mirror of
https://github.com/AtsushiSakai/PythonRobotics.git
synced 2026-01-13 17:57:55 -05:00
ellipse animation code is added
This commit is contained in:
Atsushi Sakai
@@ -1,261 +1,306 @@
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'''
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Author: Karan Chawla
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7th June, '18
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Reference: https://arxiv.org/pdf/1404.2334.pdf
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'''
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"""
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Informed RRT* path planning
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author: Karan Chawla
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Atsushi Sakai(@Atsushi_twi)
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Reference: Informed RRT*: Optimal Sampling-based Path Planning Focused via
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Direct Sampling of an Admissible Ellipsoidal Heuristichttps://arxiv.org/pdf/1404.2334.pdf
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"""
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import random
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import numpy as np
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import math
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import copy
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import numpy as np
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import math
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import copy
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import matplotlib.pyplot as plt
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show_animation = True
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show_animation = True
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class InformedRRTStar():
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def __init__(self, start, goal, obstacleList, randArea, expandDis=0.5, goalSampleRate=10, maxIter=200):
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def __init__(self, start, goal,
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obstacleList, randArea,
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expandDis=0.5, goalSampleRate=10, maxIter=200):
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self.start = Node(start[0], start[1])
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self.goal = Node(goal[0], goal[1])
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self.minrand = randArea[0]
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self.maxrand = randArea[1]
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self.expandDis = expandDis
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self.goalSampleRate = goalSampleRate
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self.maxIter = maxIter
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self.obstacleList = obstacleList
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self.start = Node(start[0], start[1])
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self.goal = Node(goal[0], goal[1])
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self.minrand = randArea[0]
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self.maxrand = randArea[1]
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self.expandDis = expandDis
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self.goalSampleRate = goalSampleRate
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self.maxIter = maxIter
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self.obstacleList = obstacleList
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def InformedRRTStarSearch(self, animation=True):
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def InformedRRTStarSearch(self, animation=True):
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self.nodeList = [self.start]
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# max length we expect to find in our 'informed' sample space, starts as infinite
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cBest = float('inf')
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pathLen = float('inf')
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treeSize = 0
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pathSize = 0
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solutionSet = set()
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path = None
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self.nodeList = [self.start]
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# max length we expect to find in our 'informed' sample space, starts as infinite
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cBest = float('inf')
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pathLen = float('inf')
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solutionSet = set()
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path = None
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# Computing the sampling space
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cMin = math.sqrt(pow(self.start.x - self.goal.x, 2) + pow(self.start.y - self.goal.y, 2))
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xCenter = np.matrix([[(self.start.x + self.goal.x) / 2.0], [(self.start.y + self.goal.y) / 2.0], [0]])
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a1 = np.matrix([[(self.goal.x - self.start.x) / cMin], [(self.goal.y - self.start.y) / cMin], [0]])
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id1_t = np.matrix([1.0, 0.0, 0.0]) # first column of idenity matrix transposed
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M = np.dot(a1 , id1_t)
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U, S, Vh = np.linalg.svd(M, 1, 1)
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C = np.dot(np.dot(U, np.diag([1.0, 1.0, np.linalg.det(U) * np.linalg.det(np.transpose(Vh))])), Vh)
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for i in range(self.maxIter):
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# Sample space is defined by cBest
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# cMin is the minimum distance between the start point and the goal
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# xCenter is the midpoint between the start and the goal
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# cBest changes when a new path is found
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# Computing the sampling space
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cMin = math.sqrt(pow(self.start.x - self.goal.x, 2) +
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pow(self.start.y - self.goal.y, 2))
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xCenter = np.matrix([[(self.start.x + self.goal.x) / 2.0],
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[(self.start.y + self.goal.y) / 2.0], [0]])
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a1 = np.matrix([[(self.goal.x - self.start.x) / cMin],
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[(self.goal.y - self.start.y) / cMin], [0]])
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etheta = math.atan2(a1[1], a1[0])
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# first column of idenity matrix transposed
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id1_t = np.matrix([1.0, 0.0, 0.0])
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M = np.dot(a1, id1_t)
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U, S, Vh = np.linalg.svd(M, 1, 1)
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C = np.dot(np.dot(U, np.diag(
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[1.0, 1.0, np.linalg.det(U) * np.linalg.det(np.transpose(Vh))])), Vh)
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rnd = self.sample(cBest, cMin, xCenter, C)
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nind = self.getNearestListIndex(self.nodeList, rnd)
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nearestNode = self.nodeList[nind]
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# steer
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theta = math.atan2(rnd[1] - nearestNode.y, rnd[0] - nearestNode.x)
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newNode = self.getNewNode(theta, nind, nearestNode)
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d = self.lineCost(nearestNode, newNode)
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if self.__CollisionCheck(newNode, self.obstacleList) and self.check_collision_extend(nearestNode, theta, d):
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nearInds = self.findNearNodes(newNode)
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newNode = self.chooseParent(newNode, nearInds)
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for i in range(self.maxIter):
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# Sample space is defined by cBest
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# cMin is the minimum distance between the start point and the goal
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# xCenter is the midpoint between the start and the goal
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# cBest changes when a new path is found
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self.nodeList.append(newNode)
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self.rewire(newNode, nearInds)
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rnd = self.informed_sample(cBest, cMin, xCenter, C)
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nind = self.getNearestListIndex(self.nodeList, rnd)
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nearestNode = self.nodeList[nind]
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# steer
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theta = math.atan2(rnd[1] - nearestNode.y, rnd[0] - nearestNode.x)
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newNode = self.getNewNode(theta, nind, nearestNode)
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d = self.lineCost(nearestNode, newNode)
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if self.isNearGoal(newNode):
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solutionSet.add(newNode)
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lastIndex = len(self.nodeList) -1
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tempPath = self.getFinalCourse(lastIndex)
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tempPathLen = self.getPathLen(tempPath)
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if tempPathLen < pathLen:
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path = tempPath
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cBest = tempPathLen
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isCollision = self.__CollisionCheck(newNode, self.obstacleList)
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isCollisionEx = self.check_collision_extend(nearestNode, theta, d)
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if animation:
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self.drawGraph(rnd)
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return path
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if isCollision and isCollisionEx:
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nearInds = self.findNearNodes(newNode)
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newNode = self.chooseParent(newNode, nearInds)
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def chooseParent(self, newNode, nearInds):
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if len(nearInds) == 0:
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return newNode
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self.nodeList.append(newNode)
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self.rewire(newNode, nearInds)
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dList = []
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for i in nearInds:
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dx = newNode.x - self.nodeList[i].x
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dy = newNode.y - self.nodeList[i].y
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d = math.sqrt(dx ** 2 + dy ** 2)
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theta = math.atan2(dy, dx)
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if self.check_collision_extend(self.nodeList[i], theta, d):
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dList.append(self.nodeList[i].cost + d)
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else:
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dList.append(float('inf'))
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if self.isNearGoal(newNode):
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solutionSet.add(newNode)
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lastIndex = len(self.nodeList) - 1
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tempPath = self.getFinalCourse(lastIndex)
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tempPathLen = self.getPathLen(tempPath)
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if tempPathLen < pathLen:
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path = tempPath
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cBest = tempPathLen
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minCost = min(dList)
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minInd = nearInds[dList.index(minCost)]
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if animation:
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self.drawGraph(xCenter=xCenter,
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cBest=cBest, cMin=cMin,
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etheta=etheta, rnd=rnd)
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if minCost == float('inf'):
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print("mincost is inf")
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return newNode
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return path
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newNode.cost = minCost
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newNode.parent = minInd
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def chooseParent(self, newNode, nearInds):
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if len(nearInds) == 0:
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return newNode
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return newNode
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dList = []
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for i in nearInds:
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dx = newNode.x - self.nodeList[i].x
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dy = newNode.y - self.nodeList[i].y
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d = math.sqrt(dx ** 2 + dy ** 2)
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theta = math.atan2(dy, dx)
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if self.check_collision_extend(self.nodeList[i], theta, d):
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dList.append(self.nodeList[i].cost + d)
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else:
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dList.append(float('inf'))
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def findNearNodes(self, newNode):
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nnode = len(self.nodeList)
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r = 50.0 * math.sqrt((math.log(nnode) / nnode))
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dlist = [(node.x - newNode.x) ** 2 +
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(node.y - newNode.y) ** 2 for node in self.nodeList]
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nearinds = [dlist.index(i) for i in dlist if i <= r ** 2]
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return nearinds
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minCost = min(dList)
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minInd = nearInds[dList.index(minCost)]
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def sample(self, cMax, cMin, xCenter, C):
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if cMax < float('inf'):
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r = [cMax /2.0, 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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xBall = self.sampleUnitBall()
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rnd = np.dot(np.dot(C, L), xBall) + xCenter
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rnd = [rnd[(0,0)], rnd[(1,0)]]
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else:
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rnd = self.sampleFreeSpace()
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if minCost == float('inf'):
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print("mincost is inf")
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return newNode
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return rnd
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newNode.cost = minCost
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newNode.parent = minInd
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def sampleUnitBall(self):
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a = random.random()
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b = random.random()
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return newNode
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if b < a:
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a, b = b, a
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def findNearNodes(self, newNode):
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nnode = len(self.nodeList)
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r = 50.0 * math.sqrt((math.log(nnode) / nnode))
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dlist = [(node.x - newNode.x) ** 2 +
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(node.y - newNode.y) ** 2 for node in self.nodeList]
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nearinds = [dlist.index(i) for i in dlist if i <= r ** 2]
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return nearinds
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sample = (b * math.cos(2 * math.pi * a / b),
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b * math.sin(2 * math.pi * a / b))
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return np.array([[sample[0]], [sample[1]], [0]])
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def informed_sample(self, cMax, cMin, xCenter, C):
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if cMax < float('inf'):
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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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xBall = self.sampleUnitBall()
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rnd = np.dot(np.dot(C, L), xBall) + xCenter
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rnd = [rnd[(0, 0)], rnd[(1, 0)]]
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else:
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rnd = self.sampleFreeSpace()
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def sampleFreeSpace(self):
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if random.randint(0,100) > self.goalSampleRate:
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rnd = [random.uniform(self.minrand, self.maxrand),
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random.uniform(self.minrand, self.maxrand)]
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else:
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rnd = [self.goal.x, self.goal.y]
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return rnd
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return rnd
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def sampleUnitBall(self):
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a = random.random()
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b = random.random()
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def getPathLen(self, path):
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pathLen = 0
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for i in range(1, len(path)):
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node1_x = path[i][0]
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node1_y = path[i][1]
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node2_x = path[i-1][0]
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node2_y = path[i-1][1]
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pathLen += math.sqrt((node1_x - node2_x)**2 + (node1_y - node2_y)**2)
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if b < a:
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a, b = b, a
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return pathLen
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sample = (b * math.cos(2 * math.pi * a / b),
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b * math.sin(2 * math.pi * a / b))
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return np.array([[sample[0]], [sample[1]], [0]])
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def lineCost(self, node1, node2):
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return math.sqrt((node1.x - node2.x)**2 + (node1.y - node2.y)**2)
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def sampleFreeSpace(self):
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if random.randint(0, 100) > self.goalSampleRate:
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rnd = [random.uniform(self.minrand, self.maxrand),
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random.uniform(self.minrand, self.maxrand)]
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else:
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rnd = [self.goal.x, self.goal.y]
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def getNearestListIndex(self, nodes, rnd):
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dList = [(node.x - rnd[0])**2 +
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(node.y - rnd[1])**2 for node in nodes]
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minIndex = dList.index(min(dList))
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return minIndex
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return rnd
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def __CollisionCheck(self, newNode, obstacleList):
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for (ox, oy, size) in obstacleList:
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dx = ox - newNode.x
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dy = oy - newNode.y
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d = dx * dx + dy * dy
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if d <= 1.1 * size**2:
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return False #collision
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def getPathLen(self, path):
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pathLen = 0
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for i in range(1, len(path)):
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node1_x = path[i][0]
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node1_y = path[i][1]
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node2_x = path[i - 1][0]
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node2_y = path[i - 1][1]
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pathLen += math.sqrt((node1_x - node2_x) **
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2 + (node1_y - node2_y)**2)
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return True # safe
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return pathLen
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def getNewNode(self, theta, nind, nearestNode):
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newNode = copy.deepcopy(nearestNode)
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def lineCost(self, node1, node2):
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return math.sqrt((node1.x - node2.x)**2 + (node1.y - node2.y)**2)
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newNode.x += self.expandDis * math.cos(theta)
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newNode.y += self.expandDis * math.sin(theta)
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def getNearestListIndex(self, nodes, rnd):
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dList = [(node.x - rnd[0])**2 +
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(node.y - rnd[1])**2 for node in nodes]
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minIndex = dList.index(min(dList))
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return minIndex
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newNode.cost += self.expandDis
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newNode.parent = nind
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return newNode
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def __CollisionCheck(self, newNode, obstacleList):
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for (ox, oy, size) in obstacleList:
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dx = ox - newNode.x
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dy = oy - newNode.y
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d = dx * dx + dy * dy
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if d <= 1.1 * size**2:
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return False # collision
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def isNearGoal(self, node):
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d = self.lineCost(node, self.goal)
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if d < self.expandDis:
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return True
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return False
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return True # safe
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def rewire(self, newNode, nearInds):
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nnode = len(self.nodeList)
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for i in nearInds:
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nearNode = self.nodeList[i]
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def getNewNode(self, theta, nind, nearestNode):
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newNode = copy.deepcopy(nearestNode)
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d = math.sqrt((nearNode.x - newNode.x)**2 +
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(nearNode.y - newNode.y)**2)
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newNode.x += self.expandDis * math.cos(theta)
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newNode.y += self.expandDis * math.sin(theta)
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scost = newNode.cost + d
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newNode.cost += self.expandDis
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newNode.parent = nind
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return newNode
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if nearNode.cost > scost:
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theta = math.atan2(newNode.y - nearNode.y ,
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newNode.x - nearNode.x)
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if self.check_collision_extend(nearNode, theta, d):
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nearNode.parent = nnode - 1
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nearNode.cost = scost
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def isNearGoal(self, node):
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d = self.lineCost(node, self.goal)
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if d < self.expandDis:
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return True
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return False
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def check_collision_extend(self, nearNode, theta, d):
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tmpNode = copy.deepcopy(nearNode)
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def rewire(self, newNode, nearInds):
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nnode = len(self.nodeList)
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for i in nearInds:
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nearNode = self.nodeList[i]
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for i in range(int(d / self.expandDis)):
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tmpNode.x += self.expandDis * math.cos(theta)
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tmpNode.y += self.expandDis * math.sin(theta)
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if not self.__CollisionCheck(tmpNode, self.obstacleList):
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return False
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d = math.sqrt((nearNode.x - newNode.x)**2 +
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(nearNode.y - newNode.y)**2)
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return True
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scost = newNode.cost + d
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def getFinalCourse(self, lastIndex):
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path = [[self.goal.x, self.goal.y]]
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while self.nodeList[lastIndex].parent is not None:
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node = self.nodeList[lastIndex]
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path.append([node.x, node.y])
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lastIndex = node.parent
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path.append([self.start.x, self.start.y])
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return path
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##################################################################################
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def drawGraph(self, rnd=None):
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if nearNode.cost > scost:
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theta = math.atan2(newNode.y - nearNode.y,
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newNode.x - nearNode.x)
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if self.check_collision_extend(nearNode, theta, d):
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nearNode.parent = nnode - 1
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nearNode.cost = scost
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||||
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plt.clf()
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if rnd is not None:
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plt.plot(rnd[0], rnd[1], "^k")
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||||
for node in self.nodeList:
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||||
if node.parent is not None:
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||||
if node.x or node.y is not None:
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||||
plt.plot([node.x, self.nodeList[node.parent].x], [
|
||||
node.y, self.nodeList[node.parent].y], "-g")
|
||||
def check_collision_extend(self, nearNode, theta, d):
|
||||
tmpNode = copy.deepcopy(nearNode)
|
||||
|
||||
for (ox, oy, size) in self.obstacleList:
|
||||
plt.plot(ox, oy, "ok", ms = 30 * size)
|
||||
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, xCenter=None, cBest=None, cMin=None, etheta=None, rnd=None):
|
||||
|
||||
plt.clf()
|
||||
if rnd is not None:
|
||||
plt.plot(rnd[0], rnd[1], "^k")
|
||||
if cBest != float('inf'):
|
||||
self.plot_ellipse(xCenter, cBest, cMin, etheta)
|
||||
|
||||
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)
|
||||
|
||||
def plot_ellipse(self, xCenter, cBest, cMin, etheta):
|
||||
|
||||
a = math.sqrt(cBest**2 - cMin**2) / 2.0
|
||||
b = cBest / 2.0
|
||||
angle = math.pi / 2.0 - etheta
|
||||
cx = xCenter[0]
|
||||
cy = xCenter[1]
|
||||
|
||||
t = np.arange(0, 2 * math.pi + 0.1, 0.1)
|
||||
x = [a * math.cos(it) for it in t]
|
||||
y = [b * math.sin(it) for it in t]
|
||||
R = np.matrix([[math.cos(angle), math.sin(angle)],
|
||||
[-math.sin(angle), math.cos(angle)]])
|
||||
fx = R * np.matrix([x, y])
|
||||
px = np.array(fx[0, :] + cx).flatten()
|
||||
py = np.array(fx[1, :] + cy).flatten()
|
||||
plt.plot(cx, cy, "xc")
|
||||
plt.plot(px, py, "--c")
|
||||
|
||||
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 __init__(self, x, y):
|
||||
self.x = x
|
||||
self.y = y
|
||||
self.cost = 0.0
|
||||
self.parent = None
|
||||
|
||||
|
||||
def main():
|
||||
@@ -267,21 +312,22 @@ def main():
|
||||
(9, 6, 1),
|
||||
(7, 5, 1),
|
||||
(1, 5, 1),
|
||||
(3, 6, 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)
|
||||
rrt = InformedRRTStar(start=[0, 0], goal=[5, 10],
|
||||
randArea=[-2, 15], obstacleList=obstacleList)
|
||||
path = rrt.InformedRRTStarSearch(animation=show_animation)
|
||||
print("Done!!")
|
||||
|
||||
# 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.pause(0.01)
|
||||
plt.show()
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user