import numpy as np from numpy.matlib import repmat import pyrr as pyrr import os import sys sys.path.append(os.path.dirname(os.path.abspath(__file__)) + "/../../Sampling-based Planning/") from rrt_3D.plot_util3D import visualization 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])) ''' 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): '''biased sampling''' x = np.random.uniform(initparams.env.boundary[0:3], initparams.env.boundary[3:6]) i = np.random.random() if isinside(initparams, x): return sampleFree(initparams) else: if i < 0.1: return initparams.env.goal + 1 else: return x return 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 isinbound(i, x): 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) # if not isinbound(initparams.env.boundary, y): # return True # 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 # for i in initparams.env.balls: # shot = pyrr.geometric_tests.ray_intersect_sphere(ray, i) # if shot != []: # dists_ball = [getDist(x, j) for j in shot] # if all(dists_ball <= dist): # collide # return True # return False def lineSphere(p0, p1, ball): # https://cseweb.ucsd.edu/classes/sp19/cse291-d/Files/CSE291_13_CollisionDetection.pdf c, r = ball[0:3], ball[-1] line = [p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2]] d1 = [c[0] - p0[0], c[1] - p0[1], c[2] - p0[2]] t = (1 / (line[0] * line[0] + line[1] * line[1] + line[2] * line[2])) * ( line[0] * d1[0] + line[1] * d1[1] + line[2] * d1[2]) if t <= 0: if (d1[0] * d1[0] + d1[1] * d1[1] + d1[2] * d1[2]) <= r ** 2: return True elif t >= 1: d2 = [c[0] - p1[0], c[1] - p1[1], c[2] - p1[2]] if (d2[0] * d2[0] + d2[1] * d2[1] + d2[2] * d2[2]) <= r ** 2: return True elif 0 < t < 1: x = [p0[0] + t * line[0], p0[1] + t * line[1], p0[2] + t * line[2]] k = [c[0] - x[0], c[1] - x[1], c[2] - x[2]] if (k[0] * k[0] + k[1] * k[1] + k[2] * k[2]) <= r ** 2: return True return False def lineAABB(p0, p1, dist, aabb): # https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php?print=1 # aabb should have the attributes of P, E as center point and extents mid = [(p0[0] + p1[0]) / 2, (p0[1] + p1[1]) / 2, (p0[2] + p1[2]) / 2] # mid point I = [(p1[0] - p0[0]) / dist, (p1[1] - p0[1]) / dist, (p1[2] - p0[2]) / dist] # unit direction hl = dist / 2 # radius T = [aabb.P[0] - mid[0], aabb.P[1] - mid[1], aabb.P[2] - mid[2]] # do any of the principal axis form a separting axis? if abs(T[0]) > (aabb.E[0] + hl * abs(I[0])): return False if abs(T[1]) > (aabb.E[1] + hl * abs(I[1])): return False if abs(T[2]) > (aabb.E[2] + hl * abs(I[2])): return False # I.cross(x axis) ? r = aabb.E[1] * abs(I[2]) + aabb.E[2] * abs(I[1]) if abs(T[1] * I[2] - T[2] * I[1]) > r: return False # I.cross(y axis) ? r = aabb.E[0] * abs(I[2]) + aabb.E[2] * abs(I[0]) if abs(T[2] * I[0] - T[0] * I[2]) > r: return False # I.cross(z axis) ? r = aabb.E[0] * abs(I[1]) + aabb.E[1] * abs(I[0]) if abs(T[0] * I[1] - T[1] * I[0]) > r: return False return True def lineOBB(p0, p1, dist, obb): # transform points to obb frame res = obb.T@np.column_stack([np.array([p0,p1]),[1,1]]).T # record old position and set the position to origin oldP, obb.P= obb.P, [0,0,0] # calculate segment-AABB testing ans = lineAABB(res[0:3,0],res[0:3,1],dist,obb) # reset the position obb.P = oldP return ans def isCollide(initparams, x, child, dist=None): '''see if line intersects obstacle''' '''specified for expansion in A* 3D lookup table''' if dist==None: dist = getDist(x, child) # check in bound if not isinbound(initparams.env.boundary, child): return True, dist # check collision in AABB for i in range(len(initparams.env.AABB)): if lineAABB(x, child, dist, initparams.env.AABB[i]): return True, dist # check collision in ball for i in initparams.env.balls: if lineSphere(x, child, i): return True, dist # check collision with obb for i in initparams.env.OBB: if lineOBB(x, child, dist, i): return True, dist return False, dist 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 tuple(initparams.V[np.argmin(dists)]) def steer(initparams, x, y): direc = (y - x) / np.linalg.norm(y - x) xnew = x + initparams.stepsize * direc return tuple(xnew) def near(initparams, x): cardV = len(initparams.V) eta = initparams.eta gamma = initparams.gamma r = min(gamma * (np.log(cardV) / cardV), eta) if initparams.done: r = 1 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 == tuple(initparams.env.start)): return 0 xparent = initparams.Parent[x] return cost(initparams, xparent) + getDist(x, xparent) def path(initparams, Path=[], dist=0): x = initparams.env.goal while not all(x == initparams.env.start): x2 = initparams.Parent[x] Path.append(np.array([x, x2])) dist += getDist(x, x2) x = x2 return Path, dist def hash3D(x): return str(x[0]) + ' ' + str(x[1]) + ' ' + str(x[2]) def dehash(x): return np.array([float(i) for i in x.split(' ')]) class edgeset(object): def __init__(self): self.E = {} def add_edge(self, edge): x, y = edge[0], edge[1] if x in self.E: self.E[x].add(y) else: self.E[x] = set(y) def remove_edge(self, edge): x, y = edge[0], edge[1] self.E[x].remove(y) def get_edge(self): edges = [] for v in self.E: for n in self.E[v]: # if (n,v) not in edges: edges.append((v, n)) return edges