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apf.py
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apf.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
"""
import numpy as np
import matplotlib.pyplot as plt
import math
from math import sin, cos, atan2, asin, pi
from robot_model import RobotModel
import logging
class ConfigAPF():
# simulation parameters
def __init__(self, max_v, min_v, max_w, max_acc_v, max_acc_w, v_reso=0.01, yawrate_reso=0.1, dt=0.1,
ka=0.04, kp=0.9, p0=8.0, max_range=10.0, robot_raduis=0.3, obstacle_radius=0.3):
# robot parameter
self.max_speed = max_v # [m/s]
self.min_speed = min_v # [m/s]
self.max_yawrate = max_w # [rad/s]
self.max_accel = max_acc_v # [m/ss]
self.max_dyawrate = max_acc_w # [rad/ss]
self.v_reso = v_reso # [m/s]
self.yawrate_reso = yawrate_reso # [rad/s]
self.dt = dt # [s]
self.robot_radius = robot_raduis # [m]
self.obstacle_radius = obstacle_radius # [m]
# potential parameter
self.ka = ka # attractive potential gain
self.kp = kp # repulsive potential gain
self.p0 = p0 # potential area width [m]
self.max_range = max_range
def calc_u(config, x, v_tar, theta_tar, theta_robo_tar, p_robo_tar, v_ob, theta_ob, theta_robo_ob, p_robo_ob):
p_robo_tar = min(p_robo_tar, config.max_range)
ob_num = len(v_ob)
n = np.zeros(ob_num)
beta = np.zeros(ob_num)
for i in range(ob_num):
Pi = (p_robo_ob[i]) - config.obstacle_radius
n[i] = config.kp * Pi**(-1) \
/ (p_robo_ob[i]) * (Pi**-1 - config.p0**-1)
beta[i] = (n[i] * (p_robo_ob[i])) / (config.ka * (p_robo_tar))
logging.info("n = %s", n)
logging.info("beta = %s", beta)
psi_hat_y = sin(theta_robo_tar)
for i in range(ob_num):
psi_hat_y -= beta[i] * sin(theta_robo_ob[i])
psi_hat_x = cos(theta_robo_tar)
for i in range(ob_num):
psi_hat_x -= beta[i] * cos(theta_robo_ob[i])
logging.info("theta_robo_ob = %s", str(theta_robo_ob))
logging.info("psi = %s", str(theta_robo_tar))
logging.info("tan(psi_hat) = %s", str([psi_hat_y, psi_hat_x]))
psi_hat = atan2(psi_hat_y, psi_hat_x)
logging.info("psi_hat = %s", str(psi_hat))
term1 = (v_tar)*cos(theta_tar-theta_robo_tar) + config.ka * (p_robo_tar)
logging.info("term1 = %s * cos(%s - %s) + %s * %s = %s", v_tar, theta_tar, theta_robo_tar, config.ka, p_robo_tar, term1)
for i in range(ob_num):
term1 -= beta[i] * (v_ob[i]) * cos(theta_ob[i] - theta_robo_ob[i])
logging.info("term1 = %s", str(term1))
v = math.sqrt(term1**2 + ((v_tar)*sin(theta_tar - psi_hat))**2)
theta_term_tmp = (v_tar) * sin(theta_tar-psi_hat) / v
logging.info("theta_term_tmp = %s * sin(%s - %s)/%s = %s", v_tar, theta_tar, psi_hat, v, theta_term_tmp)
if abs(theta_term_tmp)>1.0:
theta_term_tmp = theta_term_tmp/abs(theta_term_tmp)
theta = psi_hat + asin(theta_term_tmp)
logging.info("[v, theta] = %s", str([v, theta]))
return [v, theta]
def apf_control(config, x_robot, x_tar, ob_list):
filtered_ob_list = filter_ob(config, ob_list, x_robot, config.p0)
logging.info(x_robot)
logging.info(filtered_ob_list)
v_tar = x_tar[3]
theta_tar = x_tar[2]
theta_robo_tar = atan2(x_tar[1]-x_robot[1], x_tar[0]-x_robot[0])
p_robo_tar = np.linalg.norm(x_tar[:2]-x_robot[:2])
ob_num = len(filtered_ob_list)
v_ob = np.zeros(ob_num)
theta_ob = np.zeros(ob_num)
theta_robo_ob = []
p_robo_ob = []
for i in range(ob_num):
tmp = np.array(filtered_ob_list[i]) - x_robot[:2]
theta_robo_ob.append(atan2(tmp[1], tmp[0]))
p_robo_ob.append(np.linalg.norm(tmp))
theta_ob = np.array(theta_ob)
p_robo_ob = np.array(p_robo_ob)
u = calc_u(config, x_robot, v_tar, theta_tar, theta_robo_tar, p_robo_tar, v_ob, theta_ob, theta_robo_ob, p_robo_ob)
return u
def filter_ob(config, ob_list, x, active_distance):
def is_in_active_distance(ob):
dis = np.linalg.norm(np.array(ob) - x[:2]) - config.obstacle_radius
return dis<=active_distance
filtered_ob_list = list(filter(is_in_active_distance, ob_list))
return filtered_ob_list
def plot_arrow(x, y, yaw, length=0.5, width=0.1): # pragma: no cover
plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
head_length=width, head_width=width)
plt.plot(x, y)
def main(gx=8, gy=2):
show_animation = True
print(__file__ + " start!!")
max_v = 2
min_v = 0
max_w = pi / 3 * 2
max_acc_v = 0.7
max_acc_w = pi / 3.0 * 5
init_x = 0.0
init_y = 6
init_yaw = pi / 8.0
robot_radius = 0.3
ob_radius = 0.3
goal_radius = 0.3
pursuitor_model = RobotModel(max_v, min_v, max_w, max_acc_v, max_acc_w,
init_x, init_y, init_yaw)
target_model = RobotModel(max_v, min_v, max_w, max_acc_v, max_acc_w,
gx, gy, -pi/2.0)
# obstacles [x(m) y(m), ....]
ob = np.array([
[0, 2],
[4.0, 2.0],
[5.0, 4.0],
[5.0, 6.0],
[7.0, 9.0]
])
config = ConfigAPF(2, 0, math.pi/3, 0.7, math.pi/3)
traj = np.array(pursuitor_model.state)
traj_u = np.array([0, 0])
traj_target = np.array(target_model.state)
for i in range(2000):
logging.info("")
logging.info(i)
u = apf_control(config, pursuitor_model.state, target_model.state, ob)
traj_u = np.vstack((traj_u, u))
print(u)
u[1] = pursuitor_model.rot_to_angle(u[1])
# u[0]=0
x = pursuitor_model.motion(u, config.dt)
traj = np.vstack((traj, x)) # store state history
goal = target_model.motion([1.8, pi/5], config.dt)
traj_target = np.vstack((traj_target, goal))
# print(traj)
if show_animation:
plt.cla()
plt.plot(x[0], x[1], "xr")
plt.plot(goal[0], goal[1], "xb")
plt.plot(ob[:, 0], ob[:, 1], "ok")
plot_arrow(x[0], x[1], x[2])
plt.axis("equal")
plt.grid(True)
plt.pause(0.0001)
# check goal
if math.sqrt((x[0] - goal[0])**2 + (x[1] - goal[1])**2) <= (pursuitor_model.robot_radius + target_model.robot_radius):
print("Goal!!")
break
# check collision
collision = False
for obstacle in ob:
if math.sqrt((x[0] - obstacle[0]) ** 2 + (x[1] - obstacle[1]) ** 2) <= (
pursuitor_model.robot_radius + config.obstacle_radius):
collision = True
if collision:
print("Collision!")
break
prefix = "apf_flaw/4_"
np.save(prefix + "traj.npy", traj)
np.save(prefix + "traj_target.npy", traj_target)
np.save(prefix + "traj_u.npy", traj_u)
print("Done")
if show_animation:
plt.plot(traj[:, 0], traj[:, 1], "-r")
plt.plot(traj_target[:, 0], traj_target[:, 1], "-g")
fig = plt.gcf()
# fig.set_size_inches(6,6)
plt.xlabel('X(m)')
plt.ylabel('Y(m)')
# plt.axis("auto")
plt.tight_layout()
print(plt.xlim((-1.488585497312541, 14.14373130420207)))
print(plt.ylim((0.4404926013282211, 12.089089959876205)))
plt.figure()
plt.plot(np.arange(0, len(traj))*config.dt, traj_u[:, 1], label=r'Input $\theta$')
plt.plot(np.arange(0, len(traj))*config.dt, traj[:, 2], label=r'Actual $\theta$')
plt.xlabel('T(s)')
plt.ylabel(r'$\theta$(rad)')
plt.legend()
plt.show()
if __name__ == '__main__':
logging.basicConfig(level=logging.INFO,
format='%(asctime)s %(filename)s[line:%(lineno)d] %(levelname)s %(message)s',
datefmt='%H:%M:%S', filename="test.log", filemode='w')
main()