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+# encoding: UTF-8
+##
+##程序说明：
+##作者：赵伟     学号：201730310123
+##
+import numpy as np
+import matplotlib.pyplot as plt
+from numpy.matlib import repmat
+from numpy import *
+
+pi = 3.1415926
+steering = 0  # initial steering
+velocity = 6.0  # the velocity of the vehicle
+wheelbase = 8  # the length of wheelbase
+dt = 0.05  # time interval
+iWp = 1  # index to first waypoint
+wp = np.array([[10, 0, 20, 30, 40, 50, ],
+              [5, 20, 45, 10, 80, 40]])
+iPos = 1
+rob = np.array([[0, -wheelbase, -wheelbase], [0, -4, 4]])
+
+
+# % For details, please refer to Section 3.2.1 of R. Smith, M. Self,
+# % "Estimating uncertain spatial relationships in robotics,"
+# % Autonomous Robot Vehicles, pp. 167-193, 1990.
+# %   Xwa - should be of size 3*1 or 1*3
+# %   Xab - can be 3*n or 2*n matrix
+# % Seeded by Tim Bailey
+# % Modified by Samuel on 7 May 2013
+def compound(Xwa, Xab):
+    rot = np.array([np.cos(Xwa[2]), -np.sin(Xwa[2]), np.sin(Xwa[2]), np.cos(Xwa[2])])
+    Xwb = rot * Xab[0:1, :] + repmat(Xwa[0:1], 1, np.size(Xab[1]))
+
+    # if Xwb is a pose and not a point
+    if np.size(Xab[0]) == 2:
+        Xwb = piTopi(Xwa[2, :] + Xab[2])
+    return Xwb
+
+
+# % Input: array of angles.
+# % Output: normalised angles.
+# % Tim Bailey 2000, modified 2005.
+# % Note: either rem or mod will work correctly
+# % angle = mod(angle, 2 * pi);
+# % mod() is very slow for some versions of MatLab ( not a builtin function)
+# % angle = rem(angle, 2 * pi); % rem() is typically builtin
+def piTopi(angle):
+    twopi = 2*math.pi
+    angle = angle - twopi*fix(angle/twopi)
+    for i in range(len(angle)):
+		if angle[i] >= math.pi:
+			angle[i] = angle[i] - twopi
+		if angle[i] < -math.pi:
+			angle[i] = angle[i] + twopi
+    return angle
+
+
+def compSteer(x, wp, iwp, G, dt):
+    maxG = 60 * pi / 180  # radians, maximum steering angle(-MAXG < g < MAXG)
+    rateG = 20 * pi / 180  # rad / s, maximum rate of change in steer angle
+    minD = 0.5
+    cwp = wp[:, iwp-1]
+    d2 = (cwp[0] - x[0])**2 + (cwp[1] - x[1])**2
+    if d2 < (minD**2):
+        iwp += 1  # switch to next
+        if iwp > np.size(wp):
+            iwp = 0
+        cwp = wp[:, iwp-1]  # next waypoint
+
+    # compute change in G to point towards current waypoint
+    deltaG = piTopi(np.arctan2(cwp[1] - x[1], cwp[0] - x[0]) - x[2] - G)
+    # limit steering rate
+    maxDelta = rateG * dt
+    if abs(deltaG) > maxDelta:
+        deltaG = np.sign(deltaG) * maxDelta
+    # limit sterr angle
+    G += deltaG
+    if abs(G) > maxG:
+        G = np.sign(G) * maxG
+    return G, iwp, d2
+
+
+if __name__ == '__main__':
+    # Initialize figure
+    fig = plt.figure()
+    plt.ion()  # continuously plot
+    pos = np.zeros([3, 1])
+    path = np.zeros([3, 3390])
+    idx =0
+    while iWp != 0:
+        plt.cla()
+        pathPlot = plt.plot(0, 0, 'r.', lw=10)
+        plt.plot(wp[0, :], wp[1, :], 'g*', lw=2)
+        plt.plot(wp[0, :], wp[1, :], 'c:', lw=2)
+        plt.xlabel('X(m)')
+        plt.ylabel('Y(m)')
+        plt.axis([-110, 100, -110, 100])
+        idx+=1
+        steering, iWp, d2 = compSteer(pos, wp, iWp, steering, dt)  # compute the steering and next waypoint
+        pos[0] += velocity * dt * np.cos(steering + pos[2, :])
+        pos[1] += velocity * dt * np.sin(steering + pos[2, :])
+        pos[2] += velocity * dt * np.sin(steering) / wheelbase
+        pos[2] = piTopi(pos[2])
+        robPos = compound(pos, rob)
+        path[:, iPos+1] = pos[:,0]
+        iPos += 1
+        pathPlot = plt.plot(path[0, 0:iPos], path[1, 0:iPos], 'r-', lw=1)
+        plt.draw()
+        plt.pause(0.0001)
+
+
+