start coding of rear_wheel_feedback simulation

Author: AtsushiSakai

.gitmodules

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+[submodule "PathTracking/rear_wheel_feedback/pycubicspline"]
+	path = PathTracking/rear_wheel_feedback/pycubicspline
+	url = https://github.com/AtsushiSakai/pycubicspline.git

PathPlanning/CRRRTStar/reeds_shepp_path_planning.py

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+#! /usr/bin/python
+# -*- coding: utf-8 -*-
+"""
+
+Reeds Shepp path planner sample code
+
+author Atsushi Sakai(@Atsushi_twi)
+
+License MIT
+
+"""
+import reeds_shepp
+import math
+
+
+def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
+    u"""
+    Plot arrow
+    """
+    import matplotlib.pyplot as plt
+
+    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 reeds_shepp_path_planning(start_x, start_y, start_yaw,
+                              end_x, end_y, end_yaw, curvature):
+    q0 = [start_x, start_y, start_yaw]
+    q1 = [end_x, end_y, end_yaw]
+    step_size = 0.1
+    qs = reeds_shepp.path_sample(q0, q1, curvature, step_size)
+    xs = [q[0] for q in qs]
+    ys = [q[1] for q in qs]
+    yaw = [q[2] for q in qs]
+
+    xs.append(end_x)
+    ys.append(end_y)
+    yaw.append(end_yaw)
+
+    clen = reeds_shepp.path_length(q0, q1, curvature)
+    pathtypeTuple = reeds_shepp.path_type(q0, q1, curvature)
+
+    ptype = ""
+    for t in pathtypeTuple:
+        if t == 1:
+            ptype += "L"
+        elif t == 2:
+            ptype += "S"
+        elif t == 3:
+            ptype += "R"
+
+    return xs, ys, yaw, ptype, clen
+
+
+if __name__ == '__main__':
+    print("Reeds Shepp path planner sample start!!")
+    import matplotlib.pyplot as plt
+
+    start_x = 1.0  # [m]
+    start_y = 1.0  # [m]
+    start_yaw = math.radians(0.0)  # [rad]
+
+    end_x = -0.0  # [m]
+    end_y = -3.0  # [m]
+    end_yaw = math.radians(-45.0)  # [rad]
+
+    curvature = 1.0
+
+    px, py, pyaw, mode, clen = reeds_shepp_path_planning(
+        start_x, start_y, start_yaw, end_x, end_y, end_yaw, curvature)
+
+    plt.plot(px, py, label="final course " + str(mode))
+
+    # plotting
+    plot_arrow(start_x, start_y, start_yaw)
+    plot_arrow(end_x, end_y, end_yaw)
+
+    for (ix, iy, iyaw) in zip(px, py, pyaw):
+        plot_arrow(ix, iy, iyaw, fc="b")
+    #  print(clen)
+
+    plt.legend()
+    plt.grid(True)
+    plt.axis("equal")
+    plt.show()

PathTracking/rear_wheel_feedback/pycubicspline

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+#! /usr/bin/python
+"""
+
+Path tracking simulation with pure pursuit steering control and PID speed control.
+
+author: Atsushi Sakai
+
+"""
+#  import numpy as np
+import math
+import matplotlib.pyplot as plt
+import unicycle_model
+from pycubicspline import pycubicspline
+
+Kp = 1.0  # speed propotional gain
+Lf = 1.0  # look-ahead distance
+#  animation = True
+animation = False
+
+
+def PIDControl(target, current):
+    a = Kp * (target - current)
+
+    return a
+
+
+def pure_pursuit_control(state, cx, cy, pind):
+
+    ind = calc_target_index(state, cx, cy)
+
+    if pind >= ind:
+        ind = pind
+
+    #  print(pind, ind)
+    if ind < len(cx):
+        tx = cx[ind]
+        ty = cy[ind]
+    else:
+        tx = cx[-1]
+        ty = cy[-1]
+        ind = len(cx) - 1
+
+    alpha = math.atan2(ty - state.y, tx - state.x) - state.yaw
+
+    if state.v < 0:  # back
+        alpha = math.pi - alpha
+        #  if alpha > 0:
+        #  alpha = math.pi - alpha
+        #  else:
+        #  alpha = math.pi + alpha
+
+    delta = math.atan2(2.0 * unicycle_model.L * math.sin(alpha) / Lf, 1.0)
+
+    return delta, ind
+
+
+def calc_target_index(state, cx, cy):
+    dx = [state.x - icx for icx in cx]
+    dy = [state.y - icy for icy in cy]
+
+    d = [abs(math.sqrt(idx ** 2 + idy ** 2)) for (idx, idy) in zip(dx, dy)]
+
+    ind = d.index(min(d))
+
+    L = 0.0
+
+    while Lf > L and (ind + 1) < len(cx):
+        dx = cx[ind + 1] - cx[ind]
+        dy = cx[ind + 1] - cx[ind]
+        L += math.sqrt(dx ** 2 + dy ** 2)
+        ind += 1
+
+    return ind
+
+
+def closed_loop_prediction(cx, cy, cyaw, speed_profile, goal):
+
+    T = 500.0  # max simulation time
+    goal_dis = 0.3
+    stop_speed = 0.05
+
+    state = unicycle_model.State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
+
+    #  lastIndex = len(cx) - 1
+    time = 0.0
+    x = [state.x]
+    y = [state.y]
+    yaw = [state.yaw]
+    v = [state.v]
+    t = [0.0]
+    target_ind = calc_target_index(state, cx, cy)
+
+    while T >= time:
+        di, target_ind = pure_pursuit_control(state, cx, cy, target_ind)
+        ai = PIDControl(speed_profile[target_ind], state.v)
+        state = unicycle_model.update(state, ai, di)
+
+        if abs(state.v) <= stop_speed:
+            target_ind += 1
+
+        time = time + unicycle_model.dt
+
+        # check goal
+        dx = state.x - goal[0]
+        dy = state.y - goal[1]
+        if math.sqrt(dx ** 2 + dy ** 2) <= goal_dis:
+            print("Goal")
+            break
+
+        x.append(state.x)
+        y.append(state.y)
+        yaw.append(state.yaw)
+        v.append(state.v)
+        t.append(time)
+
+        if target_ind % 20 == 0 and animation:
+            plt.cla()
+            plt.plot(cx, cy, "-r", label="course")
+            plt.plot(x, y, "ob", label="trajectory")
+            plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
+            plt.axis("equal")
+            plt.grid(True)
+            plt.title("speed:" + str(round(state.v, 2)) +
+                      "tind:" + str(target_ind))
+            plt.pause(0.0001)
+
+    return t, x, y, yaw, v
+
+
+def set_stop_point(target_speed, cx, cy, cyaw):
+    speed_profile = [target_speed] * len(cx)
+
+    d = []
+    direction = 1.0
+
+    # Set stop point
+    for i in range(len(cx) - 1):
+        dx = cx[i + 1] - cx[i]
+        dy = cy[i + 1] - cy[i]
+        td = math.sqrt(dx ** 2.0 + dy ** 2.0)
+        d.append(td)
+        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[0] = 0.0
+    speed_profile[-1] = 0.0
+
+    d.append(d[-1])
+
+    return speed_profile, d
+
+
+def calc_speed_profile(cx, cy, cyaw, target_speed):
+
+    speed_profile, d = set_stop_point(target_speed, cx, cy, cyaw)
+
+    #  flg, ax = plt.subplots(1)
+    #  plt.plot(speed_profile, "-r")
+    #  plt.show()
+
+    return speed_profile
+
+
+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, 0.0, 5.0, -2.0]
+    goal = [ax[-1], ay[-1]]
+
+    cx, cy, cyaw, ck, s = pycubicspline.calc_spline_course(ax, ay, ds=0.1)
+    target_speed = 10.0 / 3.6
+
+    sp = calc_speed_profile(cx, cy, cyaw, target_speed)
+
+    t, x, y, yaw, v = closed_loop_prediction(cx, cy, cyaw, sp, goal)
+
+    flg, _ = plt.subplots(1)
+    print(len(ax), len(ay))
+    plt.plot(ax, ay, "xb", label="input")
+    plt.plot(cx, cy, "-r", label="spline")
+    plt.plot(x, y, "-g", label="tracking")
+    plt.grid(True)
+    plt.axis("equal")
+    plt.xlabel("x[m]")
+    plt.ylabel("y[m]")
+    plt.legend()
+
+    flg, ax = plt.subplots(1)
+    plt.plot(s, [math.degrees(iyaw) for iyaw in cyaw], "-r", label="yaw")
+    plt.grid(True)
+    plt.legend()
+    plt.xlabel("line length[m]")
+    plt.ylabel("yaw angle[deg]")
+
+    flg, ax = plt.subplots(1)
+    plt.plot(s, ck, "-r", label="curvature")
+    plt.grid(True)
+    plt.legend()
+    plt.xlabel("line length[m]")
+    plt.ylabel("curvature [1/m]")
+
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()

PathTracking/rear_wheel_feedback/rear_wheel_feedback.py

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+#! /usr/bin/python
+# -*- coding: utf-8 -*-
+"""
+
+
+author Atsushi Sakai
+"""
+
+import math
+
+dt = 0.1  # [s]
+L = 2.9  # [m]
+
+
+class State:
+
+    def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
+        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
+
+
+if __name__ == '__main__':
+    print("start unicycle simulation")
+    import matplotlib.pyplot as plt
+
+    T = 100
+    a = [1.0] * T
+    delta = [math.radians(1.0)] * T
+    #  print(delta)
+    #  print(a, delta)
+
+    state = State()
+
+    x = []
+    y = []
+    yaw = []
+    v = []
+
+    for (ai, di) in zip(a, delta):
+        state = update(state, ai, di)
+
+        x.append(state.x)
+        y.append(state.y)
+        yaw.append(state.yaw)
+        v.append(state.v)
+
+    flg, ax = plt.subplots(1)
+    plt.plot(x, y)
+    plt.axis("equal")
+    plt.grid(True)
+
+    flg, ax = plt.subplots(1)
+    plt.plot(v)
+    plt.grid(True)
+
+    plt.show()