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adding informed rrt star

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Karan
2018-06-07 18:27:37 -05:00
parent 1226325063
commit 9e93192879
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PathPlanning/InformedRRTStar/informed_rrt_star.py Normal file
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'''
Author: Karan Chawla
7th June, '18
Reference: https://arxiv.org/pdf/1404.2334.pdf
'''
import random
import numpy as np
import math
import copy
import matplotlib.pyplot as plt
show_animation = True
class InformedRRTStar():
def __init__(self, start, goal, obstacleList, randArea, expandDis=0.5, goalSampleRate=10, maxIter=200):
self.start = Node(start[0], start[1])
self.goal = Node(goal[0], goal[1])
self.minrand = randArea[0]
self.maxrand = randArea[1]
self.expandDis = expandDis
self.goalSampleRate = goalSampleRate
self.maxIter = maxIter
self.obstacleList = obstacleList
def InformedRRTStarSearch(self, animation=True):
self.nodeList = [self.start]
# max length we expect to find in our 'informed' sample space, starts as infinite
cBest = float('inf')
pathLen = float('inf')
treeSize = 0
pathSize = 0
solutionSet = set()
path = None
# Computing the sampling space
cMin = math.sqrt(pow(self.start.x - self.goal.x, 2) + pow(self.start.y - self.goal.y, 2))
xCenter = np.matrix([[(self.start.x + self.goal.x) / 2.0], [(self.start.y + self.goal.y) / 2.0], [0]])
a1 = np.matrix([[(self.goal.x - self.start.x) / cMin], [(self.goal.y - self.start.y) / cMin], [0]])
id1_t = np.matrix([1.0, 0.0, 0.0]) # first column of idenity matrix transposed
M = np.dot(a1 , id1_t)
U, S, Vh = np.linalg.svd(M, 1, 1)
C = np.dot(np.dot(U, np.diag([1.0, 1.0, np.linalg.det(U) * np.linalg.det(np.transpose(Vh))])), Vh)
for i in range(self.maxIter):
# Sample space is defined by cBest
# cMin is the minimum distance between the start point and the goal
# xCenter is the midpoint between the start and the goal
# cBest changes when a new path is found
rnd = self.sample(cBest, cMin, xCenter, C)
nind = self.getNearestListIndex(self.nodeList, rnd)
nearestNode = self.nodeList[nind]
# steer
theta = math.atan2(rnd[1] - nearestNode.y, rnd[0] - nearestNode.x)
newNode = self.getNewNode(theta, nind, nearestNode)
d = self.lineCost(nearestNode, newNode)
if self.__CollisionCheck(newNode, self.obstacleList) and self.check_collision_extend(nearestNode, theta, d):
nearInds = self.findNearNodes(newNode)
newNode = self.chooseParent(newNode, nearInds)
self.nodeList.append(newNode)
self.rewire(newNode, nearInds)
if self.isNearGoal(newNode):
solutionSet.add(newNode)
lastIndex = len(self.nodeList) -1
tempPath = self.getFinalCourse(lastIndex)
tempPathLen = self.getPathLen(tempPath)
if tempPathLen < pathLen:
path = tempPath
cBest = tempPathLen
if animation:
self.drawGraph(rnd)
return path
def chooseParent(self, newNode, nearInds):
if len(nearInds) == 0:
return newNode
dList = []
for i in nearInds:
dx = newNode.x - self.nodeList[i].x
dy = newNode.y - self.nodeList[i].y
d = math.sqrt(dx ** 2 + dy ** 2)
theta = math.atan2(dy, dx)
if self.check_collision_extend(self.nodeList[i], theta, d):
dList.append(self.nodeList[i].cost + d)
else:
dList.append(float('inf'))
minCost = min(dList)
minInd = nearInds[dList.index(minCost)]
if minCost == float('inf'):
print("mincost is inf")
return newNode
newNode.cost = minCost
newNode.parent = minInd
return newNode
def findNearNodes(self, newNode):
nnode = len(self.nodeList)
r = 50.0 * math.sqrt((math.log(nnode) / nnode))
dlist = [(node.x - newNode.x) ** 2 +
(node.y - newNode.y) ** 2 for node in self.nodeList]
nearinds = [dlist.index(i) for i in dlist if i <= r ** 2]
return nearinds
def sample(self, cMax, cMin, xCenter, C):
if cMax < float('inf'):
r = [cMax /2.0, math.sqrt(cMax**2 - cMin**2)/2.0,
math.sqrt(cMax**2 - cMin**2)/2.0]
L = np.diag(r)
xBall = self.sampleUnitBall()
rnd = np.dot(np.dot(C, L), xBall) + xCenter
rnd = [rnd[(0,0)], rnd[(1,0)]]
else:
rnd = self.sampleFreeSpace()
return rnd
def sampleUnitBall(self):
a = random.random()
b = random.random()
if b < a:
a, b = b, a
sample = (b * math.cos(2 * math.pi * a / b),
b * math.sin(2 * math.pi * a / b))
return np.array([[sample[0]], [sample[1]], [0]])
def sampleFreeSpace(self):
if random.randint(0,100) > self.goalSampleRate:
rnd = [random.uniform(self.minrand, self.maxrand),
random.uniform(self.minrand, self.maxrand)]
else:
rnd = [self.goal.x, self.goal.y]
return rnd
def getPathLen(self, path):
pathLen = 0
for i in range(1, len(path)):
node1_x = path[i][0]
node1_y = path[i][1]
node2_x = path[i-1][0]
node2_y = path[i-1][1]
pathLen += math.sqrt((node1_x - node2_x)**2 + (node1_y - node2_y)**2)
return pathLen
def lineCost(self, node1, node2):
return math.sqrt((node1.x - node2.x)**2 + (node1.y - node2.y)**2)
def getNearestListIndex(self, nodes, rnd):
dList = [(node.x - rnd[0])**2 +
(node.y - rnd[1])**2 for node in nodes]
minIndex = dList.index(min(dList))
return minIndex
def __CollisionCheck(self, newNode, obstacleList):
for (ox, oy, size) in obstacleList:
dx = ox - newNode.x
dy = oy - newNode.y
d = dx * dx + dy * dy
if d <= 1.1 * size**2:
return False #collision
return True # safe
def getNewNode(self, theta, nind, nearestNode):
newNode = copy.deepcopy(nearestNode)
newNode.x += self.expandDis * math.cos(theta)
newNode.y += self.expandDis * math.sin(theta)
newNode.cost += self.expandDis
newNode.parent = nind
return newNode
def isNearGoal(self, node):
d = self.lineCost(node, self.goal)
if d < self.expandDis:
return True
return False
def rewire(self, newNode, nearInds):
nnode = len(self.nodeList)
for i in nearInds:
nearNode = self.nodeList[i]
d = math.sqrt((nearNode.x - newNode.x)**2 +
(nearNode.y - newNode.y)**2)
scost = newNode.cost + d
if nearNode.cost > scost:
theta = math.atan2(newNode.y - nearNode.y ,
newNode.x - nearNode.x)
if self.check_collision_extend(nearNode, theta, d):
nearNode.parent = nnode - 1
nearNode.cost = scost
def check_collision_extend(self, nearNode, theta, d):
tmpNode = copy.deepcopy(nearNode)
for i in range(int(d / self.expandDis)):
tmpNode.x += self.expandDis * math.cos(theta)
tmpNode.y += self.expandDis * math.sin(theta)
if not self.__CollisionCheck(tmpNode, self.obstacleList):
return False
return True
def getFinalCourse(self, lastIndex):
path = [[self.goal.x, self.goal.y]]
while self.nodeList[lastIndex].parent is not None:
node = self.nodeList[lastIndex]
path.append([node.x, node.y])
lastIndex = node.parent
path.append([self.start.x, self.start.y])
return path
##################################################################################
def drawGraph(self, rnd=None):
plt.clf()
if rnd is not None:
plt.plot(rnd[0], rnd[1], "^k")
for node in self.nodeList:
if node.parent is not None:
if node.x or node.y is not None:
plt.plot([node.x, self.nodeList[node.parent].x], [
node.y, self.nodeList[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.goal.x, self.goal.y, "xr")
plt.axis([-2, 15, -2, 15])
plt.grid(True)
plt.pause(0.01)
class Node():
def __init__(self, x, y):
self.x = x
self.y = y
self.cost = 0.0
self.parent = None
def main():
print("Start informed rrt star planning")
# create obstacles
obstacleList = [
(5, 5, 0.5),
(9, 6, 1),
(7, 5, 1),
(1, 5, 1),
(3, 6, 1),
(7, 9, 1)
]
# Set params
rrt = InformedRRTStar(start = [0, 0], goal = [5, 10],
randArea = [-2, 15], obstacleList = obstacleList)
path = rrt.InformedRRTStarSearch(animation = show_animation)
# Plot path
if show_animation:
rrt.drawGraph()
plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
plt.grid(True)
plt.pause(0.01)
plt.show()
if __name__ == '__main__':
main()