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potential_field_planning.py
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potential_field_planning.py
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"""
Potential Field based path planner
author: Atsushi Sakai (@Atsushi_twi)
Ref:
https://www.cs.cmu.edu/~motionplanning/lecture/Chap4-Potential-Field_howie.pdf
"""
from collections import deque
import numpy as np
import matplotlib.pyplot as plt
# Parameters
KP = 5.0 # attractive potential gain
ETA = 100.0 # repulsive potential gain
AREA_WIDTH = 30.0 # potential area width [m]
# the number of previous positions used to check oscillations
OSCILLATIONS_DETECTION_LENGTH = 3
show_animation = True
def calc_potential_field(gx, gy, ox, oy, reso, rr, sx, sy):
minx = min(min(ox), sx, gx) - AREA_WIDTH / 2.0
miny = min(min(oy), sy, gy) - AREA_WIDTH / 2.0
maxx = max(max(ox), sx, gx) + AREA_WIDTH / 2.0
maxy = max(max(oy), sy, gy) + AREA_WIDTH / 2.0
xw = int(round((maxx - minx) / reso))
yw = int(round((maxy - miny) / reso))
# calc each potential
pmap = [[0.0 for i in range(yw)] for i in range(xw)]
for ix in range(xw):
x = ix * reso + minx
for iy in range(yw):
y = iy * reso + miny
ug = calc_attractive_potential(x, y, gx, gy)
uo = calc_repulsive_potential(x, y, ox, oy, rr)
uf = ug + uo
pmap[ix][iy] = uf
return pmap, minx, miny
def calc_attractive_potential(x, y, gx, gy):
return 0.5 * KP * np.hypot(x - gx, y - gy)
def calc_repulsive_potential(x, y, ox, oy, rr):
# search nearest obstacle
minid = -1
dmin = float("inf")
for i, _ in enumerate(ox):
d = np.hypot(x - ox[i], y - oy[i])
if dmin >= d:
dmin = d
minid = i
# calc repulsive potential
dq = np.hypot(x - ox[minid], y - oy[minid])
if dq <= rr:
if dq <= 0.1:
dq = 0.1
return 0.5 * ETA * (1.0 / dq - 1.0 / rr) ** 2
else:
return 0.0
def get_motion_model():
# dx, dy
motion = [[1, 0],
[0, 1],
[-1, 0],
[0, -1],
[-1, -1],
[-1, 1],
[1, -1],
[1, 1]]
return motion
def oscillations_detection(previous_ids, ix, iy):
previous_ids.append((ix, iy))
if (len(previous_ids) > OSCILLATIONS_DETECTION_LENGTH):
previous_ids.popleft()
# check if contains any duplicates by copying into a set
previous_ids_set = set()
for index in previous_ids:
if index in previous_ids_set:
return True
else:
previous_ids_set.add(index)
return False
def potential_field_planning(sx, sy, gx, gy, ox, oy, reso, rr):
# calc potential field
pmap, minx, miny = calc_potential_field(gx, gy, ox, oy, reso, rr, sx, sy)
# search path
d = np.hypot(sx - gx, sy - gy)
ix = round((sx - minx) / reso)
iy = round((sy - miny) / reso)
gix = round((gx - minx) / reso)
giy = round((gy - miny) / reso)
if show_animation:
draw_heatmap(pmap)
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect('key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(ix, iy, "*k")
plt.plot(gix, giy, "*m")
rx, ry = [sx], [sy]
motion = get_motion_model()
previous_ids = deque()
while d >= reso:
minp = float("inf")
minix, miniy = -1, -1
for i, _ in enumerate(motion):
inx = int(ix + motion[i][0])
iny = int(iy + motion[i][1])
if inx >= len(pmap) or iny >= len(pmap[0]) or inx < 0 or iny < 0:
p = float("inf") # outside area
print("outside potential!")
else:
p = pmap[inx][iny]
if minp > p:
minp = p
minix = inx
miniy = iny
ix = minix
iy = miniy
xp = ix * reso + minx
yp = iy * reso + miny
d = np.hypot(gx - xp, gy - yp)
rx.append(xp)
ry.append(yp)
if (oscillations_detection(previous_ids, ix, iy)):
print("Oscillation detected at ({},{})!".format(ix, iy))
break
if show_animation:
plt.plot(ix, iy, ".r")
plt.pause(0.01)
print("Goal!!")
return rx, ry
def draw_heatmap(data):
data = np.array(data).T
plt.pcolor(data, vmax=100.0, cmap=plt.cm.Blues)
def main():
print("potential_field_planning start")
sx = 0.0 # start x position [m]
sy = 10.0 # start y positon [m]
gx = 30.0 # goal x position [m]
gy = 30.0 # goal y position [m]
grid_size = 0.5 # potential grid size [m]
robot_radius = 5.0 # robot radius [m]
ox = [15.0, 5.0, 20.0, 25.0] # obstacle x position list [m]
oy = [25.0, 15.0, 26.0, 25.0] # obstacle y position list [m]
if show_animation:
plt.grid(True)
plt.axis("equal")
# path generation
_, _ = potential_field_planning(
sx, sy, gx, gy, ox, oy, grid_size, robot_radius)
if show_animation:
plt.show()
if __name__ == '__main__':
print(__file__ + " start!!")
main()
print(__file__ + " Done!!")