# this is the three dimensional configuration space for rrt # !/usr/bin/env python3 # -*- coding: utf-8 -*- """ @author: yue qi """ import numpy as np # from utils3D import OBB2AABB def R_matrix(z_angle, y_angle, x_angle): # s angle: row; y angle: pitch; z angle: yaw # generate rotation matrix in SO3 # RzRyRx = R, ZYX intrinsic rotation # also (r1,r2,r3) in R3*3 in {W} frame # used in obb.O # [[R p] # [0T 1]] gives transformation from body to world return np.array( [[np.cos(z_angle), -np.sin(z_angle), 0.0], [np.sin(z_angle), np.cos(z_angle), 0.0], [0.0, 0.0, 1.0]]) @ \ np.array( [[np.cos(y_angle), 0.0, np.sin(y_angle)], [0.0, 1.0, 0.0], [-np.sin(y_angle), 0.0, np.cos(y_angle)]]) @ \ np.array( [[1.0, 0.0, 0.0], [0.0, np.cos(x_angle), -np.sin(x_angle)], [0.0, np.sin(x_angle), np.cos(x_angle)]]) def getblocks(): # AABBs block = [[3.10e+00, 0.00e+00, 2.10e+00, 3.90e+00, 5.00e+00, 6.00e+00], [9.10e+00, 0.00e+00, 2.10e+00, 9.90e+00, 5.00e+00, 6.00e+00], # [1.51e+01, 0.00e+00, 2.10e+00, 1.59e+01, 5.00e+00, 6.00e+00], # [1.00e-01, 0.00e+00, 0.00e+00, 9.00e-01, 5.00e+00, 3.90e+00], # [6.10e+00, 0.00e+00, 0.00e+00, 6.90e+00, 5.00e+00, 3.90e+00], [1.21e+01, 0.00e+00, 0.00e+00, 1.29e+01, 5.00e+00, 3.90e+00], [1.81e+01, 0.00e+00, 0.00e+00, 1.89e+01, 5.00e+00, 3.90e+00]] Obstacles = [] for i in block: i = np.array(i) Obstacles.append([j for j in i]) return np.array(Obstacles) def getAABB(blocks): # used for Pyrr package for detecting collision 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 class aabb(object): # make AABB out of blocks, # P: center point # E: extents # O: Rotation matrix in SO(3), in {w} def __init__(self, AABB): self.P = [(AABB[3] + AABB[0]) / 2, (AABB[4] + AABB[1]) / 2, (AABB[5] + AABB[2]) / 2] # center point self.E = [(AABB[3] - AABB[0]) / 2, (AABB[4] - AABB[1]) / 2, (AABB[5] - AABB[2]) / 2] # extents self.O = [[1, 0, 0], [0, 1, 0], [0, 0, 1]] class obb(object): # P: center point # E: extents # O: Rotation matrix in SO(3), in {w} def __init__(self, P, E, O): self.P = P self.E = E self.O = O self.T = np.vstack([np.column_stack([self.O.T, -self.O.T @ self.P]), [0, 0, 0, 1]]) def getAABB2(blocks): # used in lineAABB AABB = [] for i in blocks: AABB.append(aabb(i)) return AABB def getballs(): spheres = [[16, 2.5, 4, 2], [10, 2.5, 1, 1]] Obstacles = [] for i in spheres: Obstacles.append([j for j in i]) return np.array(Obstacles) def add_block(block=[1.51e+01, 0.00e+00, 2.10e+00, 1.59e+01, 5.00e+00, 6.00e+00]): return block class env(): def __init__(self, xmin=0, ymin=0, zmin=0, xmax=20, ymax=5, zmax=6, resolution=1): self.resolution = resolution self.boundary = np.array([xmin, ymin, zmin, xmax, ymax, zmax]) self.blocks = getblocks() self.AABB = getAABB2(self.blocks) self.AABB_pyrr = getAABB(self.blocks) self.balls = getballs() self.OBB = np.array([obb([2.6, 2.5, 1], [0.2, 2, 1], R_matrix(0, 0, 45))]) # self.OBB = np.squeeze(np.vstack([self.OBB,OBB2AABB(self.OBB[0])])) # print(self.OBB) # self.OBB = [] self.start = np.array([0.5, 2.5, 5.5]) self.goal = np.array([19.0, 2.5, 5.5]) self.t = 0 # time def New_block(self): newblock = add_block() self.blocks = np.vstack([self.blocks, newblock]) self.AABB = getAABB2(self.blocks) self.AABB_pyrr = getAABB(self.blocks) def move_start(self, x): self.start = x def move_block(self, a=[0, 0, 0], s=0, v=[0.1, 0, 0], theta=[0, 0, 0], block_to_move=0, obb_to_move=0, mode='uniform'): # t is time , v is velocity in R3, a is acceleration in R3, s is increment ini time, # R is an orthorgonal transform in R3*3, is the rotation matrix # (s',t') = (s + tv, t) is uniform transformation if mode == 'uniform': ori = np.array(self.blocks[block_to_move]) self.blocks[block_to_move] = \ np.array([ori[0] + self.t * v[0], ori[1] + self.t * v[1], ori[2] + self.t * v[2], ori[3] + self.t * v[0], ori[4] + self.t * v[1], ori[5] + self.t * v[2]]) self.AABB[block_to_move].P = \ [self.AABB[block_to_move].P[0] + self.t * v[0], self.AABB[block_to_move].P[1] + self.t * v[1], self.AABB[block_to_move].P[2] + self.t * v[2]] # return a range of block that the block might moved a = self.blocks[block_to_move] # return np.array([a[0] - self.resolution, a[1] - self.resolution, a[2] - self.resolution, \ # a[3] + self.resolution, a[4] + self.resolution, a[5] + self.resolution]). \ # np.array([ori[0] - self.resolution, ori[1] - self.resolution, ori[2] - self.resolution, \ # ori[3] + self.resolution, ori[4] + self.resolution, ori[5] + self.resolution]) return a, ori # (s',t') = (s + a, t + s) is a translation if mode == 'translation': ori = np.array(self.blocks[block_to_move]) self.blocks[block_to_move] = \ np.array([ori[0] + a[0], ori[1] + a[1], ori[2] + a[2], ori[3] + a[0], ori[4] + a[1], ori[5] + a[2]]) self.AABB[block_to_move].P = \ [self.AABB[block_to_move].P[0] + a[0], self.AABB[block_to_move].P[1] + a[1], self.AABB[block_to_move].P[2] + a[2]] self.t += s # return a range of block that the block might moved a = self.blocks[block_to_move] return np.array([a[0] - self.resolution, a[1] - self.resolution, a[2] - self.resolution, a[3] + self.resolution, a[4] + self.resolution, a[5] + self.resolution]), \ np.array([ori[0] - self.resolution, ori[1] - self.resolution, ori[2] - self.resolution, ori[3] + self.resolution, ori[4] + self.resolution, ori[5] + self.resolution]) # return a,ori # (s',t') = (Rx, t) if mode == 'rotation': # this makes an OBB rotate ori = [self.OBB[obb_to_move]] self.OBB[obb_to_move].O = R_matrix(z_angle=theta[0], y_angle=theta[1], x_angle=theta[2]) self.OBB[obb_to_move].T = np.vstack( [np.column_stack([self.OBB[obb_to_move].O.T, -self.OBB[obb_to_move].O.T @ self.OBB[obb_to_move].P]), [0, 0, 0, 1]]) return self.OBB[obb_to_move], ori[0] if __name__ == '__main__': newenv = env()