Move to pose

PathTracking/move_to_pose.py/move_to_pose.py

@@ -0,0 +1,99 @@
+"""
+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 = 3
+Kp_alpha = 5
+Kp_beta = -2
+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
+    while True:
+        x_diff = x_goal - x
+        y_diff = y_goal - y
+
+        rho = sqrt(x_diff**2 + y_diff**2)
+        alpha = atan2(y_diff, x_diff) - theta
+        beta = theta_goal - theta - alpha
+
+        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
+        x_traj.append(x)
+        y_traj.append(y)
+
+        plot_vehicle(x, y, theta, x_start, y_start, x_goal, y_goal, x_traj, y_traj)
+
+
+def plot_vehicle(x, y, theta, x_start, y_start, x_goal, y_goal, 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.plot(x_start, y_start, 'r*')
+    plt.plot(x_goal, y_goal, 'g*')
+    plt.plot(x_traj, y_traj, 'b--')
+    plt.xlim(0, 20)
+    plt.ylim(0, 20)
+    plt.show()
+    plt.pause(dt/10)
+
+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 = 4 #20*random()
+    y_start = 15 #20*random()
+    theta_start = pi/2 #2*pi*random() - pi
+    x_goal = 13 #20*random()
+    y_goal = 3 #20*random()
+    theta_goal = -pi/2 #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)