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zhm-real
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# this is the three dimensional configuration space for rrt
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#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""
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@author: yue qi
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"""
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import numpy as np
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def getblocks(resolution):
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# AABBs
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block = [[3.10e+00,0.00e+00,2.10e+00,3.90e+00,5.00e+00,6.00e+00],
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[9.10e+00,0.00e+00,2.10e+00,9.90e+00,5.00e+00,6.00e+00],
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[1.51e+01,0.00e+00,2.10e+00,1.59e+01,5.00e+00,6.00e+00],
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[1.00e-01,0.00e+00,0.00e+00,9.00e-01,5.00e+00,3.90e+00],
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[6.10e+00,0.00e+00,0.00e+00,6.90e+00,5.00e+00,3.90e+00],
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[1.21e+01,0.00e+00,0.00e+00,1.29e+01,5.00e+00,3.90e+00],
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[1.81e+01,0.00e+00,0.00e+00,1.89e+01,5.00e+00,3.90e+00]]
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Obstacles = []
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for i in block:
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i = np.array(i)
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Obstacles.append((i[0]/resolution,i[1]/resolution,i[2]/resolution,i[3]/resolution,i[4]/resolution,i[5]/resolution))
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return np.array(Obstacles)
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class env():
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def __init__(self,xmin=0,ymin=0,zmin=0,xmax=20,ymax=5,zmax=6,resolution=1):
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self.resolution = resolution
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self.boundary = np.array([xmin,ymin,zmin,xmax,ymax,zmax])/resolution
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self.blocks = getblocks(resolution)
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self.start = np.array([0.5, 2.5, 5.5])
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self.goal = np.array([19.0, 2.5, 5.5])
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def visualize(self):
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# fig = plt.figure()
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# TODO: do visualizations
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return
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if __name__ == '__main__':
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newenv = env()
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X = StateSpace(newenv.boundary,newenv.resolution)
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print(X)
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"""
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This is rrt star code for 3D
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@author: yue qi
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"""
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import numpy as np
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from numpy.matlib import repmat
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from env3D import env
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from collections import defaultdict
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import pyrr as pyrr
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from utils3D import getDist, sampleFree, nearest, steer, isCollide, near, visualization, cost, path
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import time
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class rrtstar():
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def __init__(self):
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self.env = env()
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self.Parent = defaultdict(lambda: defaultdict(dict))
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self.V = []
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self.E = []
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self.i = 0
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self.maxiter = 10000
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self.stepsize = 0.5
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self.Path = []
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def wireup(self,x,y):
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self.E.append([x,y]) # add edge
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self.Parent[str(x[0])][str(x[1])][str(x[2])] = y
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def removewire(self,xnear):
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xparent = self.Parent[str(xnear[0])][str(xnear[1])][str(xnear[2])]
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a = np.array([xnear,xparent])
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self.E = [xx for xx in self.E if not (xx==a).all()] # remove and replace old the connection
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def run(self):
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self.V.append(self.env.start)
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ind = 0
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xnew = self.env.start
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while ind < self.maxiter and getDist(xnew,self.env.goal) > 1:
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xrand = sampleFree(self)
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xnearest = nearest(self,xrand)
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xnew = steer(self,xnearest,xrand)
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if not isCollide(self,xnearest,xnew):
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self.V.append(xnew) # add point
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self.wireup(xnew,xnearest)
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#visualization(self)
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self.i += 1
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ind += 1
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if getDist(xnew,self.env.goal) <= 1:
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self.wireup(self.env.goal,xnew)
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self.Path,D = path(self)
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print('Total distance = '+str(D))
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visualization(self)
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if __name__ == '__main__':
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p = rrtstar()
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starttime = time.time()
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p.run()
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print('time used = ' + str(time.time()-starttime))
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"""
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This is rrt star code for 3D
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@author: yue qi
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"""
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import numpy as np
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from numpy.matlib import repmat
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from env3D import env
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from collections import defaultdict
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import pyrr as pyrr
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from utils3D import getDist, sampleFree, nearest, steer, isCollide, near, visualization, cost, path
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import time
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class rrtstar():
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def __init__(self):
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self.env = env()
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self.Parent = defaultdict(lambda: defaultdict(dict))
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self.V = []
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self.E = []
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self.i = 0
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self.maxiter = 10000
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self.stepsize = 0.5
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self.Path = []
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def wireup(self,x,y):
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self.E.append([x,y]) # add edge
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self.Parent[str(x[0])][str(x[1])][str(x[2])] = y
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def removewire(self,xnear):
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xparent = self.Parent[str(xnear[0])][str(xnear[1])][str(xnear[2])]
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a = np.array([xnear,xparent])
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self.E = [xx for xx in self.E if not (xx==a).all()] # remove and replace old the connection
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def run(self):
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self.V.append(self.env.start)
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ind = 0
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xnew = self.env.start
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while ind < self.maxiter and getDist(xnew,self.env.goal) > 1:
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xrand = sampleFree(self)
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xnearest = nearest(self,xrand)
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xnew = steer(self,xnearest,xrand)
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if not isCollide(self,xnearest,xnew):
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Xnear = near(self,xnew)
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self.V.append(xnew) # add point
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# visualization(self)
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# minimal path and minimal cost
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xmin,cmin = xnearest,cost(self,xnearest) + getDist(xnearest,xnew)
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# connecting along minimal cost path
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if self.i == 0:
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c1 = cost(self,Xnear) + getDist(xnew,Xnear)
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if not isCollide(self,xnew,Xnear) and c1 < cmin:
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xmin,cmin = Xnear,c1
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self.wireup(xnew,xmin)
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else:
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for xnear in Xnear:
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c1 = cost(self,xnear) + getDist(xnew,xnear)
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if not isCollide(self,xnew,xnear) and c1 < cmin:
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xmin,cmin = xnear,c1
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self.wireup(xnew,xmin)
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# rewire
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for xnear in Xnear:
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c2 = cost(self,xnew) + getDist(xnew,xnear)
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if not isCollide(self,xnew,xnear) and c2 < cost(self,xnear):
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self.removewire(xnear)
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self.wireup(xnear,xnew)
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self.i += 1
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ind += 1
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if getDist(xnew,self.env.goal) <= 1:
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self.wireup(self.env.goal,xnew)
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self.Path,D = path(self)
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print('Total distance = '+str(D))
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visualization(self)
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if __name__ == '__main__':
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p = rrtstar()
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starttime = time.time()
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p.run()
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print('time used = ' + str(time.time()-starttime))
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import numpy as np
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from numpy.matlib import repmat
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import pyrr as pyrr
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# plotting
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D
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from mpl_toolkits.mplot3d.art3d import Poly3DCollection
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import mpl_toolkits.mplot3d as plt3d
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def getRay(x,y):
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direc = [y[0]-x[0],y[1]-x[1],y[2]-x[2]]
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return np.array([x,direc])
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def getAABB(blocks):
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AABB = []
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for i in blocks:
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AABB.append(np.array([np.add(i[0:3],-0),np.add(i[3:6],0)])) # make AABBs alittle bit of larger
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return AABB
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def getDist(pos1,pos2):
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return np.sqrt(sum([(pos1[0]-pos2[0])**2,(pos1[1]-pos2[1])**2,(pos1[2]-pos2[2])**2]))
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def draw_block_list(ax,blocks):
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'''
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Subroutine used by draw_map() to display the environment blocks
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'''
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v = np.array([[0,0,0],[1,0,0],[1,1,0],[0,1,0],[0,0,1],[1,0,1],[1,1,1],[0,1,1]],dtype='float')
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f = np.array([[0,1,5,4],[1,2,6,5],[2,3,7,6],[3,0,4,7],[0,1,2,3],[4,5,6,7]])
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#clr = blocks[:,6:]/255
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n = blocks.shape[0]
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d = blocks[:,3:6] - blocks[:,:3]
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vl = np.zeros((8*n,3))
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fl = np.zeros((6*n,4),dtype='int64')
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#fcl = np.zeros((6*n,3))
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for k in range(n):
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vl[k*8:(k+1)*8,:] = v * d[k] + blocks[k,:3]
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fl[k*6:(k+1)*6,:] = f + k*8
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#fcl[k*6:(k+1)*6,:] = clr[k,:]
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if type(ax) is Poly3DCollection:
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ax.set_verts(vl[fl])
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else:
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pc = Poly3DCollection(vl[fl], alpha=0.15, linewidths=1, edgecolors='k')
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#pc.set_facecolor(fcl)
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h = ax.add_collection3d(pc)
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return h
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''' The following utils can be used for rrt or rrt*,
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required param initparams should have
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env, environement generated from env3D
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V, node set
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E, edge set
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i, nodes added
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maxiter, maximum iteration allowed
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stepsize, leaf growth restriction
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'''
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def sampleFree(initparams):
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x = np.random.uniform(initparams.env.boundary[0:3],initparams.env.boundary[3:6])
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if isinside(initparams,x):
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return sampleFree(initparams)
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else: return np.array(x)
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def isinside(initparams,x):
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'''see if inside obstacle'''
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for i in initparams.env.blocks:
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if i[0] <= x[0] < i[3] and i[1] <= x[1] < i[4] and i[2] <= x[2] < i[5]:
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return True
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return False
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def isCollide(initparams,x,y):
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'''see if line intersects obstacle'''
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ray = getRay(x,y)
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dist = getDist(x,y)
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for i in getAABB(initparams.env.blocks):
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shot = pyrr.geometric_tests.ray_intersect_aabb(ray,i)
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if shot is not None:
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dist_wall = getDist(x,shot)
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if dist_wall <= dist: # collide
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return True
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return False
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def nearest(initparams,x):
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V = np.array(initparams.V)
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if initparams.i == 0:
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return initparams.V[0]
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xr = repmat(x,len(V),1)
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dists = np.linalg.norm(xr - V,axis = 1)
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return initparams.V[np.argmin(dists)]
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def steer(initparams,x,y):
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direc = (y - x)/np.linalg.norm(y - x)
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xnew = x + initparams.stepsize*direc
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return xnew
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def near(initparams,x,r=2):
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#TODO: r = min{gamma*log(card(V)/card(V)1/d),eta}
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V = np.array(initparams.V)
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if initparams.i == 0:
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return initparams.V[0]
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xr = repmat(x,len(V),1)
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inside = np.linalg.norm(xr - V,axis = 1) < r
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nearpoints = V[inside]
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return np.array(nearpoints)
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def cost(initparams,x):
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'''here use the additive recursive cost function'''
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if all(x == initparams.env.start):
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return 0
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xparent = initparams.Parent[str(x[0])][str(x[1])][str(x[2])]
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return cost(initparams,xparent) + getDist(x,xparent)
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def visualization(initparams):
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V = np.array(initparams.V)
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E = np.array(initparams.E)
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Path = np.array(initparams.Path)
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start = initparams.env.start
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goal = initparams.env.goal
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ax = plt.subplot(111,projection='3d')
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ax.view_init(elev=0., azim=90)
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ax.clear()
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draw_block_list(ax,initparams.env.blocks)
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if E != []:
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for i in E:
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xs = i[0][0],i[1][0]
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ys = i[0][1],i[1][1]
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zs = i[0][2],i[1][2]
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line = plt3d.art3d.Line3D(xs, ys, zs)
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ax.add_line(line)
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if Path != []:
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for i in Path:
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xs = i[0][0],i[1][0]
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ys = i[0][1],i[1][1]
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zs = i[0][2],i[1][2]
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line = plt3d.art3d.Line3D(xs, ys, zs,color='r')
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ax.add_line(line)
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ax.plot(start[0:1],start[1:2],start[2:],'go',markersize=7,markeredgecolor='k')
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ax.plot(goal[0:1],goal[1:2],goal[2:],'ro',markersize=7,markeredgecolor='k')
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ax.scatter3D(V[:,0], V[:,1], V[:,2])
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plt.xlim(initparams.env.boundary[0],initparams.env.boundary[3])
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plt.ylim(initparams.env.boundary[1],initparams.env.boundary[4])
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ax.set_zlim(initparams.env.boundary[2],initparams.env.boundary[5])
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plt.xlabel('x')
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plt.ylabel('y')
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if not Path != []:
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plt.pause(0.001)
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else: plt.show()
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def path(initparams,Path=[],dist=0):
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x = initparams.env.goal
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while not all(x==initparams.env.start):
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x2 = initparams.Parent[str(x[0])][str(x[1])][str(x[2])]
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Path.append(np.array([x,x2]))
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dist += getDist(x,x2)
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x = x2
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return Path,dist
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