mirror of
https://github.com/AtsushiSakai/PythonRobotics.git
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237 lines
6.3 KiB
Python
237 lines
6.3 KiB
Python
"""
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Path tracking simulation with rear wheel feedback steering control and PID speed control.
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author: Atsushi Sakai(@Atsushi_twi)
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"""
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import matplotlib.pyplot as plt
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import math
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import numpy as np
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from scipy import interpolate
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from scipy import optimize
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Kp = 1.0 # speed proportional gain
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# steering control parameter
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KTH = 1.0
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KE = 0.5
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dt = 0.1 # [s]
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L = 2.9 # [m]
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show_animation = True
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class State:
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def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0, direction=1):
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self.x = x
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self.y = y
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self.yaw = yaw
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self.v = v
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self.direction = direction
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def update(self, a, delta, dt):
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self.x = self.x + self.v * math.cos(self.yaw) * dt
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self.y = self.y + self.v * math.sin(self.yaw) * dt
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self.yaw = self.yaw + self.v / L * math.tan(delta) * dt
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self.v = self.v + a * dt
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class CubicSplinePath:
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def __init__(self, x, y):
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x, y = map(np.asarray, (x, y))
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s = np.append([0],(np.cumsum(np.diff(x)**2) + np.cumsum(np.diff(y)**2))**0.5)
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self.X = interpolate.CubicSpline(s, x)
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self.Y = interpolate.CubicSpline(s, y)
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self.dX = self.X.derivative(1)
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self.ddX = self.X.derivative(2)
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self.dY = self.Y.derivative(1)
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self.ddY = self.Y.derivative(2)
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self.length = s[-1]
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def calc_yaw(self, s):
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dx, dy = self.dX(s), self.dY(s)
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return np.arctan2(dy, dx)
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def calc_curvature(self, s):
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dx, dy = self.dX(s), self.dY(s)
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ddx, ddy = self.ddX(s), self.ddY(s)
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return (ddy * dx - ddx * dy) / ((dx ** 2 + dy ** 2)**(3 / 2))
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def __find_nearest_point(self, s0, x, y):
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def calc_distance(_s, *args):
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_x, _y= self.X(_s), self.Y(_s)
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return (_x - args[0])**2 + (_y - args[1])**2
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def calc_distance_jacobian(_s, *args):
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_x, _y = self.X(_s), self.Y(_s)
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_dx, _dy = self.dX(_s), self.dY(_s)
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return 2*_dx*(_x - args[0])+2*_dy*(_y-args[1])
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minimum = optimize.fmin_cg(calc_distance, s0, calc_distance_jacobian, args=(x, y), full_output=True, disp=False)
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return minimum
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def calc_track_error(self, x, y, s0):
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ret = self.__find_nearest_point(s0, x, y)
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s = ret[0][0]
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e = ret[1]
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k = self.calc_curvature(s)
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yaw = self.calc_yaw(s)
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dxl = self.X(s) - x
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dyl = self.Y(s) - y
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angle = pi_2_pi(yaw - math.atan2(dyl, dxl))
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if angle < 0:
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e*= -1
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return e, k, yaw, s
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def pid_control(target, current):
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a = Kp * (target - current)
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return a
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def pi_2_pi(angle):
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while(angle > math.pi):
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angle = angle - 2.0 * math.pi
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while(angle < -math.pi):
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angle = angle + 2.0 * math.pi
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return angle
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def rear_wheel_feedback_control(state, e, k, yaw_ref):
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v = state.v
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th_e = pi_2_pi(state.yaw - yaw_ref)
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omega = v * k * math.cos(th_e) / (1.0 - k * e) - \
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KTH * abs(v) * th_e - KE * v * math.sin(th_e) * e / th_e
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if th_e == 0.0 or omega == 0.0:
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return 0.0
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delta = math.atan2(L * omega / v, 1.0)
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return delta
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def simulate(path_ref, goal):
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T = 500.0 # max simulation time
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goal_dis = 0.3
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state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
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time = 0.0
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x = [state.x]
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y = [state.y]
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yaw = [state.yaw]
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v = [state.v]
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t = [0.0]
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goal_flag = False
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s = np.arange(0, path_ref.length, 0.1)
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e, k, yaw_ref, s0 = path_ref.calc_track_error(state.x, state.y, 0.0)
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while T >= time:
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e, k, yaw_ref, s0 = path_ref.calc_track_error(state.x, state.y, s0)
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di = rear_wheel_feedback_control(state, e, k, yaw_ref)
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speed_ref = calc_target_speed(state, yaw_ref)
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ai = pid_control(speed_ref, state.v)
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state.update(ai, di, dt)
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time = time + dt
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# check goal
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dx = state.x - goal[0]
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dy = state.y - goal[1]
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if math.hypot(dx, dy) <= goal_dis:
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print("Goal")
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goal_flag = True
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break
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x.append(state.x)
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y.append(state.y)
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yaw.append(state.yaw)
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v.append(state.v)
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t.append(time)
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if show_animation:
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plt.cla()
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# for stopping simulation with the esc key.
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plt.gcf().canvas.mpl_connect('key_release_event',
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lambda event: [exit(0) if event.key == 'escape' else None])
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plt.plot(path_ref.X(s), path_ref.Y(s), "-r", label="course")
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plt.plot(x, y, "ob", label="trajectory")
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plt.plot(path_ref.X(s0), path_ref.Y(s0), "xg", label="target")
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plt.axis("equal")
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plt.grid(True)
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plt.title("speed[km/h]:{:.2f}, target s-param:{:.2f}".format(round(state.v * 3.6, 2), s0))
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plt.pause(0.0001)
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return t, x, y, yaw, v, goal_flag
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def calc_target_speed(state, yaw_ref):
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target_speed = 10.0 / 3.6
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dyaw = yaw_ref - state.yaw
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switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
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if switch:
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state.direction *= -1
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return 0.0
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if state.direction != 1:
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return -target_speed
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return target_speed
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def main():
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print("rear wheel feedback tracking start!!")
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ax = [0.0, 6.0, 12.5, 5.0, 7.5, 3.0, -1.0]
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ay = [0.0, 0.0, 5.0, 6.5, 3.0, 5.0, -2.0]
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goal = [ax[-1], ay[-1]]
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reference_path = CubicSplinePath(ax, ay)
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s = np.arange(0, reference_path.length, 0.1)
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t, x, y, yaw, v, goal_flag = simulate(reference_path, goal)
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# Test
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assert goal_flag, "Cannot goal"
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if show_animation: # pragma: no cover
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plt.close()
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plt.subplots(1)
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plt.plot(ax, ay, "xb", label="input")
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plt.plot(reference_path.X(s), reference_path.Y(s), "-r", label="spline")
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plt.plot(x, y, "-g", label="tracking")
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plt.grid(True)
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plt.axis("equal")
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plt.xlabel("x[m]")
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plt.ylabel("y[m]")
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plt.legend()
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plt.subplots(1)
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plt.plot(s, np.rad2deg(reference_path.calc_yaw(s)), "-r", label="yaw")
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plt.grid(True)
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plt.legend()
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plt.xlabel("line length[m]")
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plt.ylabel("yaw angle[deg]")
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plt.subplots(1)
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plt.plot(s, reference_path.calc_curvature(s), "-r", label="curvature")
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plt.grid(True)
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plt.legend()
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plt.xlabel("line length[m]")
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plt.ylabel("curvature [1/m]")
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plt.show()
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if __name__ == '__main__':
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main()
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