def __init__(self, resolution=1):
        self.Alldirec = {(1, 0, 0): 1, (0, 1, 0): 1, (0, 0, 1): 1, \
                        (-1, 0, 0): 1, (0, -1, 0): 1, (0, 0, -1): 1, \
                        (1, 1, 0): np.sqrt(2), (1, 0, 1): np.sqrt(2), (0, 1, 1): np.sqrt(2), \
                        (-1, -1, 0): np.sqrt(2), (-1, 0, -1): np.sqrt(2), (0, -1, -1): np.sqrt(2), \
                        (1, -1, 0): np.sqrt(2), (-1, 1, 0): np.sqrt(2), (1, 0, -1): np.sqrt(2), \
                        (-1, 0, 1): np.sqrt(2), (0, 1, -1): np.sqrt(2), (0, -1, 1): np.sqrt(2), \
                        (1, 1, 1): np.sqrt(3), (-1, -1, -1) : np.sqrt(3), \
                        (1, -1, -1): np.sqrt(3), (-1, 1, -1): np.sqrt(3), (-1, -1, 1): np.sqrt(3), \
                        (1, 1, -1): np.sqrt(3), (1, -1, 1): np.sqrt(3), (-1, 1, 1): np.sqrt(3)}
        self.env = env(resolution=resolution)
        #self.X = StateSpace(self.env)
        #self.x0, self.xt = getNearest(self.X, self.env.start), getNearest(self.X, self.env.goal)
        self.settings = 'CollisionChecking'  # for collision checking
        self.x0, self.xt = tuple(self.env.start), tuple(self.env.goal)
        # self.OPEN = queue.QueuePrior()
        self.OPEN = queue.MinheapPQ()
        self.km = 0
        self.g = {}  # all g initialized at inf
        self.rhs = {self.xt: 0}  # rhs(x0) = 0
        self.h = {}
        self.OPEN.put(self.xt, self.CalculateKey(self.xt))
        self.CLOSED = set()

        # init children set:
        self.CHILDREN = {}
        # init Cost set
        self.COST = defaultdict(lambda: defaultdict(dict))

        # for visualization
        self.V = set()  # vertice in closed
        self.ind = 0
        self.Path = []
        self.done = False
    def __init__(self, resolution=1):
        self.Alldirec = {(1, 0, 0): 1, (0, 1, 0): 1, (0, 0, 1): 1, \
                         (-1, 0, 0): 1, (0, -1, 0): 1, (0, 0, -1): 1, \
                         (1, 1, 0): np.sqrt(2), (1, 0, 1): np.sqrt(2), (0, 1, 1): np.sqrt(2), \
                         (-1, -1, 0): np.sqrt(2), (-1, 0, -1): np.sqrt(2), (0, -1, -1): np.sqrt(2), \
                         (1, -1, 0): np.sqrt(2), (-1, 1, 0): np.sqrt(2), (1, 0, -1): np.sqrt(2), \
                         (-1, 0, 1): np.sqrt(2), (0, 1, -1): np.sqrt(2), (0, -1, 1): np.sqrt(2), \
                         (1, 1, 1): np.sqrt(3), (-1, -1, -1): np.sqrt(3), \
                         (1, -1, -1): np.sqrt(3), (-1, 1, -1): np.sqrt(3), (-1, -1, 1): np.sqrt(3), \
                         (1, 1, -1): np.sqrt(3), (1, -1, 1): np.sqrt(3), (-1, 1, 1): np.sqrt(3)}
        self.env = env(resolution=resolution)
        self.settings = 'CollisionChecking'  # for collision checking
        self.x0, self.xt = tuple(self.env.start), tuple(self.env.goal)
        self.OPEN = queue.MinheapPQ()
        self.g = {}  # all g initialized at inf
        self.h = {}
        self.rhs = {self.xt: 0}  # rhs(x0) = 0
        self.OPEN.put(self.xt, self.key(self.xt))
        self.INCONS = set()
        self.CLOSED = set()

        # init children set:
        self.CHILDREN = {}
        # init Cost set
        self.COST = defaultdict(lambda: defaultdict(dict))

        # for visualization
        self.V = set()  # vertice in closed
        self.ind = 0
        self.Path = []
        self.done = False

        # epsilon in the key caculation
        self.epsilon = 1
        self.increment = 0.1
        self.decrement = 0.2