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