addd beizer path planning sample

Author: AtsushiSakai

PathPlanning/BezierPath/Figure_1.png

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+"""
+
+Path Planning with 4 point Beizer curve
+
+author: Atsushi Sakai(@Atsushi_twi)
+
+"""
+
+import scipy.misc as scm
+import numpy as np
+import matplotlib.pyplot as plt
+import math
+
+
+def calc_4point_bezier_path(sx, sy, syaw, ex, ey, eyaw, offset):
+    D = math.sqrt((sx - ex)**2 + (sy - ey)**2) / offset
+    cp = np.array(
+        [[sx, sy],
+         [sx + D * math.cos(syaw), sy + D * math.sin(syaw)],
+         [ex - D * math.cos(eyaw), ey - D * math.sin(eyaw)],
+         [ex, ey]])
+
+    traj = []
+    for t in np.linspace(0, 1, 100):
+        traj.append(bezier(3, t, cp))
+    P = np.array(traj)
+
+    return P, cp
+
+
+def bernstein(n, i, t):
+    return scm.comb(n, i) * t**i * (1 - t)**(n - i)
+
+
+def bezier(n, t, q):
+    p = np.zeros(2)
+    for i in range(n + 1):
+        p += bernstein(n, i, t) * q[i]
+    return p
+
+
+def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
+    u"""
+    Plot arrow
+    """
+
+    if not isinstance(x, float):
+        for (ix, iy, iyaw) in zip(x, y, yaw):
+            plot_arrow(ix, iy, iyaw)
+    else:
+        plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
+                  fc=fc, ec=ec, head_width=width, head_length=width)
+        plt.plot(x, y)
+
+
+def main():
+    start_x = 10.0  # [m]
+    start_y = 1.0  # [m]
+    start_yaw = math.radians(180.0)  # [rad]
+
+    end_x = -0.0  # [m]
+    end_y = -3.0  # [m]
+    end_yaw = math.radians(-45.0)  # [rad]
+    offset = 3.0
+
+    P, cp = calc_4point_bezier_path(
+        start_x, start_y, start_yaw, end_x, end_y, end_yaw, offset)
+
+    plt.plot(P.T[0], P.T[1], label="Bezier Path")
+    plt.plot(cp.T[0], cp.T[1], '--o', label="Control Points")
+    plot_arrow(start_x, start_y, start_yaw)
+    plot_arrow(end_x, end_y, end_yaw)
+    plt.legend()
+    plt.axis("equal")
+    plt.grid(True)
+    plt.show()
+
+
+def main2():
+    start_x = 10.0  # [m]
+    start_y = 1.0  # [m]
+    start_yaw = math.radians(180.0)  # [rad]
+
+    end_x = -0.0  # [m]
+    end_y = -3.0  # [m]
+    end_yaw = math.radians(-45.0)  # [rad]
+    offset = 3.0
+
+    for offset in np.arange(1.0, 5.0, 1.0):
+        P, cp = calc_4point_bezier_path(
+            start_x, start_y, start_yaw, end_x, end_y, end_yaw, offset)
+        plt.plot(P.T[0], P.T[1], label="Offset=" + str(offset))
+    plot_arrow(start_x, start_y, start_yaw)
+    plot_arrow(end_x, end_y, end_yaw)
+    plt.legend()
+    plt.axis("equal")
+    plt.grid(True)
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()
+    #  main2()