ROS1云课→20迷宫不惑之A*大法(一种虽古老但实用全局路径规划算法)
20中有一幅图:
如何实现如下:
障碍物膨胀系数0.1
障碍物膨胀系数0.25
障碍物膨胀系数0.5
掌握了如上内容,最基础的全局路径规划算法A*,基本原理和ROS中使用就ok了。
差异性:
Note that a lot less of the potential has been calculated (indicated by the colored areas). This is indeed faster than using Dijkstra's, but has the effect of not necessarily producing the same paths. Another thing to note is that in this implementation of A*, the potentials are computed using 4-connected grid squares, while the path found by tracing the potential gradient from the goal back to the start uses the same grid in an 8-connected fashion. Thus, the actual path found may not be fully optimal in an 8-connected sense. (Also, no visited-state set is tracked while computing potentials, as in a more typical A* implementation, because such is unnecessary for 4-connected grids). To see the differences between the behavior of Dijkstra's and the behavior of A*, consider the following example.
(机器翻译)
请注意,计算的潜力要少得多(由彩色区域表示)。 这确实比使用 Dijkstra 更快,但效果不一定是产生相同的路径。 需要注意的另一件事是,在 A* 的这个实现中,使用 4 连接网格正方形计算电位,而通过追踪从目标回到起点的电位梯度找到的路径以 8 连接方式使用相同的网格 . 因此,找到的实际路径在 8 连接的意义上可能不是完全最优的。 (此外,在计算势能时没有跟踪访问状态集,就像在更典型的 A* 实现中一样,因为这对于 4 连接网格来说是不必要的)。 要查看 Dijkstra 的行为和 A* 的行为之间的差异,请考虑以下示例。
Dijkstra's
A*
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#include<global_planner/astar.h>
#include<costmap_2d/cost_values.h>
namespace global_planner {
AStarExpansion::AStarExpansion(PotentialCalculator* p_calc, int xs, int ys) :
Expander(p_calc, xs, ys) {
}
bool AStarExpansion::calculatePotentials(unsigned char* costs, double start_x, double start_y, double end_x, double end_y,
int cycles, float* potential) {
queue_.clear();
int start_i = toIndex(start_x, start_y);
queue_.push_back(Index(start_i, 0));
std::fill(potential, potential + ns_, POT_HIGH);
potential[start_i] = 0;
int goal_i = toIndex(end_x, end_y);
int cycle = 0;
while (queue_.size() > 0 && cycle < cycles) {
Index top = queue_[0];
std::pop_heap(queue_.begin(), queue_.end(), greater1());
queue_.pop_back();
int i = top.i;
if (i == goal_i)
return true;
add(costs, potential, potential[i], i + 1, end_x, end_y);
add(costs, potential, potential[i], i - 1, end_x, end_y);
add(costs, potential, potential[i], i + nx_, end_x, end_y);
add(costs, potential, potential[i], i - nx_, end_x, end_y);
cycle++;
}
return false;
}
void AStarExpansion::add(unsigned char* costs, float* potential, float prev_potential, int next_i, int end_x,
int end_y) {
if (next_i < 0 || next_i >= ns_)
return;
if (potential[next_i] < POT_HIGH)
return;
if(costs[next_i]>=lethal_cost_ && !(unknown_ && costs[next_i]==costmap_2d::NO_INFORMATION))
return;
potential[next_i] = p_calc_->calculatePotential(potential, costs[next_i] + neutral_cost_, next_i, prev_potential);
int x = next_i % nx_, y = next_i / nx_;
float distance = abs(end_x - x) + abs(end_y - y);
queue_.push_back(Index(next_i, potential[next_i] + distance * neutral_cost_));
std::push_heap(queue_.begin(), queue_.end(), greater1());
}
} //end namespace global_planner
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