import numpy as np from numpy.matlib import repmat import pyrr as pyrr # plotting import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from mpl_toolkits.mplot3d.art3d import Poly3DCollection import mpl_toolkits.mplot3d as plt3d def getRay(x,y): direc = [y[0]-x[0],y[1]-x[1],y[2]-x[2]] return np.array([x,direc]) def getAABB(blocks): AABB = [] for i in blocks: AABB.append(np.array([np.add(i[0:3],-0),np.add(i[3:6],0)])) # make AABBs alittle bit of larger return AABB def getDist(pos1,pos2): return np.sqrt(sum([(pos1[0]-pos2[0])**2,(pos1[1]-pos2[1])**2,(pos1[2]-pos2[2])**2])) def draw_block_list(ax,blocks): ''' Subroutine used by draw_map() to display the environment blocks ''' 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') 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]]) #clr = blocks[:,6:]/255 n = blocks.shape[0] d = blocks[:,3:6] - blocks[:,:3] vl = np.zeros((8*n,3)) fl = np.zeros((6*n,4),dtype='int64') #fcl = np.zeros((6*n,3)) for k in range(n): vl[k*8:(k+1)*8,:] = v * d[k] + blocks[k,:3] fl[k*6:(k+1)*6,:] = f + k*8 #fcl[k*6:(k+1)*6,:] = clr[k,:] if type(ax) is Poly3DCollection: ax.set_verts(vl[fl]) else: pc = Poly3DCollection(vl[fl], alpha=0.15, linewidths=1, edgecolors='k') #pc.set_facecolor(fcl) h = ax.add_collection3d(pc) return h ''' The following utils can be used for rrt or rrt*, required param initparams should have env, environement generated from env3D V, node set E, edge set i, nodes added maxiter, maximum iteration allowed stepsize, leaf growth restriction ''' def sampleFree(initparams): x = np.random.uniform(initparams.env.boundary[0:3],initparams.env.boundary[3:6]) if isinside(initparams,x): return sampleFree(initparams) else: return np.array(x) def isinside(initparams,x): '''see if inside obstacle''' for i in initparams.env.blocks: if i[0] <= x[0] < i[3] and i[1] <= x[1] < i[4] and i[2] <= x[2] < i[5]: return True return False def isCollide(initparams,x,y): '''see if line intersects obstacle''' ray = getRay(x,y) dist = getDist(x,y) for i in getAABB(initparams.env.blocks): shot = pyrr.geometric_tests.ray_intersect_aabb(ray,i) if shot is not None: dist_wall = getDist(x,shot) if dist_wall <= dist: # collide return True return False def nearest(initparams,x): V = np.array(initparams.V) if initparams.i == 0: return initparams.V[0] xr = repmat(x,len(V),1) dists = np.linalg.norm(xr - V,axis = 1) return initparams.V[np.argmin(dists)] def steer(initparams,x,y): direc = (y - x)/np.linalg.norm(y - x) xnew = x + initparams.stepsize*direc return xnew def near(initparams,x,r=2): #TODO: r = min{gamma*log(card(V)/card(V)1/d),eta} V = np.array(initparams.V) if initparams.i == 0: return initparams.V[0] xr = repmat(x,len(V),1) inside = np.linalg.norm(xr - V,axis = 1) < r nearpoints = V[inside] return np.array(nearpoints) def cost(initparams,x): '''here use the additive recursive cost function''' if all(x == initparams.env.start): return 0 xparent = initparams.Parent[str(x[0])][str(x[1])][str(x[2])] return cost(initparams,xparent) + getDist(x,xparent) def visualization(initparams): V = np.array(initparams.V) E = np.array(initparams.E) Path = np.array(initparams.Path) start = initparams.env.start goal = initparams.env.goal ax = plt.subplot(111,projection='3d') ax.view_init(elev=0., azim=90) ax.clear() draw_block_list(ax,initparams.env.blocks) if E != []: for i in E: xs = i[0][0],i[1][0] ys = i[0][1],i[1][1] zs = i[0][2],i[1][2] line = plt3d.art3d.Line3D(xs, ys, zs) ax.add_line(line) if Path != []: for i in Path: xs = i[0][0],i[1][0] ys = i[0][1],i[1][1] zs = i[0][2],i[1][2] line = plt3d.art3d.Line3D(xs, ys, zs,color='r') ax.add_line(line) ax.plot(start[0:1],start[1:2],start[2:],'go',markersize=7,markeredgecolor='k') ax.plot(goal[0:1],goal[1:2],goal[2:],'ro',markersize=7,markeredgecolor='k') ax.scatter3D(V[:,0], V[:,1], V[:,2]) plt.xlim(initparams.env.boundary[0],initparams.env.boundary[3]) plt.ylim(initparams.env.boundary[1],initparams.env.boundary[4]) ax.set_zlim(initparams.env.boundary[2],initparams.env.boundary[5]) plt.xlabel('x') plt.ylabel('y') if not Path != []: plt.pause(0.001) else: plt.show() def path(initparams,Path=[],dist=0): x = initparams.env.goal while not all(x==initparams.env.start): x2 = initparams.Parent[str(x[0])][str(x[1])][str(x[2])] Path.append(np.array([x,x2])) dist += getDist(x,x2) x = x2 return Path,dist