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real_wheel_feedback.py
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real_wheel_feedback.py
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"""
Path tracking simulation with rear wheel feedback steering control and PID speed control.
author: Atsushi Sakai(@Atsushi_twi)
"""
import matplotlib.pyplot as plt
import math
import numpy as np
import sys
try:
import cubic_spline_planner
except:
raise
Kp = 1.0 # speed propotional gain
# steering control parameter
KTH = 1.0
KE = 0.5
dt = 0.1 # [s]
L = 2.9 # [m]
show_animation = True
# show_animation = False
class State:
def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
self.x = x
self.y = y
self.yaw = yaw
self.v = v
def update(state, a, delta):
state.x = state.x + state.v * math.cos(state.yaw) * dt
state.y = state.y + state.v * math.sin(state.yaw) * dt
state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
state.v = state.v + a * dt
return state
def PIDControl(target, current):
a = Kp * (target - current)
return a
def pi_2_pi(angle):
while(angle > math.pi):
angle = angle - 2.0 * math.pi
while(angle < -math.pi):
angle = angle + 2.0 * math.pi
return angle
def rear_wheel_feedback_control(state, cx, cy, cyaw, ck, preind):
ind, e = calc_nearest_index(state, cx, cy, cyaw)
k = ck[ind]
v = state.v
th_e = pi_2_pi(state.yaw - cyaw[ind])
omega = v * k * math.cos(th_e) / (1.0 - k * e) - \
KTH * abs(v) * th_e - KE * v * math.sin(th_e) * e / th_e
if th_e == 0.0 or omega == 0.0:
return 0.0, ind
delta = math.atan2(L * omega / v, 1.0)
# print(k, v, e, th_e, omega, delta)
return delta, ind
def calc_nearest_index(state, cx, cy, cyaw):
dx = [state.x - icx for icx in cx]
dy = [state.y - icy for icy in cy]
d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
mind = min(d)
ind = d.index(mind)
mind = math.sqrt(mind)
dxl = cx[ind] - state.x
dyl = cy[ind] - state.y
angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
if angle < 0:
mind *= -1
return ind, mind
def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
T = 500.0 # max simulation time
goal_dis = 0.3
stop_speed = 0.05
state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
time = 0.0
x = [state.x]
y = [state.y]
yaw = [state.yaw]
v = [state.v]
t = [0.0]
goal_flag = False
target_ind = calc_nearest_index(state, cx, cy, cyaw)
while T >= time:
di, target_ind = rear_wheel_feedback_control(
state, cx, cy, cyaw, ck, target_ind)
ai = PIDControl(speed_profile[target_ind], state.v)
state = update(state, ai, di)
if abs(state.v) <= stop_speed:
target_ind += 1
time = time + dt
# check goal
dx = state.x - goal[0]
dy = state.y - goal[1]
if math.sqrt(dx ** 2 + dy ** 2) <= goal_dis:
print("Goal")
goal_flag = True
break
x.append(state.x)
y.append(state.y)
yaw.append(state.yaw)
v.append(state.v)
t.append(time)
if target_ind % 1 == 0 and show_animation:
plt.cla()
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[km/h]:" + str(round(state.v * 3.6, 2)) +
",target index:" + str(target_ind))
plt.pause(0.0001)
return t, x, y, yaw, v, goal_flag
def calc_speed_profile(cx, cy, cyaw, target_speed):
speed_profile = [target_speed] * len(cx)
direction = 1.0
# Set stop point
for i in range(len(cx) - 1):
dyaw = cyaw[i + 1] - cyaw[i]
switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
if switch:
direction *= -1
if direction != 1.0:
speed_profile[i] = - target_speed
else:
speed_profile[i] = target_speed
if switch:
speed_profile[i] = 0.0
speed_profile[-1] = 0.0
return speed_profile
def main():
print("rear wheel feedback tracking start!!")
ax = [0.0, 6.0, 12.5, 5.0, 7.5, 3.0, -1.0]
ay = [0.0, 0.0, 5.0, 6.5, 3.0, 5.0, -2.0]
goal = [ax[-1], ay[-1]]
cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
ax, ay, ds=0.1)
target_speed = 10.0 / 3.6
sp = calc_speed_profile(cx, cy, cyaw, target_speed)
t, x, y, yaw, v, goal_flag = closed_loop_prediction(
cx, cy, cyaw, ck, sp, goal)
# Test
assert goal_flag, "Cannot goal"
if show_animation: # pragma: no cover
plt.close()
plt.subplots(1)
plt.plot(ax, ay, "xb", label="input")
plt.plot(cx, cy, "-r", label="spline")
plt.plot(x, y, "-g", label="tracking")
plt.grid(True)
plt.axis("equal")
plt.xlabel("x[m]")
plt.ylabel("y[m]")
plt.legend()
plt.subplots(1)
plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("yaw angle[deg]")
plt.subplots(1)
plt.plot(s, ck, "-r", label="curvature")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("curvature [1/m]")
plt.show()
if __name__ == '__main__':
main()