import numpy as np
import matplotlib.pyplot as plt
import math
import copy
# from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
from extended_MPC import IterativeMpcController
from animation import AnimDrawer
# from control import matlab
from coordinate_trans import coordinate_transformation_in_angle, coordinate_transformation_in_position
from traj_func import make_sample_traj
from func_curvature import calc_curvatures, calc_ideal_vel
class WheeledSystem():
"""SampleSystem, this is the simulator
Kinematic model of car
Attributes
-----------
xs : numpy.ndarray
system states, [x, y, phi, beta]
history_xs : list
time history of state
tau : float
time constant of tire
FRONT_WHEEL_BASE : float
REAR_WHEEL_BASE : float
predict_xs :
"""
def __init__(self, init_states=None):
"""
Palameters
-----------
init_state : float, optional, shape(3, )
initial state of system default is None
"""
self.NUM_STATE = 4
self.xs = np.zeros(self.NUM_STATE)
self.tau = 0.01
self.FRONT_WHEELE_BASE = 1.0
self.REAR_WHEELE_BASE = 1.0
if init_states is not None:
self.xs = copy.deepcopy(init_states)
self.history_xs = [init_states]
self.history_predict_xs = []
def update_state(self, us, dt=0.01):
"""
Palameters
------------
u : numpy.ndarray
inputs of system in some cases this means the reference
dt : float in seconds, optional
sampling time of simulation, default is 0.01 [s]
"""
k0 = [0.0 for _ in range(self.NUM_STATE)]
k1 = [0.0 for _ in range(self.NUM_STATE)]
k2 = [0.0 for _ in range(self.NUM_STATE)]
k3 = [0.0 for _ in range(self.NUM_STATE)]
functions = [self._func_x_1, self._func_x_2, self._func_x_3, self._func_x_4]
# solve Runge-Kutta
for i, func in enumerate(functions):
k0[i] = dt * func(self.xs[0], self.xs[1], self.xs[2], self.xs[3], us[0], us[1])
for i, func in enumerate(functions):
k1[i] = dt * func(self.xs[0] + k0[0]/2., self.xs[1] + k0[1]/2., self.xs[2] + k0[2]/2., self.xs[3] + k0[3]/2, us[0], us[1])
for i, func in enumerate(functions):
k2[i] = dt * func(self.xs[0] + k1[0]/2., self.xs[1] + k1[1]/2., self.xs[2] + k1[2]/2., self.xs[3] + k1[3]/2., us[0], us[1])
for i, func in enumerate(functions):
k3[i] = dt * func(self.xs[0] + k2[0], self.xs[1] + k2[1], self.xs[2] + k2[2], self.xs[3] + k2[3], us[0], us[1])
self.xs[0] += (k0[0] + 2. * k1[0] + 2. * k2[0] + k3[0]) / 6.
self.xs[1] += (k0[1] + 2. * k1[1] + 2. * k2[1] + k3[1]) / 6.
self.xs[2] += (k0[2] + 2. * k1[2] + 2. * k2[2] + k3[2]) / 6.
self.xs[3] += (k0[3] + 2. * k1[3] + 2. * k2[3] + k3[3]) / 6.
# save
save_states = copy.deepcopy(self.xs)
self.history_xs.append(save_states)
# print(self.xs)
def predict_state(self, us, dt=0.01):
"""make predict state by using optimal input made by MPC
Paramaters
-----------
us : array-like, shape(2, N)
optimal input made by MPC
dt : float in seconds, optional
sampling time of simulation, default is 0.01 [s]
"""
xs = copy.deepcopy(self.xs)
predict_xs = [copy.deepcopy(xs)]
for i in range(us.shape[1]):
k0 = [0.0 for _ in range(self.NUM_STATE)]
k1 = [0.0 for _ in range(self.NUM_STATE)]
k2 = [0.0 for _ in range(self.NUM_STATE)]
k3 = [0.0 for _ in range(self.NUM_STATE)]
functions = [self._func_x_1, self._func_x_2, self._func_x_3, self._func_x_4]
# solve Runge-Kutta
for i, func in enumerate(functions):
k0[i] = dt * func(xs[0], xs[1], xs[2], xs[3], us[0, i], us[1, i])
for i, func in enumerate(functions):
k1[i] = dt * func(xs[0] + k0[0]/2., xs[1] + k0[1]/2., xs[2] + k0[2]/2., xs[3] + k0[3]/2., us[0, i], us[1, i])
for i, func in enumerate(functions):
k2[i] = dt * func(xs[0] + k1[0]/2., xs[1] + k1[1]/2., xs[2] + k1[2]/2., xs[3] + k1[3]/2., us[0, i], us[1, i])
for i, func in enumerate(functions):
k3[i] = dt * func(xs[0] + k2[0], xs[1] + k2[1], xs[2] + k2[2], xs[3] + k2[3], us[0, i], us[1, i])
xs[0] += (k0[0] + 2. * k1[0] + 2. * k2[0] + k3[0]) / 6.
xs[1] += (k0[1] + 2. * k1[1] + 2. * k2[1] + k3[1]) / 6.
xs[2] += (k0[2] + 2. * k1[2] + 2. * k2[2] + k3[2]) / 6.
xs[3] += (k0[3] + 2. * k1[3] + 2. * k2[3] + k3[3]) / 6.
predict_xs.append(copy.deepcopy(xs))
self.history_predict_xs.append(np.array(predict_xs))
def _func_x_1(self, y_1, y_2, y_3, y_4, u_1, u_2):
"""
Parameters
------------
y_1 : float
y_2 : float
y_3 : float
u_1 : float
system input
u_2 : float
system input
"""
# y_dot = u_1 * math.cos(y_3 + y_4)
y_dot = u_1 * math.cos(y_3)
return y_dot
def _func_x_2(self, y_1, y_2, y_3, y_4, u_1, u_2):
"""
Parameters
------------
y_1 : float
y_2 : float
y_3 : float
u_1 : float
system input
u_2 : float
system input
"""
# y_dot = u_1 * math.sin(y_3 + y_4)
y_dot = u_1 * math.sin(y_3)
return y_dot
def _func_x_3(self, y_1, y_2, y_3, y_4, u_1, u_2):
"""
Parameters
------------
y_1 : float
y_2 : float
y_3 : float
u_1 : float
system input
u_2 : float
system input
"""
# y_dot = u_1 / self.REAR_WHEELE_BASE * math.sin(y_4)
y_dot = u_1 * math.tan(y_4) / (self.REAR_WHEELE_BASE + self.FRONT_WHEELE_BASE)
return y_dot
def _func_x_4(self, y_1, y_2, y_3, y_4, u_1, u_2):
"""Ad, Bd, W_D, Q, R
ParAd, Bd, W_D, Q, R
---Ad, Bd, W_D, Q, R
y_1 : float
y_2 : float
y_3 : float
u_1 : float
system input
u_2 : float
system input
"""
# y_dot = math.atan2(self.REAR_WHEELE_BASE * math.tan(u_2) ,self.REAR_WHEELE_BASE + self.FRONT_WHEELE_BASE)
y_dot = - 1. / self.tau * (y_4 - u_2)
return y_dot
class SystemModel():
"""
Attributes
-----------
WHEEL_BASE : float
wheel base of the car
Ad_s : list
list of system model matrix Ad
Bd_s : list
list of system model matrix Bd
W_D_s : list
list of system model matrix W_D_s
Q : numpy.ndarray
R : numpy.ndarray
"""
def __init__(self, tau = 0.01, dt = 0.01):
"""
Parameters
-----------
tau : time constant, optional
dt : sampling time, optional
"""
self.dt = dt
self.tau = tau
self.WHEEL_BASE = 2.2
self.Ad_s = []
self.Bd_s = []
self.W_D_s = []
def calc_predict_sytem_model(self, V, curvatures, predict_step):
"""
calc next predict systemo models
V : float
current speed of car
curvatures : list
this is the next curvature's list
predict_step : int
predict step of MPC
"""
for i in range(predict_step):
delta_r = math.atan2(self.WHEEL_BASE, 1. / curvatures[i])
A12 = (V / self.WHEEL_BASE) / (math.cos(delta_r)**2)
A22 = (1. - 1. / self.tau * self.dt)
Ad = np.array([[1., V * self.dt, 0.],
[0., 1., A12 * self.dt],
[0., 0., A22]])
Bd = np.array([[0.], [0.], [1. / self.tau]]) * self.dt
# -v*curvature + v/L*(tan(delta_r)-delta_r*cos_delta_r_squared_inv);
# W_D_0 = V / self.WHEEL_BASE * (delta_r / (math.cos(delta_r)**2)
W_D_0 = -V * curvatures[i] + (V / self.WHEEL_BASE) * (math.tan(delta_r) - delta_r / (math.cos(delta_r)**2))
W_D = np.array([[0.], [W_D_0], [0.]]) * self.dt
self.Ad_s.append(Ad)
self.Bd_s.append(Bd)
self.W_D_s.append(W_D)
# return self.Ad_s, self.Bd_s, self.W_D_s
def search_nearest_point(points, base_point):
"""
Parameters
-----------
points : numpy.ndarray, shape is (2, N)
base_point : numpy.ndarray, shape is (2, 1)
Returns
-------
nearest_index :
nearest_point :
"""
distance_mat = np.sqrt(np.sum((points - base_point)**2, axis=0))
index_min = np.argmin(distance_mat)
return index_min, points[:, index_min]
def main():
# parameters
dt = 0.01
simulation_time = 20 # in seconds
PREDICT_STEP = 30
iteration_num = int(simulation_time / dt)
# make simulator with coninuous matrix
init_xs_lead = np.array([0., 0., math.pi/5, 0.])
lead_car = WheeledSystem(init_states=init_xs_lead)
# make system model
lead_car_system_model = SystemModel()
# reference
history_traj_ref = []
history_angle_ref = []
traj_ref_xs, traj_ref_ys = make_sample_traj(int(simulation_time/dt))
traj_ref = np.array([traj_ref_xs, traj_ref_ys])
# nearest point
index_min, nearest_point = search_nearest_point(traj_ref, lead_car.xs[:2].reshape(2, 1))
# get traj's curvature
NUM_SKIP = 3
MARGIN = 50
angles, curvatures = calc_curvatures(traj_ref[:, index_min + MARGIN:index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN], PREDICT_STEP, NUM_SKIP)
# save traj ref
history_traj_ref.append(traj_ref[:, index_min + MARGIN:index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN])
history_angle_ref.append(angles)
# print(history_traj_ref)
# input()
# evaluation function weight
Q = np.diag([1e2, 1., 1e3])
R = np.diag([1e2])
# System model update
V = calc_ideal_vel(traj_ref, dt) # in pratical we should calc from the state
lead_car_system_model.calc_predict_sytem_model(V, curvatures, PREDICT_STEP)
# make controller with discreted matrix
lead_controller = IterativeMpcController(lead_car_system_model, Q, R, PREDICT_STEP,
dt_input_upper=np.array([1 * dt]), dt_input_lower=np.array([-1 * dt]),
input_upper=np.array([1.]), input_lower=np.array([-1.]))
# initialize
lead_controller.initialize_controller()
for i in range(iteration_num):
print("simulation time = {0}".format(i))
## lead
# world traj
lead_states = lead_car.xs
# nearest point
index_min, nearest_point = search_nearest_point(traj_ref, lead_car.xs[:2].reshape(2, 1))
# end check
if len(traj_ref_ys) <= index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN:
print("break")
break
# get traj's curvature
angles, curvatures = calc_curvatures(traj_ref[:, index_min+MARGIN:index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN], PREDICT_STEP, NUM_SKIP)
# save
history_traj_ref.append(traj_ref[:, index_min + MARGIN:index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN])
history_angle_ref.append(angles)
# System model update
V = calc_ideal_vel(traj_ref, dt) # in pratical we should calc from the state
lead_car_system_model.calc_predict_sytem_model(V, curvatures, PREDICT_STEP)
# transformation
# car
relative_car_position = coordinate_transformation_in_position(lead_states[:2].reshape(2, 1), nearest_point)
relative_car_position = coordinate_transformation_in_angle(relative_car_position, angles[0])
relative_car_angle = lead_states[2] - angles[0]
relative_car_state = np.hstack((relative_car_position[1], relative_car_angle, lead_states[-1]))
# traj_ref
relative_traj = coordinate_transformation_in_position(traj_ref[:, index_min:index_min + PREDICT_STEP], nearest_point)
relative_traj = coordinate_transformation_in_angle(relative_traj, angles[0])
relative_ref_angle = np.array(angles) - angles[0]
# make ref
lead_reference = np.array([[relative_traj[1, -1], relative_ref_angle[-1], 0.] for i in range(PREDICT_STEP)]).flatten()
print("relative car state = {}".format(relative_car_state))
print("nearest point = {}".format(nearest_point))
# input()
# update system matrix
lead_controller.update_system_model(lead_car_system_model)
lead_opt_u, all_opt_u = lead_controller.calc_input(relative_car_state, lead_reference)
lead_opt_u = np.hstack((np.array([V]), lead_opt_u))
all_opt_u = np.stack((np.ones(PREDICT_STEP)*V, all_opt_u.flatten()))
print("opt_u = {}".format(lead_opt_u))
print("all_opt_u = {}".format(all_opt_u))
# predict
lead_car.predict_state(all_opt_u, dt=dt)
# update
lead_car.update_state(lead_opt_u, dt=dt)
# print(lead_car.history_predict_xs)
# input()
# figures and animation
lead_history_states = np.array(lead_car.history_xs)
lead_history_predict_states = lead_car.history_predict_xs
"""
time_history_fig = plt.figure()
x_fig = time_history_fig.add_subplot(311)
y_fig = time_history_fig.add_subplot(312)
theta_fig = time_history_fig.add_subplot(313)
car_traj_fig = plt.figure()
traj_fig = car_traj_fig.add_subplot(111)
traj_fig.set_aspect('equal')
x_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 0], label="lead")
x_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 0], label="follow")
x_fig.set_xlabel("time [s]")
x_fig.set_ylabel("x")
x_fig.legend()
y_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 1], label="lead")
y_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 1], label="follow")
y_fig.plot(np.arange(0, simulation_time+0.01, dt), [4. for _ in range(iteration_num+1)], linestyle="dashed")
y_fig.set_xlabel("time [s]")
y_fig.set_ylabel("y")
y_fig.legend()
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 2], label="lead")
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 2], label="follow")
theta_fig.plot(np.arange(0, simulation_time+0.01, dt), [0. for _ in range(iteration_num+1)], linestyle="dashed")
theta_fig.set_xlabel("time [s]")
theta_fig.set_ylabel("theta")
theta_fig.legend()
time_history_fig.tight_layout()
traj_fig.plot(lead_history_states[:, 0], lead_history_states[:, 1], label="lead")
traj_fig.plot(follow_history_states[:, 0], follow_history_states[:, 1], label="follow")
traj_fig.set_xlabel("x")
traj_fig.set_ylabel("y")
traj_fig.legend()
plt.show()
lead_history_us = np.array(lead_controller.history_us)
follow_history_us = np.array(follow_controller.history_us)
input_history_fig = plt.figure()
u_1_fig = input_history_fig.add_subplot(111)
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_us[:, 0], label="lead")
u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_us[:, 0], label="follow")
u_1_fig.set_xlabel("time [s]")
u_1_fig.set_ylabel("u_omega")
input_history_fig.tight_layout()
plt.show()
"""
animdrawer = AnimDrawer([lead_history_states, lead_history_predict_states, traj_ref, history_traj_ref, history_angle_ref])
animdrawer.draw_anim()
if __name__ == "__main__":
main()