mirror of
https://github.com/zhm-real/PathPlanning.git
synced 2026-08-29 08:34:46 +08:00
zhm-real
403 lines
13 KiB
Python
403 lines
13 KiB
Python
"""
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Batch Informed Trees (BIT*)
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@author: huiming zhou
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"""
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import os
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import sys
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import math
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import random
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import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.patches as patches
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from scipy.spatial.transform import Rotation as Rot
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sys.path.append(os.path.dirname(os.path.abspath(__file__)) +
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"/../../Sampling_based_Planning/")
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from Sampling_based_Planning.rrt_2D import env, plotting, utils
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class Node:
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def __init__(self, x, y):
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self.x = x
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self.y = y
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self.parent = None
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class Tree:
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def __init__(self, x_start, x_goal):
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self.x_start = x_start
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self.goal = x_goal
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self.r = 4.0
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self.V = set()
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self.E = set()
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self.QE = set()
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self.QV = set()
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self.V_old = set()
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class BITStar:
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def __init__(self, x_start, x_goal, eta, iter_max):
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self.x_start = Node(x_start[0], x_start[1])
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self.x_goal = Node(x_goal[0], x_goal[1])
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self.eta = eta
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self.iter_max = iter_max
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self.env = env.Env()
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self.plotting = plotting.Plotting(x_start, x_goal)
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self.utils = utils.Utils()
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self.fig, self.ax = plt.subplots()
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self.delta = self.utils.delta
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self.x_range = self.env.x_range
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self.y_range = self.env.y_range
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self.obs_circle = self.env.obs_circle
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self.obs_rectangle = self.env.obs_rectangle
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self.obs_boundary = self.env.obs_boundary
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self.Tree = Tree(self.x_start, self.x_goal)
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self.X_sample = set()
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self.g_T = dict()
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def init(self):
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self.Tree.V.add(self.x_start)
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self.X_sample.add(self.x_goal)
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self.g_T[self.x_start] = 0.0
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self.g_T[self.x_goal] = np.inf
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cMin, theta = self.calc_dist_and_angle(self.x_start, self.x_goal)
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C = self.RotationToWorldFrame(self.x_start, self.x_goal, cMin)
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xCenter = np.array([[(self.x_start.x + self.x_goal.x) / 2.0],
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[(self.x_start.y + self.x_goal.y) / 2.0], [0.0]])
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return theta, cMin, xCenter, C
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def planning(self):
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theta, cMin, xCenter, C = self.init()
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for k in range(500):
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if not self.Tree.QE and not self.Tree.QV:
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if k == 0:
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m = 350
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else:
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m = 200
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if self.x_goal.parent is not None:
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path_x, path_y = self.ExtractPath()
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plt.plot(path_x, path_y, linewidth=2, color='r')
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plt.pause(0.5)
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self.Prune(self.g_T[self.x_goal])
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self.X_sample.update(self.Sample(m, self.g_T[self.x_goal], cMin, xCenter, C))
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self.Tree.V_old = {v for v in self.Tree.V}
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self.Tree.QV = {v for v in self.Tree.V}
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# self.Tree.r = self.radius(len(self.Tree.V) + len(self.X_sample))
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while self.BestVertexQueueValue() <= self.BestEdgeQueueValue():
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self.ExpandVertex(self.BestInVertexQueue())
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vm, xm = self.BestInEdgeQueue()
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self.Tree.QE.remove((vm, xm))
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if self.g_T[vm] + self.calc_dist(vm, xm) + self.h_estimated(xm) < self.g_T[self.x_goal]:
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actual_cost = self.cost(vm, xm)
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if self.g_estimated(vm) + actual_cost + self.h_estimated(xm) < self.g_T[self.x_goal]:
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if self.g_T[vm] + actual_cost < self.g_T[xm]:
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if xm in self.Tree.V:
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# remove edges
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edge_delete = set()
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for v, x in self.Tree.E:
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if x == xm:
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edge_delete.add((v, x))
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for edge in edge_delete:
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self.Tree.E.remove(edge)
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else:
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self.X_sample.remove(xm)
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self.Tree.V.add(xm)
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self.Tree.QV.add(xm)
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self.g_T[xm] = self.g_T[vm] + actual_cost
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self.Tree.E.add((vm, xm))
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xm.parent = vm
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set_delete = set()
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for v, x in self.Tree.QE:
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if x == xm and self.g_T[v] + self.calc_dist(v, xm) >= self.g_T[xm]:
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set_delete.add((v, x))
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for edge in set_delete:
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self.Tree.QE.remove(edge)
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else:
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self.Tree.QE = set()
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self.Tree.QV = set()
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if k % 5 == 0:
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self.animation(xCenter, self.g_T[self.x_goal], cMin, theta)
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path_x, path_y = self.ExtractPath()
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plt.plot(path_x, path_y, linewidth=2, color='r')
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plt.pause(0.01)
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plt.show()
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def ExtractPath(self):
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node = self.x_goal
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path_x, path_y = [node.x], [node.y]
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while node.parent:
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node = node.parent
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path_x.append(node.x)
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path_y.append(node.y)
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return path_x, path_y
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def Prune(self, cBest):
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self.X_sample = {x for x in self.X_sample if self.f_estimated(x) < cBest}
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self.Tree.V = {v for v in self.Tree.V if self.f_estimated(v) <= cBest}
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self.Tree.E = {(v, w) for v, w in self.Tree.E
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if self.f_estimated(v) <= cBest and self.f_estimated(w) <= cBest}
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self.X_sample.update({v for v in self.Tree.V if self.g_T[v] == np.inf})
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self.Tree.V = {v for v in self.Tree.V if self.g_T[v] < np.inf}
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def cost(self, start, end):
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if self.utils.is_collision(start, end):
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return np.inf
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return self.calc_dist(start, end)
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def f_estimated(self, node):
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return self.g_estimated(node) + self.h_estimated(node)
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def g_estimated(self, node):
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return self.calc_dist(self.x_start, node)
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def h_estimated(self, node):
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return self.calc_dist(node, self.x_goal)
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def Sample(self, m, cMax, cMin, xCenter, C):
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if cMax < np.inf:
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return self.SampleEllipsoid(m, cMax, cMin, xCenter, C)
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else:
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return self.SampleFreeSpace(m)
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def SampleEllipsoid(self, m, cMax, cMin, xCenter, C):
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r = [cMax / 2.0,
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math.sqrt(cMax ** 2 - cMin ** 2) / 2.0,
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math.sqrt(cMax ** 2 - cMin ** 2) / 2.0]
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L = np.diag(r)
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ind = 0
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delta = self.delta
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Sample = set()
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while ind < m:
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xBall = self.SampleUnitNBall()
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x_rand = np.dot(np.dot(C, L), xBall) + xCenter
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node = Node(x_rand[(0, 0)], x_rand[(1, 0)])
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in_obs = self.utils.is_inside_obs(node)
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in_x_range = self.x_range[0] + delta <= node.x <= self.x_range[1] - delta
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in_y_range = self.y_range[0] + delta <= node.y <= self.y_range[1] - delta
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if not in_obs and in_x_range and in_y_range:
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Sample.add(node)
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ind += 1
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return Sample
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def SampleFreeSpace(self, m):
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delta = self.utils.delta
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Sample = set()
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ind = 0
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while ind < m:
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node = Node(random.uniform(self.x_range[0] + delta, self.x_range[1] - delta),
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random.uniform(self.y_range[0] + delta, self.y_range[1] - delta))
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if self.utils.is_inside_obs(node):
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continue
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else:
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Sample.add(node)
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ind += 1
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return Sample
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def radius(self, q):
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cBest = self.g_T[self.x_goal]
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lambda_X = len([1 for v in self.Tree.V if self.f_estimated(v) <= cBest])
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radius = 2 * self.eta * (1.5 * lambda_X / math.pi * math.log(q) / q) ** 0.5
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return radius
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def ExpandVertex(self, v):
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self.Tree.QV.remove(v)
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X_near = {x for x in self.X_sample if self.calc_dist(x, v) <= self.Tree.r}
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for x in X_near:
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if self.g_estimated(v) + self.calc_dist(v, x) + self.h_estimated(x) < self.g_T[self.x_goal]:
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self.g_T[x] = np.inf
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self.Tree.QE.add((v, x))
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if v not in self.Tree.V_old:
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V_near = {w for w in self.Tree.V if self.calc_dist(w, v) <= self.Tree.r}
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for w in V_near:
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if (v, w) not in self.Tree.E and \
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self.g_estimated(v) + self.calc_dist(v, w) + self.h_estimated(w) < self.g_T[self.x_goal] and \
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self.g_T[v] + self.calc_dist(v, w) < self.g_T[w]:
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self.Tree.QE.add((v, w))
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if w not in self.g_T:
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self.g_T[w] = np.inf
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def BestVertexQueueValue(self):
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if not self.Tree.QV:
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return np.inf
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return min(self.g_T[v] + self.h_estimated(v) for v in self.Tree.QV)
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def BestEdgeQueueValue(self):
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if not self.Tree.QE:
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return np.inf
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return min(self.g_T[v] + self.calc_dist(v, x) + self.h_estimated(x)
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for v, x in self.Tree.QE)
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def BestInVertexQueue(self):
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if not self.Tree.QV:
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print("QV is Empty!")
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return None
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v_value = {v: self.g_T[v] + self.h_estimated(v) for v in self.Tree.QV}
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return min(v_value, key=v_value.get)
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def BestInEdgeQueue(self):
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if not self.Tree.QE:
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print("QE is Empty!")
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return None
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e_value = {(v, x): self.g_T[v] + self.calc_dist(v, x) + self.h_estimated(x)
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for v, x in self.Tree.QE}
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return min(e_value, key=e_value.get)
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@staticmethod
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def SampleUnitNBall():
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while True:
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x, y = random.uniform(-1, 1), random.uniform(-1, 1)
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if x ** 2 + y ** 2 < 1:
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return np.array([[x], [y], [0.0]])
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@staticmethod
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def RotationToWorldFrame(x_start, x_goal, L):
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a1 = np.array([[(x_goal.x - x_start.x) / L],
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[(x_goal.y - x_start.y) / L], [0.0]])
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e1 = np.array([[1.0], [0.0], [0.0]])
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M = a1 @ e1.T
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U, _, V_T = np.linalg.svd(M, True, True)
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C = U @ np.diag([1.0, 1.0, np.linalg.det(U) * np.linalg.det(V_T.T)]) @ V_T
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return C
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@staticmethod
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def calc_dist(start, end):
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return math.hypot(start.x - end.x, start.y - end.y)
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@staticmethod
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def calc_dist_and_angle(node_start, node_end):
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dx = node_end.x - node_start.x
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dy = node_end.y - node_start.y
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return math.hypot(dx, dy), math.atan2(dy, dx)
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def animation(self, xCenter, cMax, cMin, theta):
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plt.cla()
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self.plot_grid("Batch Informed Trees (BIT*)")
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plt.gcf().canvas.mpl_connect(
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'key_release_event',
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lambda event: [exit(0) if event.key == 'escape' else None])
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for v in self.X_sample:
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plt.plot(v.x, v.y, marker='.', color='lightgrey', markersize='2')
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if cMax < np.inf:
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self.draw_ellipse(xCenter, cMax, cMin, theta)
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for v, w in self.Tree.E:
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plt.plot([v.x, w.x], [v.y, w.y], '-g')
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plt.pause(0.001)
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def plot_grid(self, name):
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for (ox, oy, w, h) in self.obs_boundary:
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self.ax.add_patch(
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patches.Rectangle(
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(ox, oy), w, h,
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edgecolor='black',
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facecolor='black',
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fill=True
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)
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)
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for (ox, oy, w, h) in self.obs_rectangle:
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self.ax.add_patch(
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patches.Rectangle(
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(ox, oy), w, h,
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edgecolor='black',
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facecolor='gray',
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fill=True
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)
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)
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for (ox, oy, r) in self.obs_circle:
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self.ax.add_patch(
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patches.Circle(
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(ox, oy), r,
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edgecolor='black',
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facecolor='gray',
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fill=True
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)
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)
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plt.plot(self.x_start.x, self.x_start.y, "bs", linewidth=3)
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plt.plot(self.x_goal.x, self.x_goal.y, "rs", linewidth=3)
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plt.title(name)
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plt.axis("equal")
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@staticmethod
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def draw_ellipse(x_center, c_best, dist, theta):
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a = math.sqrt(c_best ** 2 - dist ** 2) / 2.0
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b = c_best / 2.0
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angle = math.pi / 2.0 - theta
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cx = x_center[0]
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cy = x_center[1]
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t = np.arange(0, 2 * math.pi + 0.1, 0.2)
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x = [a * math.cos(it) for it in t]
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y = [b * math.sin(it) for it in t]
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rot = Rot.from_euler('z', -angle).as_dcm()[0:2, 0:2]
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fx = rot @ np.array([x, y])
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px = np.array(fx[0, :] + cx).flatten()
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py = np.array(fx[1, :] + cy).flatten()
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plt.plot(cx, cy, marker='.', color='darkorange')
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plt.plot(px, py, linestyle='--', color='darkorange', linewidth=2)
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def main():
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x_start = (18, 8) # Starting node
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x_goal = (37, 18) # Goal node
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eta = 2
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iter_max = 200
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print("start!!!")
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bit = BITStar(x_start, x_goal, eta, iter_max)
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# bit.animation("Batch Informed Trees (BIT*)")
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bit.planning()
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if __name__ == '__main__':
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main()
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