■Rapidly-exploring random tree(PythonRobotics)
＊コード参考サイト
！！！PythonRobotics！！！
https://github.com/AtsushiSakai/PythonRobotics/tree/master/PathPlanning/RRT
🔸こちらのGitHub参考にしております。ものすごく良いコードがたくさんあるので、ぜひ覗いてみては、、、
🔸RRTのアルゴリズムの説明。
私のサイト：RRTアルゴリズム
https://meerobots.blogspot.com/2019/07/rapidly-exploring-random-treerrt.html
【Pythonコード説明】
説明の流れ
１．全体コード
２．メイン文
３．ＲＲＴのコード
ざっくり書いてます。少しでも参考になれば、、、また何かご指摘があれば宜しくお願い致します。
■注意
現在コード修正中なようです！！！！お気を付けください。
A1．コード全体
rrt.py
"""
Path planning Sample Code with Randomized Rapidly-Exploring Random Trees (RRT)
author: AtsushiSakai(@Atsushi_twi)
"""
import math
import random
import matplotlib.pyplot as plt
show_animation = True
class RRT:
"""
Class for RRT planning
"""
class Node():
"""
RRT Node
"""
def __init__(self, x, y):
self.x = x
self.y = y
self.parent = None
def __init__(self, start, goal, obstacle_list,
rand_area, expand_dis=1.0, goal_sample_rate=5, max_iter=500):
"""
Setting Parameter
start:Start Position [x,y]
goal:Goal Position [x,y]
obstacleList:obstacle Positions [[x,y,size],...]
randArea:Ramdom Samping Area [min,max]
"""
self.start = self.Node(start[0], start[1])
self.end = self.Node(goal[0], goal[1])
self.min_rand = rand_area[0]
self.max_rand = rand_area[1]
self.expand_dis = expand_dis
self.goal_sample_rate = goal_sample_rate
self.max_iter = max_iter
self.obstacleList = obstacle_list
self.node_list = []
def planning(self, animation=True):
"""
rrt path planning
animation: flag for animation on or off
"""
self.node_list = [self.start]
for i in range(self.max_iter):
rnd = self.get_random_point()
nearest_ind = self.get_nearest_list_index(self.node_list, rnd)
nearest_node = self.node_list[nearest_ind]
new_node = self.steer(rnd, nearest_node)
new_node.parent = nearest_node
if not self.check_collision(new_node, self.obstacleList):
continue
self.node_list.append(new_node)
print("nNodelist:", len(self.node_list))
# check goal
if self.calc_dist_to_goal(new_node.x, new_node.y) <= self.expand_dis:
print("Goal!!")
return self.generate_final_course(len(self.node_list) - 1)
if animation and i % 5:
self.draw_graph(rnd)
return None # cannot find path
def steer(self, rnd, nearest_node):
new_node = self.Node(rnd[0], rnd[1])
d, theta = self.calc_distance_and_angle(nearest_node, new_node)
if d > self.expand_dis:
new_node.x = nearest_node.x + self.expand_dis * math.cos(theta)
new_node.y = nearest_node.y + self.expand_dis * math.sin(theta)
return new_node
def generate_final_course(self, goal_ind):
path = [[self.end.x, self.end.y]]
node = self.node_list[goal_ind]
while node.parent is not None:
path.append([node.x, node.y])
node = node.parent
path.append([node.x, node.y])
return path
def calc_dist_to_goal(self, x, y):
dx = x - self.end.x
dy = y - self.end.y
return math.sqrt(dx ** 2 + dy ** 2)
def get_random_point(self):
if random.randint(0, 100) > self.goal_sample_rate:
rnd = [random.uniform(self.min_rand, self.max_rand),
random.uniform(self.min_rand, self.max_rand)]
else: # goal point sampling
rnd = [self.end.x, self.end.y]
return rnd
def draw_graph(self, rnd=None):
plt.clf()
if rnd is not None:
plt.plot(rnd[0], rnd[1], "^k")
for node in self.node_list:
if node.parent:
plt.plot([node.x, node.parent.x],
[node.y, node.parent.y],
"-g")
for (ox, oy, size) in self.obstacleList:
plt.plot(ox, oy, "ok", ms=30 * size)
plt.plot(self.start.x, self.start.y, "xr")
plt.plot(self.end.x, self.end.y, "xr")
plt.axis([-2, 15, -2, 15])
plt.grid(True)
plt.pause(0.01)
@staticmethod
def get_nearest_list_index(node_list, rnd):
dlist = [(node.x - rnd[0]) ** 2 + (node.y - rnd[1])
** 2 for node in node_list]
minind = dlist.index(min(dlist))
return minind
@staticmethod
def check_collision(node, obstacleList):
for (ox, oy, size) in obstacleList:
dx = ox - node.x
dy = oy - node.y
d = dx * dx + dy * dy
if d <= size ** 2:
return False # collision
return True # safe
@staticmethod
def calc_distance_and_angle(from_node, to_node):
dx = to_node.x - from_node.x
dy = to_node.y - from_node.y
d = math.sqrt(dx ** 2 + dy ** 2)
theta = math.atan2(dy, dx)
return d, theta
def main(gx=5.0, gy=10.0):
print("start " + __file__)
# ====Search Path with RRT====
obstacleList = [
(5, 5, 1),
(3, 6, 2),
(3, 8, 2),
(3, 10, 2),
(7, 5, 2),
(9, 5, 2)
] # [x,y,size]
# Set Initial parameters
rrt = RRT(start=[0, 0],
goal=[gx, gy],
rand_area=[-2, 15],
obstacle_list=obstacleList)
path = rrt.planning(animation=show_animation)
if path is None:
print("Cannot find path")
else:
print("found path!!")
# Draw final path
if show_animation:
rrt.draw_graph()
plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
plt.grid(True)
plt.pause(0.01) # Need for Mac
plt.show()
if __name__ == '__main__':
main()
B1. メイン文
1 : スタート、ゴール、障害物の位置、設定
2 : RRT実行
rrt.py
def main(gx=5.0, gy=10.0):
print("start " + __file__)
# ====Search Path with RRT====
obstacleList = [
(5, 5, 1),
(3, 6, 2),
(3, 8, 2),
(3, 10, 2),
(7, 5, 2),
(9, 5, 2)
] # [x,y,size]
# Set Initial parameters
rrt = RRT(start=[0, 0],
goal=[gx, gy],
rand_area=[-2, 15],
obstacle_list=obstacleList)
path = rrt.planning(animation=show_animation)
if path is None:
print("Cannot find path")
else:
print("found path!!")
# Draw final path
if show_animation:
rrt.draw_graph()
plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
plt.grid(True)
plt.pause(0.01) # Need for Mac
plt.show()
if __name__ == '__main__':
main()
C1．変数定義：位置XY
rrt.py
class RRT:
"""
Class for RRT planning
"""
class Node():
"""
RRT Node
"""
def __init__(self, x, y):
self.x = x
self.y = y
self.parent = None
C2．定義：スタート、ゴール、障害物（位置とサイズ）、ゴール選ぶ割合、ノードのバス距離、
rrt.py
def __init__(self, start, goal, obstacle_list,
rand_area, expand_dis=1.0, goal_sample_rate=5, max_iter=500):
"""
Setting Parameter
start:Start Position [x,y]
goal:Goal Position [x,y]
obstacleList:obstacle Positions [[x,y,size],...]
randArea:Ramdom Samping Area [min,max]
"""
self.start = self.Node(start[0], start[1])
self.end = self.Node(goal[0], goal[1])
self.min_rand = rand_area[0]
self.max_rand = rand_area[1]
self.expand_dis = expand_dis
self.goal_sample_rate = goal_sample_rate
self.max_iter = max_iter
self.obstacleList = obstacle_list
self.node_list = []
C3．アニメーション用データ
rrt.py
def planning(self, animation=True):
"""
rrt path planning
animation: flag for animation on or off
"""
self.node_list = [self.start]
for i in range(self.max_iter):
rnd = self.get_random_point()
nearest_ind = self.get_nearest_list_index(self.node_list, rnd)
nearest_node = self.node_list[nearest_ind]
new_node = self.steer(rnd, nearest_node)
new_node.parent = nearest_node
if not self.check_collision(new_node, self.obstacleList):
continue
self.node_list.append(new_node)
print("nNodelist:", len(self.node_list))
# check goal
if self.calc_dist_to_goal(new_node.x, new_node.y) <= self.expand_dis:
print("Goal!!")
return self.generate_final_course(len(self.node_list) - 1)
if animation and i % 5:
self.draw_graph(rnd)
return None # cannot find path
C4．現在の位置とランダム位置との関係から新しい位置を計算
rrt.py
def steer(self, rnd, nearest_node):
new_node = self.Node(rnd[0], rnd[1])
d, theta = self.calc_distance_and_angle(nearest_node, new_node)
if d > self.expand_dis:
new_node.x = nearest_node.x + self.expand_dis * math.cos(theta)
new_node.y = nearest_node.y + self.expand_dis * math.sin(theta)
return new_node
C5．コース結果？
rrt.py
def generate_final_course(self, goal_ind):
path = [[self.end.x, self.end.y]]
node = self.node_list[goal_ind]
while node.parent is not None:
path.append([node.x, node.y])
node = node.parent
path.append([node.x, node.y])
return path
C6．ゴールまでの距離計算
rrt.py
def calc_dist_to_goal(self, x, y):
dx = x - self.end.x
dy = y - self.end.y
return math.sqrt(dx ** 2 + dy ** 2)
C7．ランダム位置生成 任意の回数後ゴール地点選ぶ
rrt.py
def get_random_point(self):
if random.randint(0, 100) > self.goal_sample_rate:
rnd = [random.uniform(self.min_rand, self.max_rand),
random.uniform(self.min_rand, self.max_rand)]
else: # goal point sampling
rnd = [self.end.x, self.end.y]
return rnd
C8．グラフ生成
rrt.py
def draw_graph(self, rnd=None):
plt.clf()
if rnd is not None:
plt.plot(rnd[0], rnd[1], "^k")
for node in self.node_list:
if node.parent:
plt.plot([node.x, node.parent.x],
[node.y, node.parent.y],
"-g")
for (ox, oy, size) in self.obstacleList:
plt.plot(ox, oy, "ok", ms=30 * size)
plt.plot(self.start.x, self.start.y, "xr")
plt.plot(self.end.x, self.end.y, "xr")
plt.axis([-2, 15, -2, 15])
plt.grid(True)
plt.pause(0.01)
C9．ランダム点から近い点を探索
rrt.py
@staticmethod
def get_nearest_list_index(node_list, rnd):
dlist = [(node.x - rnd[0]) ** 2 + (node.y - rnd[1])
** 2 for node in node_list]
minind = dlist.index(min(dlist))
return minind
C10．衝突判定：この方法では点で見ている。
・障害物の位置と次の位置のから距離ｄ算出
・障害物を円として定義し、距離ｄが半径より小さいと衝突
rrt.py
@staticmethod
def check_collision(node, obstacleList):
for (ox, oy, size) in obstacleList:
dx = ox - node.x
dy = oy - node.y
d = dx * dx + dy * dy
if d <= size ** 2:
return False # collision
return True # safe
C11．今の位置からランダム位置の距離と角度を算出
次の位置を計算するため
rrt.py
@staticmethod
def calc_distance_and_angle(from_node, to_node):
dx = to_node.x - from_node.x
dy = to_node.y - from_node.y
d = math.sqrt(dx ** 2 + dy ** 2)
theta = math.atan2(dy, dx)
return d, theta
これにて終了！
最適性は担保してないけど、簡単に実装できそう。。。