Robot Localization AMCL原理以及代码

先讲几个坐标系的关系吧，在机器人定位中很重要。

• base_link 一般指的是机器人自身的坐标系，随着机器人的移动而移动。
• odom的原点是机器人刚启动时刻的位置，理论上这个odom坐标系是固定的不会变化的，但是odom是会随着时间发生漂移且存在累积误差，因此odom坐标系实际上会随着时间移动
• map是地图的坐标系，当地图建立完成之后，map坐标系就固定下来了，不会随时间发生变化。
• 一般我们的odom坐标系和map坐标系是重合的，假设机器人启动位置就是地图的原点

一般机器人定位时坐标系的关系是 base_link <-> odom <-> map 

• 这里 base_link <-> odom两个坐标系时间的转换关系一般由里程计odomerty，IMU或者视觉里程计提供。
• 由于odom会发生漂移和累积误差，因此odom<->map之间会有一段未知的、待估计的转换关系
• 定位一般用base_link <-> map，但是在AMCL中我们估计odom<->map，由此完成机器人的定位问题

 

Adaptive Monte Carlo Localization

是一套适用于二维机器人运动的定位算法。其主要的算法原理源于《Probabilistic Robotics》一书8.3中描述的MCL, Augmented_MCL, 和KLD_Sampling_MCL算法的结合与实现。同时书中第5章描述的Motion Model和第6章描述的Sensor Model，用于AMCL中运动的预测和粒子权重的更新。

1,粒子滤波和蒙特卡洛

蒙特卡洛：是一种思想或方法。举例：一个矩形里面有个不规则形状，怎么计算不规则形状的面积？不好算。但我们可以近似。拿一堆豆子，均匀的撒在矩形上，然后统计不规则形状里的豆子的个数和剩余地方的豆子个数。矩形面积知道的呀，所以就通过估计得到了不规则形状的面积。拿机器人定位来讲，它处在地图中的任何一个位置都有可能，这种情况我们怎么表达一个位置的置信度呢？我们也使用粒子，哪里的粒子多，就代表机器人在哪里的可能性高。

 粒子滤波：粒子数代表某个东西的可能性高低。通过某种评价方法（评价这个东西的可能性），改变粒子的分布情况。比如在机器人定位中，某个粒子A，我觉得这个粒子在这个坐标（比如这个坐标就属于之前说的“这个东西”）的可能性很高，那么我给他打高分。下次重新安排所有的粒子的位置的时候，就在这个位置附近多安排一些。这样多来几轮，粒子就都集中到可能性高的位置去了。

2,重要性采样

就像转盘抽奖一样，原本分数高（我们给它打分）的粒子，它在转盘上对应的面积就大。原本有100个粒子，那下次我就转100次，转到什么就取个对应的粒子。这样多重复几次，仍然是100个粒子，但是分数高的粒子越来越多了，它们代表的东西（比如位姿）几乎是一样的。

3,机器人绑架

        举例，机器人突然被抱走，放到了另外一个地方。类似这种情况。

4,自适应蒙特卡洛

       解决了机器人绑架问题，它会在发现粒子们的平均分数突然降低了（意味着正确的粒子在某次迭代中被抛弃了）的时候，在全局再重新的撒一些粒子。

       解决了粒子数固定的问题，因为有时候当机器人定位差不多得到了的时候，比如这些粒子都集中在一块了，还要维持这么多的粒子没必要，这个时候粒子数可以少一点了。

5,KLD采样

       就是为了控制上述粒子数冗余而设计的。比如在栅格地图中，看粒子占了多少栅格。占得多，说明粒子很分散，在每次迭代重采样的时候，允许粒子数量的上限高一些。占得少，说明粒子都已经集中了，那就将上限设低，采样到这个数就行了。

 

amcl/sensors/odom

  case ODOM_MODEL_DIFF:
  {
    // Implement sample_motion_odometry (Prob Rob p 136)
    double delta_rot1, delta_trans, delta_rot2;
    double delta_rot1_hat, delta_trans_hat, delta_rot2_hat;
    double delta_rot1_noise, delta_rot2_noise;

    // Avoid computing a bearing from two poses that are extremely near each
    // other (happens on in-place rotation).
    if(sqrt(ndata->delta.v[1]*ndata->delta.v[1] + 
            ndata->delta.v[0]*ndata->delta.v[0]) < 0.01)
      delta_rot1 = 0.0;
    else
      delta_rot1 = angle_diff(atan2(ndata->delta.v[1], ndata->delta.v[0]),
                              old_pose.v[2]);
    delta_trans = sqrt(ndata->delta.v[0]*ndata->delta.v[0] +
                       ndata->delta.v[1]*ndata->delta.v[1]);
    delta_rot2 = angle_diff(ndata->delta.v[2], delta_rot1);

    // We want to treat backward and forward motion symmetrically for the
    // noise model to be applied below.  The standard model seems to assume
    // forward motion.
    delta_rot1_noise = std::min(fabs(angle_diff(delta_rot1,0.0)),
                                fabs(angle_diff(delta_rot1,M_PI)));
    delta_rot2_noise = std::min(fabs(angle_diff(delta_rot2,0.0)),
                                fabs(angle_diff(delta_rot2,M_PI)));

    for (int i = 0; i < set->sample_count; i++)
    {
      pf_sample_t* sample = set->samples + i;

      // Sample pose differences
      delta_rot1_hat = angle_diff(delta_rot1,
                                  pf_ran_gaussian(this->alpha1*delta_rot1_noise*delta_rot1_noise +
                                                  this->alpha2*delta_trans*delta_trans));
      delta_trans_hat = delta_trans - 
              pf_ran_gaussian(this->alpha3*delta_trans*delta_trans +
                              this->alpha4*delta_rot1_noise*delta_rot1_noise +
                              this->alpha4*delta_rot2_noise*delta_rot2_noise);
      delta_rot2_hat = angle_diff(delta_rot2,
                                  pf_ran_gaussian(this->alpha1*delta_rot2_noise*delta_rot2_noise +
                                                  this->alpha2*delta_trans*delta_trans));

      // Apply sampled update to particle pose
      sample->pose.v[0] += delta_trans_hat * 
              cos(sample->pose.v[2] + delta_rot1_hat);
      sample->pose.v[1] += delta_trans_hat * 
              sin(sample->pose.v[2] + delta_rot1_hat);
      sample->pose.v[2] += delta_rot1_hat + delta_rot2_hat;
    }
  }

amcl/sensors/laser

// Determine the probability for the given pose
double AMCLLaser::BeamModel(AMCLLaserData *data, pf_sample_set_t* set)
{
  AMCLLaser *self;
  int i, j, step;
  double z, pz;
  double p;
  double map_range;
  double obs_range, obs_bearing;
  double total_weight;
  pf_sample_t *sample;
  pf_vector_t pose;

  self = (AMCLLaser*) data->sensor;

  total_weight = 0.0;

  // Compute the sample weights
  for (j = 0; j < set->sample_count; j++)
  {
    sample = set->samples + j;
    pose = sample->pose;

    // Take account of the laser pose relative to the robot
    pose = pf_vector_coord_add(self->laser_pose, pose);

    p = 1.0;

    step = (data->range_count - 1) / (self->max_beams - 1);
    for (i = 0; i < data->range_count; i += step)
    {
      obs_range = data->ranges[i][0];
      obs_bearing = data->ranges[i][1];

      // Compute the range according to the map
      map_range = map_calc_range(self->map, pose.v[0], pose.v[1],
                                 pose.v[2] + obs_bearing, data->range_max);
      pz = 0.0;

      // Part 1: good, but noisy, hit
      z = obs_range - map_range;
      pz += self->z_hit * exp(-(z * z) / (2 * self->sigma_hit * self->sigma_hit));

      // Part 2: short reading from unexpected obstacle (e.g., a person)
      if(z < 0)
        pz += self->z_short * self->lambda_short * exp(-self->lambda_short*obs_range);

      // Part 3: Failure to detect obstacle, reported as max-range
      if(obs_range == data->range_max)
        pz += self->z_max * 1.0;

      // Part 4: Random measurements
      if(obs_range < data->range_max)
        pz += self->z_rand * 1.0/data->range_max;

      // TODO: outlier rejection for short readings

      assert(pz <= 1.0);
      assert(pz >= 0.0);
      //      p *= pz;
      // here we have an ad-hoc weighting scheme for combining beam probs
      // works well, though...
      p += pz*pz*pz;
    }

    sample->weight *= p;
    total_weight += sample->weight;
  }

  return(total_weight);
}

double AMCLLaser::LikelihoodFieldModel(AMCLLaserData *data, pf_sample_set_t* set)
{
  AMCLLaser *self;
  int i, j, step;
  double z, pz;
  double p;
  double obs_range, obs_bearing;
  double total_weight;
  pf_sample_t *sample;
  pf_vector_t pose;
  pf_vector_t hit;

  self = (AMCLLaser*) data->sensor;

  total_weight = 0.0;

  // Compute the sample weights
  for (j = 0; j < set->sample_count; j++)
  {
    sample = set->samples + j;
    pose = sample->pose;

    // Take account of the laser pose relative to the robot
    pose = pf_vector_coord_add(self->laser_pose, pose);

    p = 1.0;

    // Pre-compute a couple of things
    double z_hit_denom = 2 * self->sigma_hit * self->sigma_hit;
    double z_rand_mult = 1.0/data->range_max;

    step = (data->range_count - 1) / (self->max_beams - 1);

    // Step size must be at least 1
    if(step < 1)
      step = 1;

    for (i = 0; i < data->range_count; i += step)
    {
      obs_range = data->ranges[i][0];
      obs_bearing = data->ranges[i][1];

      // This model ignores max range readings
      if(obs_range >= data->range_max)
        continue;

      // Check for NaN
      if(obs_range != obs_range)
        continue;

      pz = 0.0;

      // Compute the endpoint of the beam
      hit.v[0] = pose.v[0] + obs_range * cos(pose.v[2] + obs_bearing);
      hit.v[1] = pose.v[1] + obs_range * sin(pose.v[2] + obs_bearing);

      // Convert to map grid coords.
      int mi, mj;
      mi = MAP_GXWX(self->map, hit.v[0]);
      mj = MAP_GYWY(self->map, hit.v[1]);
      
      // Part 1: Get distance from the hit to closest obstacle.
      // Off-map penalized as max distance
      if(!MAP_VALID(self->map, mi, mj))
        z = self->map->max_occ_dist;
      else
        z = self->map->cells[MAP_INDEX(self->map,mi,mj)].occ_dist;
      // Gaussian model
      // NOTE: this should have a normalization of 1/(sqrt(2pi)*sigma)
      pz += self->z_hit * exp(-(z * z) / z_hit_denom);
      // Part 2: random measurements
      pz += self->z_rand * z_rand_mult;

      // TODO: outlier rejection for short readings

      assert(pz <= 1.0);
      assert(pz >= 0.0);
      //      p *= pz;
      // here we have an ad-hoc weighting scheme for combining beam probs
      // works well, though...
      p += pz*pz*pz;
    }

    sample->weight *= p;
    total_weight += sample->weight;
  }

  return(total_weight);
}

particle filter

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;
}

 

 

// 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;

  // 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;isample_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;

  w_diff = 1.0 - pf->w_fast / pf->w_slow;
  if(w_diff < 0.0)
    w_diff = 0.0;
  //printf("w_diff: %9.6f\n", w_diff);

  // 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)
      sample_b->pose = (pf->random_pose_fn)(pf->random_pose_data);
    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;isample_count;i++)
      {
        if((c[i] <= r) && (r < c[i+1]))
          break;
      }
      assert(isample_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;
}

 

Reference

http://wiki.ros.org/amcl

https://github.com/ros-planning/navigation/tree/melodic-devel/amcl

https://robomaster.github.io/RoboRTS-Tutorial/#/sdk_docs/roborts_localization?id=amcl算法

https://github.com/RoboMaster/RoboRTS/tree/ros/roborts_localization/amcl

https://cse.sc.edu/~terejanu/files/tutorialMC.pdf

https://blog.csdn.net/hmbxsy/article/details/80509876

https://blog.csdn.net/wyang9x/article/details/84034333

https://blog.csdn.net/u013834525/article/details/80166552

https://blog.csdn.net/xyz599/article/details/52942485

https://blog.csdn.net/crazyquhezheng/article/details/49154805

https://blog.csdn.net/ethan_guo/article/details/81809054