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RVO.py
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RVO.py
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from math import ceil, floor, sqrt
import copy
import numpy
from math import cos, sin, tan, atan2, asin
from math import pi as PI
def distance(pose1, pose2):
""" compute Euclidean distance for 2D """
return sqrt((pose1[0]-pose2[0])**2+(pose1[1]-pose2[1])**2)+0.001
def RVO_update(X, V_des, V_current, ws_model):
""" compute best velocity given the desired velocity, current velocity and workspace model"""
ROB_RAD = ws_model['robot_radius']+0.1
V_opt = list(V_current)
for i in range(len(X)):
vA = [V_current[i][0], V_current[i][1]]
pA = [X[i][0], X[i][1]]
RVO_BA_all = []
for j in range(len(X)):
if i!=j:
vB = [V_current[j][0], V_current[j][1]]
pB = [X[j][0], X[j][1]]
# use RVO
# transl_vB_vA = [pA[0]+0.5*(vB[0]+vA[0]), pA[1]+0.5*(vB[1]+vA[1])]
# use VO
transl_vB_vA = [pA[0]+vB[0], pA[1]+vB[1]]
dist_BA = distance(pA, pB)
theta_BA = atan2(pB[1]-pA[1], pB[0]-pA[0])
if 2*ROB_RAD > dist_BA:
dist_BA = 2*ROB_RAD
theta_BAort = asin(2*ROB_RAD/dist_BA)
theta_ort_left = theta_BA+theta_BAort
bound_left = [cos(theta_ort_left), sin(theta_ort_left)]
theta_ort_right = theta_BA-theta_BAort
bound_right = [cos(theta_ort_right), sin(theta_ort_right)]
# use HRVO
# dist_dif = distance([0.5*(vB[0]-vA[0]),0.5*(vB[1]-vA[1])],[0,0])
# transl_vB_vA = [pA[0]+vB[0]+cos(theta_ort_left)*dist_dif, pA[1]+vB[1]+sin(theta_ort_left)*dist_dif]
RVO_BA = [transl_vB_vA, bound_left, bound_right, dist_BA, 2*ROB_RAD]
RVO_BA_all.append(RVO_BA)
for hole in ws_model['circular_obstacles']:
# hole = [x, y, rad]
vB = [0, 0]
pB = hole[0:2]
transl_vB_vA = [pA[0]+vB[0], pA[1]+vB[1]]
dist_BA = distance(pA, pB)
theta_BA = atan2(pB[1]-pA[1], pB[0]-pA[0])
# over-approximation of square to circular
OVER_APPROX_C2S = 1.5
rad = hole[2]*OVER_APPROX_C2S
if (rad+ROB_RAD) > dist_BA:
dist_BA = rad+ROB_RAD
theta_BAort = asin((rad+ROB_RAD)/dist_BA)
theta_ort_left = theta_BA+theta_BAort
bound_left = [cos(theta_ort_left), sin(theta_ort_left)]
theta_ort_right = theta_BA-theta_BAort
bound_right = [cos(theta_ort_right), sin(theta_ort_right)]
RVO_BA = [transl_vB_vA, bound_left, bound_right, dist_BA, rad+ROB_RAD]
RVO_BA_all.append(RVO_BA)
vA_post = intersect(pA, V_des[i], RVO_BA_all)
V_opt[i] = vA_post[:]
return V_opt
def intersect(pA, vA, RVO_BA_all):
# print '----------------------------------------'
# print 'Start intersection test'
norm_v = distance(vA, [0, 0])
suitable_V = []
unsuitable_V = []
for theta in numpy.arange(0, 2*PI, 0.1):
for rad in numpy.arange(0.02, norm_v+0.02, norm_v/5.0):
new_v = [rad*cos(theta), rad*sin(theta)]
suit = True
for RVO_BA in RVO_BA_all:
p_0 = RVO_BA[0]
left = RVO_BA[1]
right = RVO_BA[2]
dif = [new_v[0]+pA[0]-p_0[0], new_v[1]+pA[1]-p_0[1]]
theta_dif = atan2(dif[1], dif[0])
theta_right = atan2(right[1], right[0])
theta_left = atan2(left[1], left[0])
if in_between(theta_right, theta_dif, theta_left):
suit = False
break
if suit:
suitable_V.append(new_v)
else:
unsuitable_V.append(new_v)
new_v = vA[:]
suit = True
for RVO_BA in RVO_BA_all:
p_0 = RVO_BA[0]
left = RVO_BA[1]
right = RVO_BA[2]
dif = [new_v[0]+pA[0]-p_0[0], new_v[1]+pA[1]-p_0[1]]
theta_dif = atan2(dif[1], dif[0])
theta_right = atan2(right[1], right[0])
theta_left = atan2(left[1], left[0])
if in_between(theta_right, theta_dif, theta_left):
suit = False
break
if suit:
suitable_V.append(new_v)
else:
unsuitable_V.append(new_v)
#----------------------
if suitable_V:
# print 'Suitable found'
vA_post = min(suitable_V, key = lambda v: distance(v, vA))
new_v = vA_post[:]
for RVO_BA in RVO_BA_all:
p_0 = RVO_BA[0]
left = RVO_BA[1]
right = RVO_BA[2]
dif = [new_v[0]+pA[0]-p_0[0], new_v[1]+pA[1]-p_0[1]]
theta_dif = atan2(dif[1], dif[0])
theta_right = atan2(right[1], right[0])
theta_left = atan2(left[1], left[0])
else:
# print 'Suitable not found'
tc_V = dict()
for unsuit_v in unsuitable_V:
tc_V[tuple(unsuit_v)] = 0
tc = []
for RVO_BA in RVO_BA_all:
p_0 = RVO_BA[0]
left = RVO_BA[1]
right = RVO_BA[2]
dist = RVO_BA[3]
rad = RVO_BA[4]
dif = [unsuit_v[0]+pA[0]-p_0[0], unsuit_v[1]+pA[1]-p_0[1]]
theta_dif = atan2(dif[1], dif[0])
theta_right = atan2(right[1], right[0])
theta_left = atan2(left[1], left[0])
if in_between(theta_right, theta_dif, theta_left):
small_theta = abs(theta_dif-0.5*(theta_left+theta_right))
if abs(dist*sin(small_theta)) >= rad:
rad = abs(dist*sin(small_theta))
big_theta = asin(abs(dist*sin(small_theta))/rad)
dist_tg = abs(dist*cos(small_theta))-abs(rad*cos(big_theta))
if dist_tg < 0:
dist_tg = 0
tc_v = dist_tg/distance(dif, [0,0])
tc.append(tc_v)
tc_V[tuple(unsuit_v)] = min(tc)+0.001
WT = 0.2
vA_post = min(unsuitable_V, key = lambda v: ((WT/tc_V[tuple(v)])+distance(v, vA)))
return vA_post
def in_between(theta_right, theta_dif, theta_left):
if abs(theta_right - theta_left) <= PI:
if theta_right <= theta_dif <= theta_left:
return True
else:
return False
else:
if (theta_left <0) and (theta_right >0):
theta_left += 2*PI
if theta_dif < 0:
theta_dif += 2*PI
if theta_right <= theta_dif <= theta_left:
return True
else:
return False
if (theta_left >0) and (theta_right <0):
theta_right += 2*PI
if theta_dif < 0:
theta_dif += 2*PI
if theta_left <= theta_dif <= theta_right:
return True
else:
return False
def compute_V_des(X, goal, V_max):
V_des = []
for i in range(len(X)):
dif_x = [goal[i][k]-X[i][k] for k in range(2)]
norm = distance(dif_x, [0, 0])
norm_dif_x = [dif_x[k]*V_max[k]/norm for k in range(2)]
V_des.append(norm_dif_x[:])
if reach(X[i], goal[i], 0.1):
V_des[i][0] = 0
V_des[i][1] = 0
return V_des
def reach(p1, p2, bound=0.5):
if distance(p1,p2)< bound:
return True
else:
return False