路径规划—PRM(Probabilistic Road Map)

一、原理：

Probabilistic Road Map, 分为两个过程

Learning phase和Query phase.

Learning phase（学习阶段）:

1. Sample N points in C-space.（在空间内撒N个点）

2. Delete points that are not collision-free.（删掉在障碍物上的点）

3. Connect to nearest points and get collision-free segments.（最近的几个点之间连线，距离太远的点之间不连线如红色线，距离提前规定相距多远的点之间连线）

4. Delete segments that are not collision free.（删除连线过障碍物的边如绿线）

Query phase（查询阶段）:

1. Search on the road map to find a path from the start to the goal(using Dijkstra‘s algorithm or the A* algorithm).
   （使用A*、Dijkstra等算法进行路径查询）
2. Road map is now similar with the grid map(or a simplified grid map).

二、优缺点：

优势：

概率完备；不用在整个环境搜索，简化了环境，相对于A*更加高效

劣势：

Required to solve 2 point boundary value problem.

Build graph over state space but no particular focus on generating a path.

Not efficient.

改进方法：Lazy collision-checking

一、基本思想：

Collision-checking process is time-consuming, especially in complex or high-dimensional environments.
So sample points and generates segments without considering the collision.

二、流程：

1.Find a path on the road map generated without collision-checking.（在地图上不使用障碍物碰撞检测的方式寻找一个路径）

2. Delete the corresponding edges and nodes if the path is not collision free.
（如果路径不是无碰撞的，则删除发生碰撞的边和节点。）

3. Restart path finding.