全局路径规划

一、什么是全局路径规划

全局路径规划是指在给定的地图中，通过使用搜索算法和路径规划算法，寻找从起点到目标点的最佳路径，并将其转换为机器人可以遵循的指令序列，使得机器人能够在给定地图上避开障碍物，沿最优路径到达目标点。

全局路径规划通常用于自动驾驶车辆、无人机及移动机器人等领域，在实际应用中起到了重要的作用。

二、全局路径规划的算法

1. Dijkstra算法

Dijkstra算法是一种常见的最短路径搜索算法，适用于无权图或者权值都为正数的图。它以起点为中心向外层层扩展，直到扩展到目标点位置。

def dijkstra(graph, start, end):
    #初始化
    inf = float('inf')
    distance = {vertex: inf for vertex in graph}
    path = {vertex: [] for vertex in graph}
    visited = []
    queue = [start]
    distance[start] = 0

    #搜索
    while queue:
        current = queue.pop(0)
        visited.append(current)
        
        if current == end:
            break
        
        for neighbor in graph[current]:
            if neighbor not in visited:
                new_distance = distance[current] + graph[current][neighbor]
                if new_distance < distance[neighbor]:
                    distance[neighbor] = new_distance
                    path[neighbor] = path[current] + [current]
                queue.append(neighbor)

    return path[end] + [end]

2. A*算法

A*算法结合了Dijkstra算法和启发式函数（Heuristic Function）的思想，在搜索过程中通过评估函数评估某个节点是否为最优解。它适用于连续空间的最短路径规划，具有搜索速度快、路径优秀等优点。

def heuristic(node1, node2):
    #曼哈顿距离
    return abs(node1.x - node2.x) + abs(node1.y - node2.y)

def a_star(start, end):
    #初始化
    open_list = [start]
    closed_list = []
    start.g = 0
    start.f = start.h = heuristic(start, end)
    
    #搜索
    while open_list:
        current = min(open_list, key = lambda x:x.f)
        
        if current == end:
            path = []
            while current.parent != None:
                path.append(current)
                current = current.parent
            path.append(start)
            path.reverse()
            return path

        open_list.remove(current)
        closed_list.append(current)
        
        for neighbor in current.adjacent:
            if neighbor in closed_list:
                continue
            
            if neighbor not in open_list:
                neighbor.g = current.g + heuristic(current, neighbor)
                neighbor.h = heuristic(neighbor, end)
                neighbor.f = neighbor.g + neighbor.h
                neighbor.parent = current
                open_list.append(neighbor)
                
            else:
                new_g = current.g + heuristic(current, neighbor)
                if neighbor.g > new_g:
                    neighbor.g = new_g
                    neighbor.f = neighbor.g + neighbor.h
                    neighbor.parent = current
    return None

三、实例

下面是一个简单的例子，给定一个地图和起点终点，使用A*算法寻找最优路径。

class Node:
    def __init__(self, value, x, y):
        self.value = value
        self.x = x
        self.y = y
        self.adjacent = []
        self.parent = None
        self.f = 0
        self.g = 0
        self.h = 0

def create_graph(grid):
    height = len(grid)
    width = len(grid[0])
    graph = {}
    for i in range(height):
        for j in range(width):
            node = Node(grid[i][j], i, j)
            if i+1 < height and grid[i+1][j] != "#":
                node.adjacent.append(Node(grid[i+1][j], i+1, j))
            if j+1 < width and grid[i][j+1] != "#":
                node.adjacent.append(Node(grid[i][j+1], i, j+1))
            graph[(i, j)] = node
    return graph

grid = [
  ["S", 0, 0, "#"],
  [0, "#", 0, "#"],
  ["#", 0, 0, 0],
  ["#", "#", 0, "E"]
]
graph = create_graph(grid)
start = graph[(0, 0)]
end = graph[(3, 3)]

print(a_star(start, end))

四、总结

全局路径规划是自动驾驶车辆、无人机等移动机器人领域必备的技术之一，Dijkstra算法、A*算法是其中常用的两种算法，它们都可以用来寻找起点到目标点的最短路径。对于不同场景可以根据需要选择不同的算法进行路径规划。