diff --git a/PathTracking/rear_wheel_feedback/rear_wheel_feedback.py b/PathTracking/rear_wheel_feedback/rear_wheel_feedback.py index 758e9ad9..52b4a11a 100644 --- a/PathTracking/rear_wheel_feedback/rear_wheel_feedback.py +++ b/PathTracking/rear_wheel_feedback/rear_wheel_feedback.py @@ -8,14 +8,9 @@ author: Atsushi Sakai(@Atsushi_twi) 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 @@ dt = 0.1 # [s] 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 + 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 -def update(state, a, delta): +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) - 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 + self.X = interpolate.CubicSpline(s, x) + self.Y = interpolate.CubicSpline(s, y) - return state + self.dX = self.X.derivative(1) + self.ddX = self.X.derivative(2) + self.dY = self.Y.derivative(1) + self.ddY = self.Y.derivative(2) -def PIDControl(target, current): + 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 + return delta -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) - - 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 @@ -147,49 +160,35 @@ 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): + dyaw = yaw_ref - state.yaw + switch = math.pi / 4.0 <= dyaw < math.pi / 2.0 - 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 - - 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!!") @@ -197,14 +196,10 @@ 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) - target_speed = 10.0 / 3.6 + reference_path = CubicSplinePath(ax, ay) + s = np.arange(0, reference_path.length, 0.1) - sp = calc_speed_profile(cx, cy, cyaw, 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 = 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") @@ -222,14 +217,14 @@ 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(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]") @@ -237,6 +232,5 @@ def main(): plt.show() - if __name__ == '__main__': main()