import numpy as np import matplotlib.pyplot as plt import math import copy from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt from animation import AnimDrawer # from control import matlab class TwoWheeledSystem(): """SampleSystem, this is the simulator Attributes ----------- xs : numpy.ndarray system states, [x, y, theta] history_xs : list time history of state """ def __init__(self, init_states=None): """ Palameters ----------- init_state : float, optional, shape(3, ) initial state of system default is None """ self.xs = np.zeros(3) if init_states is not None: self.xs = copy.deepcopy(init_states) self.history_xs = [init_states] 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] """ # for theta 1, theta 1 dot, theta 2, theta 2 dot k0 = [0.0 for _ in range(3)] k1 = [0.0 for _ in range(3)] k2 = [0.0 for _ in range(3)] k3 = [0.0 for _ in range(3)] functions = [self._func_x_1, self._func_x_2, self._func_x_3] # solve Runge-Kutta for i, func in enumerate(functions): k0[i] = dt * func(self.xs[0], self.xs[1], self.xs[2], 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., us[0], us[1]) for i, func in enumerate(functions): k2[i] = dt * func(self.xs[0] + k0[0]/2., self.xs[1] + k0[1]/2., self.xs[2] + k0[2]/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], 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. # save save_states = copy.deepcopy(self.xs) self.history_xs.append(save_states) print(self.xs) def _func_x_1(self, y_1, y_2, y_3, 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 = math.cos(y_3) * u_1 return y_dot def _func_x_2(self, y_1, y_2, y_3, 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 = math.sin(y_3) * u_1 return y_dot def _func_x_3(self, y_1, y_2, y_3, 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_2 return y_dot def main(): dt = 0.05 simulation_time = 10 # in seconds iteration_num = int(simulation_time / dt) # you must be care about this matrix # these A and B are for continuos system if you want to use discret system matrix please skip this step # lineared car system V = 5.0 Ad = np.array([[1., V * dt], [0., 1.]]) Bd = np.array([[0.], [1. * dt]]) C = np.eye(2) D = np.zeros((2, 1)) # make simulator with coninuous matrix init_xs_lead = np.array([5., 0., 0.]) init_xs_follow = np.array([0., 0., 0.]) lead_car = TwoWheeledSystem(init_states=init_xs_lead) follow_car = TwoWheeledSystem(init_states=init_xs_follow) # create system # sysc = matlab.ss(A, B, C, D) # discrete system # sysd = matlab.c2d(sysc, dt) # evaluation function weight Q = np.diag([1., 1.]) R = np.diag([5.]) pre_step = 15 # make controller with discreted matrix # please check the solver, if you want to use the scipy, set the MpcController_scipy lead_controller = MpcController_cvxopt(Ad, Bd, Q, R, pre_step, dt_input_upper=np.array([30 * dt]), dt_input_lower=np.array([-30 * dt]), input_upper=np.array([30.]), input_lower=np.array([-30.])) follow_controller = MpcController_cvxopt(Ad, Bd, Q, R, pre_step, dt_input_upper=np.array([30 * dt]), dt_input_lower=np.array([-30 * dt]), input_upper=np.array([30.]), input_lower=np.array([-30.])) lead_controller.initialize_controller() follow_controller.initialize_controller() # reference lead_reference = np.array([[0., 0.] for _ in range(pre_step)]).flatten() for i in range(iteration_num): print("simulation time = {0}".format(i)) # make lead car's move if i > int(iteration_num / 3): lead_reference = np.array([[4., 0.] for _ in range(pre_step)]).flatten() lead_states = lead_car.xs lead_opt_u = lead_controller.calc_input(lead_states[1:], lead_reference) lead_opt_u = np.hstack((np.array([V]), lead_opt_u)) # make follow car follow_reference = np.array([lead_states[1:] for _ in range(pre_step)]).flatten() follow_states = follow_car.xs follow_opt_u = follow_controller.calc_input(follow_states[1:], follow_reference) follow_opt_u = np.hstack((np.array([V]), follow_opt_u)) lead_car.update_state(lead_opt_u, dt=dt) follow_car.update_state(follow_opt_u, dt=dt) # figures and animation lead_history_states = np.array(lead_car.history_xs) follow_history_states = np.array(follow_car.history_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, follow_history_states]) animdrawer.draw_anim() if __name__ == "__main__": main()