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。