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?附C++/Python/Matlab全套代码?课程设计、毕业设计、创新竞赛必备！详细介绍全局规划(图搜索、采样法、智能算法等)；局部规划(DWA、APF等)；曲线优化(贝塞尔曲线、B样条曲线等)。

?详情：图解自动驾驶中的运动规划(Motion Planning)，附几十种规划算法

1 Informed RRT*原理

传统的RRT算法存在一些局限性。在复杂的环境中，RRT算法可能会生成较长的路径，因为它主要依赖于随机采样，路径的探索性较强，而对于局部信息的利用较少，这可能导致路径搜索效率低。

Informed RRT*算法针对RRT*算法进行了采样优化，用椭圆采样代替全局均匀采样，避免了RRT*算法搜索树上产生过多冗余分支的缺陷，提高了搜索效率和收敛速度。在Informed RRT*算法中，以起点、终点为焦点，二者的直线距离为焦距$c_{\min }$；当前规划的起点、终点最佳路径长度为$c_{\mathrm{best}}$，以$c_{\mathrm{best}}$为长轴，$\sqrt{c_{\mathrm{best}}^2-c_{\min }^2}$为短轴构造椭圆采样区域。

工程上一般先在标准圆内采样，再通过齐次变换

$$T=\left[\begin{array}{cc}\mathbf{R}& \mathbf{p}\end{array}\right],\mathbf{R}=\left[\begin{array}{cc}a\cos \theta & b\sin \theta \\ -a\sin \theta & b\cos \theta \end{array}\right],\mathbf{p}=\left[\begin{array}{c}{x}_{\mathrm{center}}\\ y_{\mathrm{center}}\end{array}\right]$$

将采样点映射到地图中，其中$\theta$是起点、终点连线与$x$轴的夹角；$\mathbf{p}$是起点、终点的中点；$a$、$b$分别是长轴、短轴，$\mathbf{R}$是伸缩变换和旋转变换的复合。我们通过代码来直观看看是如何实现椭圆采样的

Node InformedRRT::_transform(double x, double y)
{
  // center
  double center_x = (start_.x_ + goal_.x_) / 2;
  double center_y = (start_.y_ + goal_.y_) / 2;

  // rotation
  double theta = -_angle(start_, goal_);

  // ellipse
  double a = c_best_ / 2.0;
  double c = c_min_ / 2.0;
  double b = std::sqrt(a * a - c * c);

  // transform
  int tx = (int)(a * cos(theta) * x + b * sin(theta) * y + center_x);
  int ty = (int)(-a * sin(theta) * x + b * cos(theta) * y + center_y);
  int id = grid2Index(tx, ty);
  return Node(tx, ty, 0, 0, id, 0);
}

2 Informed RRT*流程

Informed RRT*算法流程如下

3 ROS C++实现

核心代码如下所示

bool InformedRRT::plan(const unsigned char* gloal_costmap, const Node& start, const Node& goal, std::vector<Node>& path,
                       std::vector<Node>& expand)
{
  // initialization
  c_best_ = std::numeric_limits<double>::max();
  c_min_ = _dist(start, goal);
  int best_parent = -1;
  sample_list_.clear();

  // copy
  start_ = start, goal_ = goal;
  costs_ = gloal_costmap;
  sample_list_.insert(start);
  expand.push_back(start);

  // main loop
  int iteration = 0;
  while (iteration < sample_num_)
  {
    iteration++;

    // generate a random node in the map
    Node sample_node = _generateRandomNode();

    // obstacle
    if (gloal_costmap[sample_node.id_] >= lethal_cost_ * factor_)
      continue;

    // visited
    if (sample_list_.find(sample_node) != sample_list_.end())
      continue;

    // regular the sample node
    Node new_node = _findNearestPoint(sample_list_, sample_node);
    if (new_node.id_ == -1)
      continue;
    else
    {
      sample_list_.insert(new_node);
      expand.push_back(new_node);
    }

    // goal found
    auto dist = _dist(new_node, goal_);
    if (dist <= max_dist_ && !_isAnyObstacleInPath(new_node, goal_))
    {
      double cost = dist + new_node.g_;
      if (cost < c_best_)
      {
        best_parent = new_node.id_;
        c_best_ = cost;
      }
    }
  }

  if (best_parent != -1)
  {
    Node goal_(goal_.x_, goal_.y_, c_best_, 0, grid2Index(goal_.x_, goal_.y_),
               best_parent);
    sample_list_.insert(goal_);
    path = _convertClosedListToPath(sample_list_, start, goal);
    return true;
  }
  return false;
}

运行效果图

4 Python实现

核心代码如下所示

def plan(self):
	# generate a random node in the map
	node_rand = self.generateRandomNode()
	
	# visited
	if node_rand in self.sample_list:
	   return 0, None
	
	# generate new node
	node_new = self.getNearest(self.sample_list, node_rand)
	if node_new:
	   self.sample_list.append(node_new)
	   dist = self.dist(node_new, self.goal)
	   # goal found
	   if dist <= self.max_dist and not self.isCollision(node_new, self.goal):
	       self.goal.parent = node_new.current
	       self.goal.g = node_new.g + self.dist(self.goal, node_new)
	       self.sample_list.append(self.goal)
	       return self.extractPath(self.sample_list)
	return 0, None

运行效果图

5 Matlab实现

核心代码如下：

function [cost, flag, node_list, path] = plan(node_list, start, goal, map, param)
    cost = 0;
    flag = false;
    path = [];

    % generate a random node in the map
    node_rand = generate_node(start, goal, param);

    % visited
    if loc_list(node_rand, node_list, [1, 2])
        return
    end

    % generate new node
    [node_new, success] = get_nearest(node_list, node_rand, map, param);
    if success
        node_list = [node_new; node_list];
        distance = dist(node_new(1:2), goal');

        % goal found
        if distance <= param.max_dist && ~is_collision(node_new(1:2), goal, map, param)
            goal_ = [goal, node_new(3) + distance, node_new(1:2)];
            node_list = [goal_; node_list];
            flag = true;
            cost = goal_(3);
            path = extract_path(node_list, start);
            node_list(1, :) = [];
            return
        end
    end
end

运行效果图

完整工程代码请联系下方博主名片获取

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