++)
{
free(pf->sets[i].clusters);
pf_kdtree_free(pf->sets[i].kdtree);
free(pf->sets[i].samples);
}
free(pf);
return;
}
// Initialize the filter using a guassian
void pf_init(pf_t *pf, pf_vector_t mean, pf_matrix_t cov)
{
int i;
pf_sample_set_t *set;
pf_sample_t *sample;
pf_pdf_gaussian_t *pdf;
set = pf->sets + pf->current_set;
// Create the kd tree for adaptive sampling
pf_kdtree_clear(set->kdtree);
set->sample_count = pf->max_samples;
pdf = pf_pdf_gaussian_alloc(mean, cov);
// Compute the new sample poses
for (i = 0; i < set->sample_count; i++)
{
sample = set->samples + i;
sample->weight = 1.0 / pf->max_samples;
sample->pose = pf_pdf_gaussian_sample(pdf);
// Add sample to histogram
pf_kdtree_insert(set->kdtree, sample->pose, sample->weight);
}
pf->w_slow = pf->w_fast = 0.0;
pf_pdf_gaussian_free(pdf);
// Re-compute cluster statistics
pf_cluster_stats(pf, set);
//set converged to 0
pf_init_converged(pf);
return;
}
// Initialize the filter using some model
void pf_init_model(pf_t *pf, pf_init_model_fn_t init_fn, void *init_data)
{
int i;
pf_sample_set_t *set;
pf_sample_t *sample;
set = pf->sets + pf->current_set;
// Create the kd tree for adaptive sampling
pf_kdtree_clear(set->kdtree);
set->sample_count = pf->max_samples;
// Compute the new sample poses
for (i = 0; i < set->sample_count; i++)
{
sample = set->samples + i;
sample->weight = 1.0 / pf->max_samples;
sample->pose = (*init_fn) (init_data);
// Add sample to histogram
pf_kdtree_insert(set->kdtree, sample->pose, sample->weight);
}
pf->w_slow = pf->w_fast = 0.0;
// Re-compute cluster statistics
pf_cluster_stats(pf, set);
//set converged to 0
pf_init_converged(pf);
return;
}
void pf_init_converged(pf_t *pf){
pf_sample_set_t *set;
set = pf->sets + pf->current_set;
set->converged = 0;
pf->converged = 0;
}
int pf_update_converged(pf_t *pf)
{
int i;
pf_sample_set_t *set;
pf_sample_t *sample;
double total;
set = pf->sets + pf->current_set;
double mean_x = 0, mean_y = 0;
for (i = 0; i < set->sample_count; i++){
sample = set->samples + i;
mean_x += sample->pose.v[0];
mean_y += sample->pose.v[1];
}
mean_x /= set->sample_count;
mean_y /= set->sample_count;
for (i = 0; i < set->sample_count; i++){
sample = set->samples + i;
if(fabs(sample->pose.v[0] - mean_x) > pf->dist_threshold ||
fabs(sample->pose.v[1] - mean_y) > pf->dist_threshold){
set->converged = 0;
pf->converged = 0;
return 0;
}
}
set->converged = 1;
pf->converged = 1;
return 1;
}
// Update the filter with some new action
void pf_update_action(pf_t *pf, pf_action_model_fn_t action_fn, void *action_data)
{
pf_sample_set_t *set;
set = pf->sets + pf->current_set;
(*action_fn) (action_data, set);
return;
}
#include <float.h>
// Update the filter with some new sensor observation
void pf_update_sensor(pf_t *pf, pf_sensor_model_fn_t sensor_fn, void *sensor_data)
{
int i;
pf_sample_set_t *set;
pf_sample_t *sample;
double total;
set = pf->sets + pf->current_set;
// Compute the sample weights
total = (*sensor_fn) (sensor_data, set);
if (total > 0.0)
{
// Normalize weights
double w_avg=0.0;
for (i = 0; i < set->sample_count; i++)
{
sample = set->samples + i;
w_avg += sample->weight;
sample->weight /= total;
}
// Update running averages of likelihood of samples (Prob Rob p258)
w_avg /= set->sample_count;
if(pf->w_slow == 0.0)
pf->w_slow = w_avg;
else
pf->w_slow += pf->alpha_slow * (w_avg - pf->w_slow);
if(pf->w_fast == 0.0)
pf->w_fast = w_avg;
else
pf->w_fast += pf->alpha_fast * (w_avg - pf->w_fast);
//printf("w_avg: %e slow: %e fast: %e\n",
//w_avg, pf->w_slow, pf->w_fast);
}
else
{
// Handle zero total
for (i = 0; i < set->sample_count; i++)
{
sample = set->samples + i;
sample->weight = 1.0 / set->sample_count;
}
}
return;
}
double get_determinant(double *cov_matrix)
{
double det = cov_matrix[0] * cov_matrix[4] * cov_matrix[8] +
cov_matrix[1] * cov_matrix[5] * cov_matrix[6] +
cov_matrix[3] * cov_matrix[7] * cov_matrix[2] -
cov_matrix[2] * cov_matrix[4] * cov_matrix[6] -
cov_matrix[1] * cov_matrix[3] * cov_matrix[8] -
cov_matrix[0] * cov_matrix[5] * cov_matrix[7];
return det;
}
int get_inverse(double *cov_matrix, double *result)
{
double det = get_determinant(cov_matrix);
double inv[9] = { 1 * (cov_matrix[4] * cov_matrix[8] - cov_matrix[5] * cov_matrix[7]) / det,
-1 * (cov_matrix[3] * cov_matrix[8] - cov_matrix[5] * cov_matrix[6]) / det,
1 * (cov_matrix[3] * cov_matrix[7] - cov_matrix[4] * cov_matrix[6]) / det,
-1 * (cov_matrix[1] * cov_matrix[8] - cov_matrix[2] * cov_matrix[7]) / det,
1 * (cov_matrix[0] * cov_matrix[8] - cov_matrix[2] * cov_matrix[6]) / det,
-1 * (cov_matrix[0] * cov_matrix[7] - cov_matrix[1] * cov_matrix[6]) / det,
1 * (cov_matrix[1] * cov_matrix[5] - cov_matrix[2] * cov_matrix[4]) / det,
-1 * (cov_matrix[0] * cov_matrix[5] - cov_matrix[2] * cov_matrix[3]) / det,
1 * (cov_matrix[0] * cov_matrix[4] - cov_matrix[1] * cov_matrix[3]) / det};
memcpy(result, inv, 9*sizeof(double));
return 0;
}
int mult_1_3_x_3_3(double *mat_1_3, double *mat_3_3, double *result)
{
double r[3] = { mat_1_3[0] * mat_3_3[0] + mat_1_3[1] * mat_3_3[3] + mat_1_3[2] * mat_3_3[6],
mat_1_3[0] * mat_3_3[1] + mat_1_3[1] * mat_3_3[4] + mat_1_3[2] * mat_3_3[7],
mat_1_3[0] * mat_3_3[2] + mat_1_3[1] * mat_3_3[5] + mat_1_3[2] * mat_3_3[8]};
memcpy(result, r, 3*sizeof(double));
return 0;
}
double mult_1_3_x_3_1(double *mat_1_3, double *mat_3_1)
{
double result = mat_1_3[0] * mat_3_1[0] + mat_1_3[1] * mat_3_1[1] + mat_1_3[2] * mat_3_1[2];
return result;
}
int generate_random_particle(double gps_x, double gps_y, double gps_yaw, double *cov_matrix, double *pose_v)
{
double pose[3] = {norm_random(), norm_random(), norm_random()};
mult_1_3_x_3_3(pose, cov_matrix, pose);
pose[0] = pose[0] + gps_x;
pose[1] = pose[1] + gps_y;
pose[2] = pose[2] + gps_yaw;
memcpy(pose_v, pose, 3*sizeof(double));
return 0;
}
//Return random std mean number
double norm_random()
{
double u = (double)rand()/RAND_MAX;
double v = (double)rand()/RAND_MAX;
double x = sqrt(-2*log(u))*cos(2*3.14159*v); // Check this
return x;
}
// Resample the distribution
void pf_update_resample(pf_t *pf)
{
int i;
double total;
pf_sample_set_t *set_a, *set_b;
pf_sample_t *sample_a, *sample_b;
//double r,c,U;
//int m;
//double count_inv;
double* c;
double w_diff;
set_a = pf->sets + pf->current_set;
set_b = pf->sets + (pf->current_set + 1) % 2;
///////////////////////////////////// NEW WEIGHT FUNCTION
/////
/// New weight
double total_weight = 0;
double total_dist_prob = 0;
for(int i=0;i<set_a->sample_count;i++)
{
double distance = (pow(set_a->samples[i].pose.v[0]-pf->gps_x, 2)/pf->cov_matrix[0] + pow(set_a->samples[i].pose.v[1]-pf->gps_y, 2)/pf->cov_matrix[4] + pow(set_a->samples[i].pose.v[2]-pf->gps_yaw, 2)/pf->cov_matrix[8]);
double cov = (pf->cov_matrix[0] * pf->cov_matrix[4] * pf->cov_matrix[8]);
total_dist_prob += 1/sqrt(pow(2*3.14159, 3) * cov)*exp(-1*distance/2);
//Multivariable gausian
double mat[3] = {set_a->samples[i].pose.v[0]-pf->gps_x, set_a->samples[i].pose.v[1]-pf->gps_y, set_a->samples[i].pose.v[2]-pf->gps_yaw};
double result[3];
double inverse[9];
get_inverse(pf->cov_matrix, inverse);
mult_1_3_x_3_3(mat, inverse, result);
double temp = mult_1_3_x_3_1(result, mat);
double d = 1/(pow(3.14159 * 2, 1.5) * sqrt(get_determinant(pf->cov_matrix))) * exp(-0.5 * temp);
set_a->samples[i].weight = set_a->samples[i].weight * pf->k_l + d;
total_weight += set_a->samples[i].weight;
}
/// Handle total weight of 0
if(total_weight == 0)
{
for(int i=0;i<set_a->sample_count;i++)
{
set_a->samples[i].weight = 1;
total_weight += set_a->samples[i].weight;
}
}
/// Normalization
for(int i=0;i<set_a->sample_count;i++)
{
set_a->samples[i].weight = set_a->samples[i].weight / total_weight;
}
/////
/////////////////////////////////////
// Build up cumulative probability table for resampling.
// TODO: Replace this with a more efficient procedure
// (e.g., http://www.network-theory.co.uk/docs/gslref/GeneralDiscreteDistributions.html)
c = (double*)malloc(sizeof(double)*(set_a->sample_count+1));
c[0] = 0.0;
for(i=0;i<set_a->sample_count;i++)
c[i+1] = c[i]+set_a->samples[i].weight;
// Create the kd tree for adaptive sampling
pf_kdtree_clear(set_b->kdtree);
// Draw samples from set a to create set b.
total = 0;
set_b->sample_count = 0;
/////////////////////////// CHANGED WDIFF func
/////
total_dist_prob = total_dist_prob/set_a->sample_count;
w_diff = 0.01 - total_dist_prob;
if(w_diff < 0.0)
w_diff = 0.0;
//ORIGINAL
// w_diff = 1.0 - pf->w_fast / pf->w_slow;
// if(w_diff < 0.0)
// w_diff = 0.0;
/////
////////////////////////////////////////////////////
// Can't (easily) combine low-variance sampler with KLD adaptive
// sampling, so we'll take the more traditional route.
/*
// Low-variance resampler, taken from Probabilistic Robotics, p110
count_inv = 1.0/set_a->sample_count;
r = drand48() * count_inv;
c = set_a->samples[0].weight;
i = 0;
m = 0;
*/
while(set_b->sample_count < pf->max_samples)
{
sample_b = set_b->samples + set_b->sample_count++;
if(drand48() < w_diff)
{
// printf("******RANDOM FUNCTION*********%f - %f\n", w_diff, total_dist_prob);
generate_random_particle(pf->gps_x, pf->gps_y, pf->gps_yaw, pf->eigen_matrix, sample_b->pose.v);
}
else
{
// Can't (easily) combine low-variance sampler with KLD adaptive
// sampling, so we'll take the more traditional route.
/*
// Low-variance resampler, taken from Probabilistic Robotics, p110
U = r + m * count_inv;
while(U>c)
{
i++;
// Handle wrap-around by resetting counters and picking a new random
// number
if(i >= set_a->sample_count)
{
r = drand48() * count_inv;
c = set_a->samples[0].weight;
i = 0;
m = 0;
U = r + m * count_inv;
continue;
}
c += set_a->samples[i].weight;
}
m++;
*/
// Naive discrete event sampler
double r;
r = drand48();
for(i=0;i<set_a->sample_count;i++)
{
if((c[i] <= r) && (r < c[i+1]))
break;
}
assert(i<set_a->sample_count);
sample_a = set_a->samples + i;
assert(sample_a->weight > 0);
// Add sample to list
sample_b->pose = sample_a->pose;
}
sample_b->weight = 1.0;
total += sample_b->weight;
// Add sample to histogram
pf_kdtree_insert(set_b->kdtree, sample_b->pose, sample_b->weight);
// See if we have enough samples yet
if (set_b->sample_count > pf_resample_limit(pf, set_b->kdtree->leaf_count))
break;
}
// Reset averages, to avoid spiraling off into complete randomness.
if(w_diff > 0.0)
pf->w_slow = pf->w_fast = 0.0;
//fprintf(stderr, "\n\n");
// Normalize weights
for (i = 0; i < set_b->sample_count; i++)
{
sample_b = set_b->samples + i;
sample_b->weight /= total;
}
// Re-compute cluster statistics
pf_cluster_stats(pf, set_b);
// Use the newly created sample set
pf->current_set = (pf->current_set + 1) % 2;
pf_update_converged(pf);
free(c);
return;
}
// Compute the required number of samples, given that there are k bins
// with samples in them. This is taken directly from Fox et al.
int pf_resample_limit(pf_t *pf, int k)
{
double a, b, c, x;
int n;
if (k <= 1)
return pf->max_samples;
a = 1;
b = 2 / (9 * ((double) k - 1));
c = sqrt(2 / (9 * ((double) k - 1))) * pf->pop_z;
x = a - b + c;
n = (int) ceil((k - 1) / (2 * pf->pop_err) * x * x * x);
if (n < pf->min_samples)
return pf->min_samples;
if (n > pf->max_samples)
return pf->max_samples;
return n;
}
// Re-compute the cluster statistics for a sample set
void pf_cluster_stats(pf_t *pf, pf_sample_set_t *set)
{
int i, j, k, cidx;
pf_sample_t *sample;
pf_cluster_t *cluster;
// Workspace
double m[4], c[2][2];
size_t count;
double weight;
// Cluster the samples
pf_kdtree_cluster(set->kdtree);
// Initialize cluster stats
set->cluster_count = 0;
for (i = 0; i < set->cluster_max_count; i++)
{
cluster = set->clusters + i;
cluster->count = 0;
cluster->weight = 0;
cluster->mean = pf_vector_zero();
cluster->cov = pf_matrix_zero();
for (j = 0; j < 4; j++)
cluster->m[j] = 0.0;
for (j = 0; j < 2; j++)
for (k = 0; k < 2; k++)
cluster->c[j][k] = 0.0;
}
// Initialize overall filter stats
count = 0;
weight = 0.0;
set->mean = pf_vector_zero();
set->cov = pf_matrix_zero();
for (j = 0; j < 4; j++)
m[j] = 0.0;
for (j = 0; j < 2; j++)
for (k = 0; k < 2; k++)
c[j][k] = 0.0;
// Compute cluster stats
for (i = 0; i < set->sample_count; i++)
{
sample = set->samples + i;
//printf("%d %f %f %f\n", i, sample->pose.v[0], sample->pose.v[1], sample->pose.v[2]);
// Get the cluster label for this sample
cidx = pf_kdtree_get_cluster(set->kdtree, sample->pose);
assert(cidx >= 0);
if (cidx >= set->cluster_max_count)
continue;
if (cidx + 1 > set->cluster_count)
set->cluster_count = cidx + 1;
cluster = set->clusters + cidx;
cluster->count += 1;
cluster->weight += sample->weight;
count += 1;
weight += sample->weight;
// Compute mean
cluster->m[0] += sample->weight * sample->pose.v[0];
cluster->m[1] += sample->weight * sample->pose.v[1];
cluster->m[2] += sample->weight * cos(sample->pose.v[2]);
cluster->m[3] += sample->weight * sin(sample->pose.v[2]);
m[0] += sample->weight * sample->pose.v[0];
m[1] += sample->weight * sample->pose.v[1];
m[2] += sample->weight * cos(sample->pose.v[2]);
m[3] += sample->weight * sin(sample->pose.v[2]);
// Compute covariance in linear components
for (j = 0; j < 2; j++)
for (k = 0; k < 2; k++)
{
cluster->c[j][k] += sample->weight * sample->pose.v[j] * sample->pose.v[k];
c[j][k] += sample->weight * sample->pose.v[j] * sample->pose.v[k];
}
}
// Normalize
for (i = 0; i < set->cluster_count; i++)
{
cluster = set->clusters + i;
cluster->mean.v[0] = cluster->m[0] / cluster->weight;
cluster->mean.v[1] = cluster->m[1] / cluster->weight;
cluster->mean.v[2] = atan2(cluster->m[3], cluster->m[2]);
cluster->cov = pf_matrix_zero();
// Covariance in linear components
for (j = 0; j < 2; j++)
for (k = 0; k < 2; k++)
cluster->cov.m[j][k] = cluster->c[j][k] / cluster->weight -
cluster->mean.v[j] * cluster->mean.v[k];
// Covariance in angular components; I think this is the correct
// formula for circular statistics.
cluster->cov.m[2][2] = -2 * log(sqrt(cluster->m[2] * cluster->m[2] +
cluster->m[3] * cluster->m[3]));
//printf("cluster %d %d %f (%f %f %f)\n", i, cluster->count, cluster->weight,
//cluster->mean.v[0], cluster->mean.v[1], cluster->mean.v[2]);
//pf_matrix_fprintf(cluster->cov, stdout, "%e");
}
// Compute overall filter stats
set->mean.v[0] = m[0] / weight;
set->mean.v[1] = m[1] / weight;
set->mean.v[2] = atan2(m[3], m[2]);
// Covariance in linear components
for (j = 0; j < 2; j++)
for (k = 0; k < 2; k++)
set->cov.m[j][k] = c[j][k] / weight - set->mean.v[j] * set->mean.v[k];
// Covariance in angular components; I think this is the correct
// formula for circular statistics.
set->cov.m[2][2] = -2 * log(sqrt(m[2] * m[2] + m[3] * m[3]));
return;
}
// Compute the CEP statistics (mean and variance).
void pf_get_cep_stats(pf_t *pf, pf_vector_t *mean, double *var)
{
int i;
double mn, mx, my, mrr;
pf_sample_set_t *set;
pf_sample_t *sample;
set = pf->sets + pf->current_set;
mn = 0.0;
mx = 0.0;
my = 0.0;
mrr = 0.0;
for (i = 0; i < set->sample_count; i++)
{
sample = set->samples + i;
mn += sample->weight;
mx += sample->weight * sample->pose.v[0];
my += sample->weight * sample->pose.v[1];
mrr += sample->weight * sample->pose.v[0] * sample->pose.v[0];
mrr += sample->weight * sample->pose.v[1] * sample->pose.v[1];
}
mean->v[0] = mx / mn;
mean->v[1] = my / mn;
mean->v[2] = 0.0;
*var = mrr / mn - (mx * mx / (mn * mn) + my * my / (mn * mn));
return;
}
// Get the statistics for a particular cluster.
int pf_get_cluster_stats(pf_t *pf, int clabel, double *weight,
pf_vector_t *mean, pf_matrix_t *cov)
{
pf_sample_set_t *set;
pf_cluster_t *cluster;
set = pf->sets + pf->current_set;
if (clabel >= set->cluster_count)
return 0;
cluster = set->clusters + clabel;
*weight = cluster->weight;
*mean = cluster->mean;
*cov = cluster->cov;
return 1;
}