""" 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 Kp = 2.0 # speed propotional gain Lf = 0.5 # look-ahead distance T = 100.0 # max simulation time goal_dis = 0.5 stop_speed = 0.5 # animation = True animation = False def PIDControl(target, current): a = Kp * (target - current) if a > unicycle_model.accel_max: a = unicycle_model.accel_max elif a < -unicycle_model.accel_max: a = -unicycle_model.accel_max return a def pure_pursuit_control(state, cx, cy, pind): ind, dis = 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 <= 0.0: # back alpha = math.pi - alpha delta = math.atan2(2.0 * unicycle_model.L * math.sin(alpha) / Lf, 1.0) if delta > unicycle_model.steer_max: delta = unicycle_model.steer_max elif delta < - unicycle_model.steer_max: delta = -unicycle_model.steer_max return delta, ind, dis 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)] mindis = min(d) ind = d.index(mindis) 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 # print(mindis) return ind, mindis def closed_loop_prediction(cx, cy, cyaw, speed_profile, goal): 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] a = [0.0] d = [0.0] target_ind, mindis = calc_target_index(state, cx, cy) find_goal = False maxdis = 0.5 while T >= time: di, target_ind, dis = pure_pursuit_control(state, cx, cy, target_ind) target_speed = speed_profile[target_ind] target_speed = target_speed * \ (maxdis - min(dis, maxdis - 0.1)) / maxdis ai = PIDControl(target_speed, state.v) state = unicycle_model.update(state, ai, di) if abs(state.v) <= stop_speed and target_ind <= len(cx) - 2: 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: find_goal = True break x.append(state.x) y.append(state.y) yaw.append(state.yaw) v.append(state.v) t.append(time) a.append(ai) d.append(di) if target_ind % 1 == 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) else: print("Time out!!") return t, x, y, yaw, v, a, d, find_goal def set_stop_point(target_speed, cx, cy, cyaw): speed_profile = [target_speed] * len(cx) forward = True d = [] # Set stop point for i in range(len(cx) - 1): dx = cx[i + 1] - cx[i] dy = cy[i + 1] - cy[i] d.append(math.sqrt(dx ** 2.0 + dy ** 2.0)) iyaw = cyaw[i] move_direction = math.atan2(dy, dx) is_back = abs(move_direction - iyaw) >= math.pi / 2.0 if dx == 0.0 and dy == 0.0: continue if is_back: speed_profile[i] = - target_speed else: speed_profile[i] = target_speed if is_back and forward: speed_profile[i] = 0.0 forward = False # plt.plot(cx[i], cy[i], "xb") # print(iyaw, move_direction, dx, dy) elif not is_back and not forward: speed_profile[i] = 0.0 forward = True # plt.plot(cx[i], cy[i], "xb") # print(iyaw, move_direction, dx, dy) speed_profile[0] = 0.0 if is_back: speed_profile[-1] = -stop_speed else: speed_profile[-1] = stop_speed 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) if animation: plt.plot(speed_profile, "xb") return speed_profile def extend_path(cx, cy, cyaw): dl = 0.1 dl_list = [dl] * (int(Lf / dl) + 1) move_direction = math.atan2(cy[-1] - cy[-3], cx[-1] - cx[-3]) is_back = abs(move_direction - cyaw[-1]) >= math.pi / 2.0 for idl in dl_list: if is_back: idl *= -1 cx = np.append(cx, cx[-1] + idl * math.cos(cyaw[-1])) cy = np.append(cy, cy[-1] + idl * math.sin(cyaw[-1])) cyaw = np.append(cyaw, cyaw[-1]) return cx, cy, cyaw def main(): # target course import numpy as np cx = np.arange(0, 50, 0.1) cy = [math.sin(ix / 5.0) * ix / 2.0 for ix in cx] target_speed = 5.0 / 3.6 T = 15.0 # max simulation time state = unicycle_model.State(x=-0.0, y=-3.0, yaw=0.0, v=0.0) # state = unicycle_model.State(x=-1.0, y=-5.0, yaw=0.0, v=-30.0 / 3.6) # state = unicycle_model.State(x=10.0, y=5.0, yaw=0.0, v=-30.0 / 3.6) # state = unicycle_model.State( # x=3.0, y=5.0, yaw=np.deg2rad(-40.0), v=-10.0 / 3.6) # state = unicycle_model.State( # x=3.0, y=5.0, yaw=np.deg2rad(40.0), v=50.0 / 3.6) 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 and lastIndex > target_ind: ai = PIDControl(target_speed, state.v) di, target_ind, _ = pure_pursuit_control(state, cx, cy, target_ind) state = unicycle_model.update(state, ai, di) time = time + unicycle_model.dt x.append(state.x) y.append(state.y) yaw.append(state.yaw) v.append(state.v) t.append(time) # plt.cla() # plt.plot(cx, cy, ".r", label="course") # plt.plot(x, y, "-b", label="trajectory") # plt.plot(cx[target_ind], cy[target_ind], "xg", label="target") # plt.axis("equal") # plt.grid(True) # plt.pause(0.1) # input() flg, ax = plt.subplots(1) plt.plot(cx, cy, ".r", label="course") plt.plot(x, y, "-b", label="trajectory") plt.legend() plt.xlabel("x[m]") plt.ylabel("y[m]") plt.axis("equal") plt.grid(True) flg, ax = plt.subplots(1) plt.plot(t, [iv * 3.6 for iv in v], "-r") plt.xlabel("Time[s]") plt.ylabel("Speed[km/h]") plt.grid(True) plt.show() def main2(): import pandas as pd data = pd.read_csv("rrt_course.csv") cx = np.array(data["x"]) cy = np.array(data["y"]) cyaw = np.array(data["yaw"]) target_speed = 10.0 / 3.6 goal = [cx[-1], cy[-1]] cx, cy, cyaw = extend_path(cx, cy, cyaw) speed_profile = calc_speed_profile(cx, cy, cyaw, target_speed) t, x, y, yaw, v, a, d, flag = closed_loop_prediction( cx, cy, cyaw, speed_profile, goal) flg, ax = plt.subplots(1) plt.plot(cx, cy, ".r", label="course") plt.plot(x, y, "-b", label="trajectory") plt.plot(goal[0], goal[1], "xg", label="goal") plt.legend() plt.xlabel("x[m]") plt.ylabel("y[m]") plt.axis("equal") plt.grid(True) flg, ax = plt.subplots(1) plt.plot(t, [iv * 3.6 for iv in v], "-r") plt.xlabel("Time[s]") plt.ylabel("Speed[km/h]") plt.grid(True) plt.show() if __name__ == '__main__': print("Pure pursuit path tracking simulation start") # main() main2()