PathPlanning/Sampling-based Planning/rrt_3D/utils3D.py

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

# ---------------------- Collision checking algorithms
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 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

# ---------------------- leaf node extending algorithms
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 near(initparams, x):
    x = np.array(x)
    V = np.array(initparams.V)
    cardV = len(initparams.V)
    eta = initparams.eta
    gamma = initparams.gamma
    r = min(gamma * (np.log(cardV) / cardV), eta)
    if initparams.done: 
        r = 1
    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 steer(initparams, x, y):
    dist, step = getDist(y, x), initparams.stepsize
    increment = ((y[0] - x[0]) / dist * step, (y[1] - x[1]) / dist * step, (y[2] - x[2]) / dist * step)
    xnew = (x[0] + increment[0], x[1] + increment[1], x[2] + increment[2])
    # direc = (y - x) / np.linalg.norm(y - x)
    # xnew = x + initparams.stepsize * direc
    return xnew

def cost(initparams, x):
    '''here use the additive recursive cost function'''
    if 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 = tuple(initparams.env.goal)
    while x != tuple(initparams.env.start):
        x2 = initparams.Parent[x]
        Path.append(np.array([x, x2]))
        dist += getDist(x, x2)
        x = x2
    return Path, dist

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()
            self.E[x].add(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