“D* Lite”(D星Lite)是一种用于动态环境中路径规划的增量式搜索算法。它旨在在已知地图上解决由动态环境变化引起的路径规划问题。下面是一个简单的示例Python代码,展示了D* Lite算法的基本实现:
import heapq
class Cell:
def __init__(self, x, y):
self.x = x
self.y = y
self.g = float('inf') # 到达该细胞的成本
self.rhs = float('inf') # 启发式成本
self.parent = None
def __lt__(self, other):
return (self.g, self.rhs) < (other.g, other.rhs)
class DStarLite:
def __init__(self, grid, start, goal):
self.grid = grid
self.start = start
self.goal = goal
self.km = 0 # 估算的最短路径长度
self.cells = {} # 存储细胞信息
self.open_list = [] # 存储待扩展的细胞
def heuristic(self, cell):
# 启发式函数,例如使用欧几里得距离
return abs(cell.x - self.goal[0]) + abs(cell.y - self.goal[1])
def initialize(self):
# 初始化网格
for x in range(len(self.grid)):
for y in range(len(self.grid[0])):
if self.grid[x][y] != 1:
self.cells[(x, y)] = Cell(x, y)
self.cells[self.goal].rhs = 0
heapq.heappush(self.open_list, self.cells[self.goal])
def update_vertex(self, u):
# 更新细胞u的启发式成本
if u != self.goal:
min_rhs = min((self.cells[(x, y)].g + self.cost(u, (x, y)) for x, y in self.neighbors(u)))
self.cells[u].rhs = min_rhs
if self.cells[u] in self.open_list:
self.open_list.remove(self.cells[u])
if self.cells[u].g != self.cells[u].rhs:
heapq.heappush(self.open_list, self.cells[u])
def compute_shortest_path(self):
while self.open_list and (self.open_list[0].g < self.heuristic(self.start) or self.cells[self.start].rhs != self.cells[self.start].g):
u = heapq.heappop(self.open_list)
if u.g > u.rhs:
u.g = u.rhs
for pred in self.predecessors(u):
self.update_vertex(pred)
else:
u.g = float('inf')
self.update_vertex(u)
for pred in self.predecessors(u):
self.update_vertex(pred)
def predecessors(self, cell):
# 获取细胞的前驱细胞
x, y = cell.x, cell.y
preds = [(x-1, y), (x+1, y), (x, y-1), (x, y+1)]
return [p for p in preds if p in self.cells]
def neighbors(self, cell):
# 获取细胞的邻居细胞
x, y = cell.x, cell.y
neighbors = [(x-1, y), (x+1, y), (x, y-1), (x, y+1)]
return [n for n in neighbors if n in self.cells and self.grid[n[0]][n[1]] != 1]
def cost(self, u, v):
# 计算细胞u到细胞v的成本
return 1 if self.grid[v[0]][v[1]] != 1 else float('inf')
def replan(self):
# 重新规划路径
while self.start != self.goal:
self.compute_shortest_path()
min_rhs = min((self.cells[(x, y)].g + self.cost(self.start, (x, y)) for x, y in self.neighbors(self.start)))
self.km += self.heuristic(self.start)
self.start = min((self.neighbors(self.start), key=lambda n: self.cells[n].g + self.cost(self.start, n)))
if min_rhs == float('inf'):
break
# 示例用法
grid = [[0, 0, 0, 0, 0],
[0, 1, 1, 0, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0]]
start = (0, 0)
goal = (3, 4)
d_star_lite = DStarLite(grid, start, goal)
d_star_lite.initialize()
d_star_lite.compute_shortest_path()
d_star_lite.replan()
以上是一个简单的D* Lite算法的实现示例。在实际应用中,你可能需要根据具体的情况进行更改和优化。