"""
Path tracking simulation with pure pursuit steering control and PID speed control.
author: Atsushi Sakai
"""
import math
import matplotlib.pyplot as plt
import numpy as np
import sys
import pathlib
sys.path.append(str(pathlib.Path(__file__).parent.parent))
from ClosedLoopRRTStar import unicycle_model
Kp = 2.0 # speed propotional gain
Lf = 0.5 # look-ahead distance
T = 100.0 # max simulation time
goal_dis = 0.5
stop_speed = 0.5
# animation = True
animation = False
def PIDControl(target, current):
a = Kp * (target - current)
if a > unicycle_model.accel_max:
a = unicycle_model.accel_max
elif a < -unicycle_model.accel_max:
a = -unicycle_model.accel_max
return a
def pure_pursuit_control(state, cx, cy, pind):
ind, dis = calc_target_index(state, cx, cy)
if pind >= ind:
ind = pind
# print(parent_index, ind)
if ind < len(cx):
tx = cx[ind]
ty = cy[ind]
else:
tx = cx[-1]
ty = cy[-1]
ind = len(cx) - 1
alpha = math.atan2(ty - state.y, tx - state.x) - state.yaw
if state.v <= 0.0: # back
alpha = math.pi - alpha
delta = math.atan2(2.0 * unicycle_model.L * math.sin(alpha) / Lf, 1.0)
if delta > unicycle_model.steer_max:
delta = unicycle_model.steer_max
elif delta < - unicycle_model.steer_max:
delta = -unicycle_model.steer_max
return delta, ind, dis
def calc_target_index(state, cx, cy):
dx = [state.x - icx for icx in cx]
dy = [state.y - icy for icy in cy]
d = np.hypot(dx, dy)
mindis = min(d)
ind = np.argmin(d)
L = 0.0
while Lf > L and (ind + 1) < len(cx):
dx = cx[ind + 1] - cx[ind]
dy = cy[ind + 1] - cy[ind]
L += math.hypot(dx, dy)
ind += 1
# print(mindis)
return ind, mindis
def closed_loop_prediction(cx, cy, cyaw, speed_profile, goal):
state = unicycle_model.State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
# lastIndex = len(cx) - 1
time = 0.0
x = [state.x]
y = [state.y]
yaw = [state.yaw]
v = [state.v]
t = [0.0]
a = [0.0]
d = [0.0]
target_ind, mindis = calc_target_index(state, cx, cy)
find_goal = False
maxdis = 0.5
while T >= time:
di, target_ind, dis = pure_pursuit_control(state, cx, cy, target_ind)
target_speed = speed_profile[target_ind]
target_speed = target_speed * \
(maxdis - min(dis, maxdis - 0.1)) / maxdis
ai = PIDControl(target_speed, state.v)
state = unicycle_model.update(state, ai, di)
if abs(state.v) <= stop_speed and target_ind <= len(cx) - 2:
target_ind += 1
time = time + unicycle_model.dt
# check goal
dx = state.x - goal[0]
dy = state.y - goal[1]
if math.hypot(dx, dy) <= goal_dis:
find_goal = True
break
x.append(state.x)
y.append(state.y)
yaw.append(state.yaw)
v.append(state.v)
t.append(time)
a.append(ai)
d.append(di)
if target_ind % 1 == 0 and animation: # pragma: no cover
plt.cla()
# 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(cx, cy, "-r", label="course")
plt.plot(x, y, "ob", label="trajectory")
plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
plt.axis("equal")
plt.grid(True)
plt.title("speed:" + str(round(state.v, 2))
+ "tind:" + str(target_ind))
plt.pause(0.0001)
else:
print("Time out!!")
return t, x, y, yaw, v, a, d, find_goal
def set_stop_point(target_speed, cx, cy, cyaw):
speed_profile = [target_speed] * len(cx)
forward = True
d = []
is_back = False
# Set stop point
for i in range(len(cx) - 1):
dx = cx[i + 1] - cx[i]
dy = cy[i + 1] - cy[i]
d.append(math.hypot(dx, dy))
iyaw = cyaw[i]
move_direction = math.atan2(dy, dx)
is_back = abs(move_direction - iyaw) >= math.pi / 2.0
if dx == 0.0 and dy == 0.0:
continue
if is_back:
speed_profile[i] = - target_speed
else:
speed_profile[i] = target_speed
if is_back and forward:
speed_profile[i] = 0.0
forward = False
# plt.plot(cx[i], cy[i], "xb")
# print(i_yaw, move_direction, dx, dy)
elif not is_back and not forward:
speed_profile[i] = 0.0
forward = True
# plt.plot(cx[i], cy[i], "xb")
# print(i_yaw, move_direction, dx, dy)
speed_profile[0] = 0.0
if is_back:
speed_profile[-1] = -stop_speed
else:
speed_profile[-1] = stop_speed
d.append(d[-1])
return speed_profile, d
def calc_speed_profile(cx, cy, cyaw, target_speed):
speed_profile, d = set_stop_point(target_speed, cx, cy, cyaw)
if animation: # pragma: no cover
plt.plot(speed_profile, "xb")
return speed_profile
def extend_path(cx, cy, cyaw):
dl = 0.1
dl_list = [dl] * (int(Lf / dl) + 1)
move_direction = math.atan2(cy[-1] - cy[-3], cx[-1] - cx[-3])
is_back = abs(move_direction - cyaw[-1]) >= math.pi / 2.0
for idl in dl_list:
if is_back:
idl *= -1
cx = np.append(cx, cx[-1] + idl * math.cos(cyaw[-1]))
cy = np.append(cy, cy[-1] + idl * math.sin(cyaw[-1]))
cyaw = np.append(cyaw, cyaw[-1])
return cx, cy, cyaw
def main(): # pragma: no cover
# target course
cx = np.arange(0, 50, 0.1)
cy = [math.sin(ix / 5.0) * ix / 2.0 for ix in cx]
target_speed = 5.0 / 3.6
T = 15.0 # max simulation time
state = unicycle_model.State(x=-0.0, y=-3.0, yaw=0.0, v=0.0)
# state = unicycle_model.State(x=-1.0, y=-5.0, yaw=0.0, v=-30.0 / 3.6)
# state = unicycle_model.State(x=10.0, y=5.0, yaw=0.0, v=-30.0 / 3.6)
# state = unicycle_model.State(
# x=3.0, y=5.0, yaw=np.deg2rad(-40.0), v=-10.0 / 3.6)
# state = unicycle_model.State(
# x=3.0, y=5.0, yaw=np.deg2rad(40.0), v=50.0 / 3.6)
lastIndex = len(cx) - 1
time = 0.0
x = [state.x]
y = [state.y]
yaw = [state.yaw]
v = [state.v]
t = [0.0]
target_ind, dis = calc_target_index(state, cx, cy)
while T >= time and lastIndex > target_ind:
ai = PIDControl(target_speed, state.v)
di, target_ind, _ = pure_pursuit_control(state, cx, cy, target_ind)
state = unicycle_model.update(state, ai, di)
time = time + unicycle_model.dt
x.append(state.x)
y.append(state.y)
yaw.append(state.yaw)
v.append(state.v)
t.append(time)
# plt.cla()
# plt.plot(cx, cy, ".r", label="course")
# plt.plot(x, y, "-b", label="trajectory")
# plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
# plt.axis("equal")
# plt.grid(True)
# plt.pause(0.1)
# input()
plt.subplots(1)
plt.plot(cx, cy, ".r", label="course")
plt.plot(x, y, "-b", label="trajectory")
plt.legend()
plt.xlabel("x[m]")
plt.ylabel("y[m]")
plt.axis("equal")
plt.grid(True)
plt.subplots(1)
plt.plot(t, [iv * 3.6 for iv in v], "-r")
plt.xlabel("Time[s]")
plt.ylabel("Speed[km/h]")
plt.grid(True)
plt.show()
if __name__ == '__main__': # pragma: no cover
print("Pure pursuit path tracking simulation start")
main()
