A*作为最常用的路径搜索算法，值得我们去深刻的研究。路径规划项目。先看一下维基百科给的算法解释：https://en.wikipedia.org/wiki/A*_search_algorithm

A *是最佳优先搜索它通过在解决方案的所有可能路径（目标）中搜索导致成本最小（行进距离最短，时间最短等）的问题来解决问题。 ），并且在这些路径中，它首先考虑那些似乎最快速地引导到解决方案的路径。它是根据加权图制定的：从图的特定节点开始，它构造从该节点开始的路径树，一次一步地扩展路径，直到其一个路径在预定目标节点处结束。

在其主循环的每次迭代中，A *需要确定将其部分路径中的哪些扩展为一个或多个更长的路径。它是基于成本（总重量）的估计仍然到达目标节点。具体而言，A *选择最小化的路径

F（N）= G（N）+ H（n）

其中n是路径上的最后一个节点，g（n）是从起始节点到n的路径的开销，h（n）是一个启发式，用于估计从n到目标的最便宜路径的开销。启发式是特定于问题的。为了找到实际最短路径的算法，启发函数必须是可接受的，这意味着它永远不会高估实际成本到达最近的目标节点。

维基百科给出的伪代码：

function A*(start, goal) // The set of nodes already evaluated closedSet := {} // The set of currently discovered nodes that are not evaluated yet. // Initially, only the start node is known. openSet := {start} // For each node, which node it can most efficiently be reached from. // If a node can be reached from many nodes, cameFrom will eventually contain the // most efficient previous step. cameFrom := an empty map // For each node, the cost of getting from the start node to that node. gScore := map with default value of Infinity // The cost of going from start to start is zero. gScore[start] := 0 // For each node, the total cost of getting from the start node to the goal // by passing by that node. That value is partly known, partly heuristic. fScore := map with default value of Infinity // For the first node, that value is completely heuristic. fScore[start] := heuristic_cost_estimate(start, goal) while openSet is not empty current := the node in openSet having the lowest fScore[] value if current = goal return reconstruct_path(cameFrom, current) openSet.Remove(current) closedSet.Add(current) for each neighbor of current if neighbor in closedSet continue // Ignore the neighbor which is already evaluated. if neighbor not in openSet // Discover a new node openSet.Add(neighbor) // The distance from start to a neighbor //the "dist_between" function may vary as per the solution requirements. tentative_gScore := gScore[current] + dist_between(current, neighbor) if tentative_gScore >= gScore[neighbor] continue // This is not a better path. // This path is the best until now. Record it! cameFrom[neighbor] := current gScore[neighbor] := tentative_gScore fScore[neighbor] := gScore[neighbor] + heuristic_cost_estimate(neighbor, goal) return failurefunction reconstruct_path(cameFrom, current) total_path := {current} while current in cameFrom.Keys: current := cameFrom[current] total_path.append(current) return total_path

下面是UDACITY课程中路径规划项目，结合上面的伪代码，用python 实现A*

import mathdef shortest_path(M,start,goal): sx=M.intersections[start][0] sy=M.intersections[start][1] gx=M.intersections[goal][0] gy=M.intersections[goal][1] h=math.sqrt((sx-gx)*(sx-gx)+(sy-gy)*(sy-gy)) closedSet=set() openSet=set() openSet.add(start) gScore={} gScore[start]=0 fScore={} fScore[start]=h cameFrom={} sumg=0 NEW=0 BOOL=False while len(openSet)!=0: MAX=1000 for new in openSet: print("new",new) if fScore[new]<MAX: MAX=fScore[new] #print("MAX=",MAX) NEW=new current=NEW print("current=",current) if current==goal: return reconstruct_path(cameFrom,current) openSet.remove(current) closedSet.add(current) #dafult=M.roads(current) for neighbor in M.roads[current]: BOOL=False print("key=",neighbor) a={neighbor} if len(a&closedSet)>0: continue print("key is not in closeSet") if len(a&openSet)==0: openSet.add(neighbor) else: BOOL=True x= M.intersections[current][0] y= M.intersections[current][1] x1=M.intersections[neighbor][0] y1=M.intersections[neighbor][1] g=math.sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1)) h=math.sqrt((x1-gx)*(x1-gx)+(y1-gy)*(y1-gy)) new_gScore=gScore[current]+g if BOOL==True: if new_gScore>=gScore[neighbor]: continue print("new_gScore",new_gScore) cameFrom[neighbor]=current gScore[neighbor]=new_gScore fScore[neighbor] = new_gScore+h print("fScore",neighbor,"is",new_gScore+h) print("fScore=",new_gScore+h) print("__________++--------------++_________") def reconstruct_path(cameFrom,current): print("已到达lllll") total_path=[] total_path.append(current) for key,value in cameFrom.items(): print("key",key,":","value",value) while current in cameFrom.keys(): current=cameFrom[current] total_path.append(current) total_path=list(reversed(total_path)) return total_path

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