Files
PythonRobotics/PathTracking/move_to_pose/move_to_pose.py
2018-08-14 00:08:16 -04:00

116 lines
3.2 KiB
Python

"""
Move to specified pose
Author: Daniel Ingram (daniel-s-ingram)
P. I. Corke, "Robotics, Vision & Control", Springer 2017, ISBN 978-3-319-54413-7
"""
from __future__ import print_function, division
import matplotlib.pyplot as plt
import numpy as np
from math import cos, sin, sqrt, atan2, pi
from random import random
Kp_rho = 9
Kp_alpha = 15
Kp_beta = -3
dt = 0.01
#Corners of triangular vehicle when pointing to the right (0 radians)
p1_i = np.array([0.5, 0, 1]).T
p2_i = np.array([-0.5, 0.25, 1]).T
p3_i = np.array([-0.5, -0.25, 1]).T
x_traj = []
y_traj = []
plt.ion()
def move_to_pose(x_start, y_start, theta_start, x_goal, y_goal, theta_goal):
"""
rho is the distance between the robot and the goal position
alpha is the angle to the goal relative to the heading of the robot
beta is the angle between the robot's position and the goal position plus the goal angle
Kp_rho*rho and Kp_alpha*alpha drive the robot along a line towards the goal
Kp*beta*beta rotates the line so that it is parallel to the goal angle
"""
x = x_start
y = y_start
theta = theta_start
x_diff = x_goal - x
y_diff = y_goal - y
rho = sqrt(x_diff**2 + y_diff**2)
while rho > 0.001:
x_traj.append(x)
y_traj.append(y)
x_diff = x_goal - x
y_diff = y_goal - y
"""
Restrict alpha and beta (angle differences) to the range
[-pi, pi] to prevent unstable behavior e.g. difference going
from 0 rad to 2*pi rad with slight turn
"""
rho = sqrt(x_diff**2 + y_diff**2)
alpha = (atan2(y_diff, x_diff) - theta + pi)%(2*pi) - pi
beta = (theta_goal - theta - alpha + pi)%(2*pi) - pi
v = Kp_rho*rho
w = Kp_alpha*alpha + Kp_beta*beta
if alpha > pi/2 or alpha < -pi/2:
v = -v
theta = theta + w*dt
x = x + v*cos(theta)*dt
y = y + v*sin(theta)*dt
plot_vehicle(x, y, theta, x_traj, y_traj)
def plot_vehicle(x, y, theta, x_traj, y_traj):
T = transformation_matrix(x, y, theta)
p1 = np.matmul(T, p1_i)
p2 = np.matmul(T, p2_i)
p3 = np.matmul(T, p3_i)
plt.cla()
plt.plot([p1[0], p2[0]], [p1[1], p2[1]], 'k-')
plt.plot([p2[0], p3[0]], [p2[1], p3[1]], 'k-')
plt.plot([p3[0], p1[0]], [p3[1], p1[1]], 'k-')
plt.arrow(x_start, y_start, cos(theta_start), sin(theta_start), color='r', width=0.1)
plt.arrow(x_goal, y_goal, cos(theta_goal), sin(theta_goal), color='g', width=0.1)
plt.plot(x_traj, y_traj, 'b--')
plt.xlim(0, 20)
plt.ylim(0, 20)
plt.show()
plt.pause(dt)
def transformation_matrix(x, y, theta):
return np.array([
[cos(theta), -sin(theta), x],
[sin(theta), cos(theta), y],
[0, 0, 1]
])
if __name__ == '__main__':
x_start = 20*random()
y_start = 20*random()
theta_start = 2*pi*random() - pi
x_goal = 20*random()
y_goal = 20*random()
theta_goal = 2*pi*random() - pi
print("Initial x: %.2f m\nInitial y: %.2f m\nInitial theta: %.2f rad\n" % (x_start, y_start, theta_start))
print("Goal x: %.2f m\nGoal y: %.2f m\nGoal theta: %.2f rad\n" % (x_goal, y_goal, theta_goal))
move_to_pose(x_start, y_start, theta_start, x_goal, y_goal, theta_goal)