Merge pull request AtsushiSakai#303 from Chachay/MPC

[Proposal] Reduce internal dependancy

Author: AtsushiSakai

PathTracking/rear_wheel_feedback/rear_wheel_feedback.py

@@ -8,14 +8,9 @@
 import matplotlib.pyplot as plt
 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
@@ -26,34 +21,80 @@
 L = 2.9  # [m]
 
 show_animation = True
-#  show_animation = False
-
 
 class State:
-
-    def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
+    def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0, direction=1):
         self.x = x
         self.y = y
         self.yaw = yaw
         self.v = v
-
-
-def update(state, a, delta):
-
-    state.x = state.x + state.v * math.cos(state.yaw) * dt
-    state.y = state.y + state.v * math.sin(state.yaw) * dt
-    state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
-    state.v = state.v + a * dt
-
-    return state
-
-
-def PIDControl(target, current):
+        self.direction = direction
+
+    def update(self, a, delta, dt):
+        self.x   = self.x + self.v * math.cos(self.yaw) * dt
+        self.y   = self.y + self.v * math.sin(self.yaw) * dt
+        self.yaw = self.yaw + self.v / L * math.tan(delta) * dt
+        self.v   = self.v + a * dt
+
+class CubicSplinePath:
+    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 calc_yaw(self, s):
+        dx, dy = self.dX(s), self.dY(s)
+        return np.arctan2(dy, dx)
+    
+    def calc_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 __find_nearest_point(self, s0, x, y):
+        def calc_distance(_s, *args):
+            _x, _y= self.X(_s), self.Y(_s)
+            return (_x - args[0])**2 + (_y - args[1])**2
+        
+        def calc_distance_jacobian(_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(calc_distance, s0, calc_distance_jacobian, args=(x, y), full_output=True, disp=False)
+        return minimum
+
+    def calc_track_error(self, x, y, s0):
+        ret = self.__find_nearest_point(s0, x, y)
+        
+        s = ret[0][0]
+        e = ret[1]
+
+        k   = self.calc_curvature(s)
+        yaw = self.calc_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 pid_control(target, current):
     a = Kp * (target - current)
-
     return a
 
-
 def pi_2_pi(angle):
     while(angle > math.pi):
         angle = angle - 2.0 * math.pi
@@ -63,53 +104,24 @@ 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_ref):
     v = state.v
-    th_e = pi_2_pi(state.yaw - cyaw[ind])
+    th_e = pi_2_pi(state.yaw - yaw_ref)
 
     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)
-    #  print(k, v, e, th_e, omega, delta)
-
-    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 simulate(path_ref, goal):
     T = 500.0  # max simulation time
     goal_dis = 0.3
-    stop_speed = 0.05
 
     state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
 
@@ -120,16 +132,17 @@ 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, path_ref.length, 0.1)
+    e, k, yaw_ref, s0 = path_ref.calc_track_error(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)
-        state = update(state, ai, di)
+        e, k, yaw_ref, s0 = path_ref.calc_track_error(state.x, state.y, s0)
+        di = rear_wheel_feedback_control(state, e, k, yaw_ref)
 
-        if abs(state.v) <= stop_speed:
-            target_ind += 1
+        speed_ref = calc_target_speed(state, yaw_ref)
+        ai = pid_control(speed_ref, state.v)
+        state.update(ai, di, dt)
 
         time = time + dt
 
@@ -147,64 +160,46 @@ 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(path_ref.X(s), path_ref.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(path_ref.X(s0), path_ref.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_target_speed(state, yaw_ref):
+    target_speed = 10.0 / 3.6
 
-def calc_speed_profile(cx, cy, cyaw, target_speed):
-
-    speed_profile = [target_speed] * len(cx)
-
-    direction = 1.0
-
-    # Set stop point
-    for i in range(len(cx) - 1):
-        dyaw = cyaw[i + 1] - cyaw[i]
-        switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
-
-        if switch:
-            direction *= -1
-
-        if direction != 1.0:
-            speed_profile[i] = - target_speed
-        else:
-            speed_profile[i] = target_speed
-
-        if switch:
-            speed_profile[i] = 0.0
-
-    speed_profile[-1] = 0.0
+    dyaw = yaw_ref - state.yaw
+    switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
 
-    return speed_profile
+    if switch:
+        state.direction *= -1
+        return 0.0
+    
+    if state.direction != 1:
+        return -target_speed
 
+    return target_speed
 
 def main():
     print("rear wheel feedback tracking start!!")
     ax = [0.0, 6.0, 12.5, 5.0, 7.5, 3.0, -1.0]
     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)
-    target_speed = 10.0 / 3.6
-
-    sp = calc_speed_profile(cx, cy, cyaw, target_speed)
+    reference_path = CubicSplinePath(ax, ay)
+    s = np.arange(0, reference_path.length, 0.1)
 
-    t, x, y, yaw, v, goal_flag = closed_loop_prediction(
-        cx, cy, cyaw, ck, sp, goal)
+    t, x, y, yaw, v, goal_flag = simulate(reference_path, goal)
 
     # Test
     assert goal_flag, "Cannot goal"
@@ -213,7 +208,7 @@ def main():
         plt.close()
         plt.subplots(1)
         plt.plot(ax, ay, "xb", label="input")
-        plt.plot(cx, cy, "-r", label="spline")
+        plt.plot(reference_path.X(s), reference_path.Y(s), "-r", label="spline")
         plt.plot(x, y, "-g", label="tracking")
         plt.grid(True)
         plt.axis("equal")
@@ -222,21 +217,20 @@ 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(reference_path.calc_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, reference_path.calc_curvature(s), "-r", label="curvature")
         plt.grid(True)
         plt.legend()
         plt.xlabel("line length[m]")
         plt.ylabel("curvature [1/m]")
 
         plt.show()
 
-
 if __name__ == '__main__':
     main()