Replace Spline module to Scipy interpolate

Author: Chachay

PathTracking/rear_wheel_feedback/rear_wheel_feedback.py

@@ -9,12 +9,9 @@
 import math
 import numpy as np
 import sys
-sys.path.append("../../PathPlanning/CubicSpline/")
 
-try:
-    import cubic_spline_planner
-except:
-    raise
+from scipy import interpolate
+from scipy import optimize
 
 Kp = 1.0  # speed propotional gain
 # steering control parameter
@@ -39,6 +36,61 @@ def update(self, a, delta, dt):
         self.yaw = self.yaw + self.v / L * math.tan(delta) * dt
         self.v   = self.v + a * dt
 
+class TrackSpline:
+    def __init__(self, x, y):
+        x, y = map(np.asarray, (x, y))
+        s = np.append([0],(np.cumsum(np.diff(x)**2) + np.cumsum(np.diff(y)**2))**0.5)
+
+        self.X = interpolate.CubicSpline(s, x)
+        self.Y = interpolate.CubicSpline(s, y)
+
+        self.dX = self.X.derivative(1)
+        self.ddX = self.X.derivative(2)
+
+        self.dY = self.Y.derivative(1)
+        self.ddY = self.Y.derivative(2)
+
+        self.length = s[-1]
+    
+    def yaw(self, s):
+        dx, dy = self.dX(s), self.dY(s)
+        return np.arctan2(dy, dx)
+    
+    def curvature(self, s):
+        dx, dy   = self.dX(s), self.dY(s)
+        ddx, ddy   = self.ddX(s), self.ddY(s)
+        return (ddy * dx - ddx * dy) / ((dx ** 2 + dy ** 2)**(3 / 2))
+    
+    def __findClosestPoint(self, s0, x, y):
+        def f(_s, *args):
+            _x, _y= self.X(_s), self.Y(_s)
+            return (_x - args[0])**2 + (_y - args[1])**2
+        
+        def jac(_s, *args):
+            _x, _y = self.X(_s), self.Y(_s)
+            _dx, _dy = self.dX(_s), self.dY(_s)
+            return 2*_dx*(_x - args[0])+2*_dy*(_y-args[1])
+
+        minimum = optimize.fmin_cg(f, s0, jac, args=(x, y), full_output=True, disp=False)
+        return minimum
+
+    def TrackError(self, x, y, s0):
+        ret = self.__findClosestPoint(s0, x, y)
+        
+        s = ret[0][0]
+        e = ret[1]
+
+        k   = self.curvature(s)
+        yaw = self.yaw(s)
+
+        dxl = self.X(s) - x
+        dyl = self.Y(s) - y
+        angle = pi_2_pi(yaw - math.atan2(dyl, dxl))
+        if angle < 0:
+            e*= -1
+
+        return e, k, yaw, s
+
 def PIDControl(target, current):
     a = Kp * (target - current)
     return a
@@ -52,46 +104,22 @@ def pi_2_pi(angle):
 
     return angle
 
-def rear_wheel_feedback_control(state, cx, cy, cyaw, ck, preind):
-    ind, e = calc_nearest_index(state, cx, cy, cyaw)
-
-    k = ck[ind]
+def rear_wheel_feedback_control(state, e, k, yaw_r):
     v = state.v
-    th_e = pi_2_pi(state.yaw - cyaw[ind])
+    th_e = pi_2_pi(state.yaw - yaw_r)
 
     omega = v * k * math.cos(th_e) / (1.0 - k * e) - \
         KTH * abs(v) * th_e - KE * v * math.sin(th_e) * e / th_e
 
     if th_e == 0.0 or omega == 0.0:
-        return 0.0, ind
+        return 0.0
 
     delta = math.atan2(L * omega / v, 1.0)
 
-    return delta, ind
-
-
-def calc_nearest_index(state, cx, cy, cyaw):
-    dx = [state.x - icx for icx in cx]
-    dy = [state.y - icy for icy in cy]
-
-    d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
-
-    mind = min(d)
-
-    ind = d.index(mind)
+    return delta
 
-    mind = math.sqrt(mind)
 
-    dxl = cx[ind] - state.x
-    dyl = cy[ind] - state.y
-
-    angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
-    if angle < 0:
-        mind *= -1
-
-    return ind, mind
-
-def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
+def closed_loop_prediction(track, speed_profile, goal):
     T = 500.0  # max simulation time
     goal_dis = 0.3
     stop_speed = 0.05
@@ -105,17 +133,17 @@ def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
     v = [state.v]
     t = [0.0]
     goal_flag = False
-    target_ind = calc_nearest_index(state, cx, cy, cyaw)
+
+    s = np.arange(0, track.length, 0.1)
+    e, k, yaw_r, s0 = track.TrackError(state.x, state.y, 0.0)
 
     while T >= time:
-        di, target_ind = rear_wheel_feedback_control(
-            state, cx, cy, cyaw, ck, target_ind)
-        ai = PIDControl(speed_profile[target_ind], state.v)
+        e, k, yaw_r, s0 = track.TrackError(state.x, state.y, s0)
+        di = rear_wheel_feedback_control(state, e, k, yaw_r)
+        #ai = PIDControl(speed_profile[target_ind], state.v)
+        ai = PIDControl(speed_profile, state.v)
         state.update(ai, di, dt)
 
-        if abs(state.v) <= stop_speed:
-            target_ind += 1
-
         time = time + dt
 
         # check goal
@@ -132,23 +160,22 @@ def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
         v.append(state.v)
         t.append(time)
 
-        if target_ind % 1 == 0 and show_animation:
+        if show_animation:
             plt.cla()
             # for stopping simulation with the esc key.
             plt.gcf().canvas.mpl_connect('key_release_event',
                     lambda event: [exit(0) if event.key == 'escape' else None])
-            plt.plot(cx, cy, "-r", label="course")
+            plt.plot(track.X(s), track.Y(s), "-r", label="course")
             plt.plot(x, y, "ob", label="trajectory")
-            plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
+            plt.plot(track.X(s0), track.Y(s0), "xg", label="target")
             plt.axis("equal")
             plt.grid(True)
-            plt.title("speed[km/h]:" + str(round(state.v * 3.6, 2)) +
-                      ",target index:" + str(target_ind))
+            plt.title("speed[km/h]:{:.2f}, target s-param:{:.2f}".format(round(state.v * 3.6, 2), s0))
             plt.pause(0.0001)
 
     return t, x, y, yaw, v, goal_flag
 
-def calc_speed_profile(cx, cy, cyaw, target_speed):
+def calc_speed_profile(track, target_speed, s):
     speed_profile = [target_speed] * len(cx)
     direction = 1.0
 
@@ -178,14 +205,16 @@ def main():
     ay = [0.0, 0.0, 5.0, 6.5, 3.0, 5.0, -2.0]
     goal = [ax[-1], ay[-1]]
 
-    cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
-        ax, ay, ds=0.1)
+    track = TrackSpline(ax, ay)
+    s = np.arange(0, track.length, 0.1)
+
     target_speed = 10.0 / 3.6
 
-    sp = calc_speed_profile(cx, cy, cyaw, target_speed)
+    # Note: disable backward direction temporary
+    #sp = calc_speed_profile(track, target_speed, s)
+    sp = target_speed 
 
-    t, x, y, yaw, v, goal_flag = closed_loop_prediction(
-        cx, cy, cyaw, ck, sp, goal)
+    t, x, y, yaw, v, goal_flag = closed_loop_prediction(track, sp, goal)
 
     # Test
     assert goal_flag, "Cannot goal"
@@ -194,7 +223,7 @@ def main():
         plt.close()
         plt.subplots(1)
         plt.plot(ax, ay, "xb", label="input")
-        plt.plot(cx, cy, "-r", label="spline")
+        plt.plot(track.X(s), track.Y(s), "-r", label="spline")
         plt.plot(x, y, "-g", label="tracking")
         plt.grid(True)
         plt.axis("equal")
@@ -203,14 +232,14 @@ def main():
         plt.legend()
 
         plt.subplots(1)
-        plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
+        plt.plot(s, np.rad2deg(track.yaw(s)), "-r", label="yaw")
         plt.grid(True)
         plt.legend()
         plt.xlabel("line length[m]")
         plt.ylabel("yaw angle[deg]")
 
         plt.subplots(1)
-        plt.plot(s, ck, "-r", label="curvature")
+        plt.plot(s, track.curvature(s), "-r", label="curvature")
         plt.grid(True)
         plt.legend()
         plt.xlabel("line length[m]")