464 lines
16 KiB
Python
464 lines
16 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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import math
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import copy
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# from mpc_func_with_cvxopt import MpcController as MpcController_cvxopt
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from iterative_MPC import IterativeMpcController
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from animation import AnimDrawer
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# from control import matlab
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from coordinate_trans import coordinate_transformation_in_angle, coordinate_transformation_in_position
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from traj_func import make_sample_traj
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from func_curvature import calc_curvatures, calc_ideal_vel
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class WheeledSystem():
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"""SampleSystem, this is the simulator
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Kinematic model of car
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Attributes
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-----------
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xs : numpy.ndarray
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system states, [x, y, phi, beta]
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history_xs : list
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time history of state
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tau : float
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time constant of tire
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FRONT_WHEEL_BASE : float
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REAR_WHEEL_BASE : float
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predict_xs :
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"""
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def __init__(self, init_states=None):
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"""
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Palameters
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-----------
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init_state : float, optional, shape(3, )
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initial state of system default is None
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"""
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self.NUM_STATE = 4
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self.xs = np.zeros(self.NUM_STATE)
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self.tau = 0.01
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self.FRONT_WHEELE_BASE = 1.0
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self.REAR_WHEELE_BASE = 1.0
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if init_states is not None:
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self.xs = copy.deepcopy(init_states)
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self.history_xs = [init_states]
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self.history_predict_xs = []
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def update_state(self, us, dt=0.01):
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"""
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Palameters
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------------
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u : numpy.ndarray
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inputs of system in some cases this means the reference
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dt : float in seconds, optional
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sampling time of simulation, default is 0.01 [s]
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"""
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k0 = [0.0 for _ in range(self.NUM_STATE)]
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k1 = [0.0 for _ in range(self.NUM_STATE)]
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k2 = [0.0 for _ in range(self.NUM_STATE)]
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k3 = [0.0 for _ in range(self.NUM_STATE)]
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functions = [self._func_x_1, self._func_x_2, self._func_x_3, self._func_x_4]
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# solve Runge-Kutta
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for i, func in enumerate(functions):
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k0[i] = dt * func(self.xs[0], self.xs[1], self.xs[2], self.xs[3], us[0], us[1])
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for i, func in enumerate(functions):
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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])
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for i, func in enumerate(functions):
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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])
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for i, func in enumerate(functions):
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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])
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self.xs[0] += (k0[0] + 2. * k1[0] + 2. * k2[0] + k3[0]) / 6.
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self.xs[1] += (k0[1] + 2. * k1[1] + 2. * k2[1] + k3[1]) / 6.
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self.xs[2] += (k0[2] + 2. * k1[2] + 2. * k2[2] + k3[2]) / 6.
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self.xs[3] += (k0[3] + 2. * k1[3] + 2. * k2[3] + k3[3]) / 6.
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# save
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save_states = copy.deepcopy(self.xs)
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self.history_xs.append(save_states)
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# print(self.xs)
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def predict_state(self, us, dt=0.01):
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"""make predict state by using optimal input made by MPC
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Paramaters
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-----------
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us : array-like, shape(2, N)
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optimal input made by MPC
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dt : float in seconds, optional
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sampling time of simulation, default is 0.01 [s]
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"""
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xs = copy.deepcopy(self.xs)
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predict_xs = [copy.deepcopy(xs)]
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for i in range(us.shape[1]):
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k0 = [0.0 for _ in range(self.NUM_STATE)]
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k1 = [0.0 for _ in range(self.NUM_STATE)]
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k2 = [0.0 for _ in range(self.NUM_STATE)]
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k3 = [0.0 for _ in range(self.NUM_STATE)]
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functions = [self._func_x_1, self._func_x_2, self._func_x_3, self._func_x_4]
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# solve Runge-Kutta
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for i, func in enumerate(functions):
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k0[i] = dt * func(xs[0], xs[1], xs[2], xs[3], us[0, i], us[1, i])
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for i, func in enumerate(functions):
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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])
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for i, func in enumerate(functions):
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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])
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for i, func in enumerate(functions):
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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])
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xs[0] += (k0[0] + 2. * k1[0] + 2. * k2[0] + k3[0]) / 6.
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xs[1] += (k0[1] + 2. * k1[1] + 2. * k2[1] + k3[1]) / 6.
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xs[2] += (k0[2] + 2. * k1[2] + 2. * k2[2] + k3[2]) / 6.
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xs[3] += (k0[3] + 2. * k1[3] + 2. * k2[3] + k3[3]) / 6.
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predict_xs.append(copy.deepcopy(xs))
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self.history_predict_xs.append(np.array(predict_xs))
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def _func_x_1(self, y_1, y_2, y_3, y_4, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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# y_dot = u_1 * math.cos(y_3 + y_4)
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y_dot = u_1 * math.cos(y_3)
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return y_dot
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def _func_x_2(self, y_1, y_2, y_3, y_4, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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# y_dot = u_1 * math.sin(y_3 + y_4)
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y_dot = u_1 * math.sin(y_3)
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return y_dot
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def _func_x_3(self, y_1, y_2, y_3, y_4, u_1, u_2):
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"""
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Parameters
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------------
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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# y_dot = u_1 / self.REAR_WHEELE_BASE * math.sin(y_4)
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y_dot = u_1 * math.tan(y_4) / (self.REAR_WHEELE_BASE + self.FRONT_WHEELE_BASE)
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return y_dot
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def _func_x_4(self, y_1, y_2, y_3, y_4, u_1, u_2):
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"""Ad, Bd, W_D, Q, R
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ParAd, Bd, W_D, Q, R
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---Ad, Bd, W_D, Q, R
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y_1 : float
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y_2 : float
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y_3 : float
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u_1 : float
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system input
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u_2 : float
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system input
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"""
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# y_dot = math.atan2(self.REAR_WHEELE_BASE * math.tan(u_2) ,self.REAR_WHEELE_BASE + self.FRONT_WHEELE_BASE)
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y_dot = - 1. / self.tau * (y_4 - u_2)
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return y_dot
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class SystemModel():
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"""
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Attributes
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-----------
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WHEEL_BASE : float
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wheel base of the car
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Ad_s : list
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list of system model matrix Ad
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Bd_s : list
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list of system model matrix Bd
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W_D_s : list
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list of system model matrix W_D_s
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Q : numpy.ndarray
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R : numpy.ndarray
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"""
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def __init__(self, tau = 0.01, dt = 0.01):
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"""
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Parameters
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-----------
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tau : time constant, optional
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dt : sampling time, optional
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"""
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self.dt = dt
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self.tau = tau
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self.WHEEL_BASE = 2.2
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self.Ad_s = []
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self.Bd_s = []
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self.W_D_s = []
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def calc_predict_sytem_model(self, V, curvatures, predict_step):
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"""
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calc next predict systemo models
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V : float
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current speed of car
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curvatures : list
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this is the next curvature's list
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predict_step : int
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predict step of MPC
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"""
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for i in range(predict_step):
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delta_r = math.atan2(self.WHEEL_BASE, 1. / curvatures[i])
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A12 = (V / self.WHEEL_BASE) / (math.cos(delta_r)**2)
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A22 = (1. - 1. / self.tau * self.dt)
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Ad = np.array([[1., V * self.dt, 0.],
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[0., 1., A12 * self.dt],
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[0., 0., A22]])
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Bd = np.array([[0.], [0.], [1. / self.tau]]) * self.dt
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# -v*curvature + v/L*(tan(delta_r)-delta_r*cos_delta_r_squared_inv);
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# W_D_0 = V / self.WHEEL_BASE * (delta_r / (math.cos(delta_r)**2)
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W_D_0 = -V * curvatures[i] + (V / self.WHEEL_BASE) * (math.tan(delta_r) - delta_r / (math.cos(delta_r)**2))
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W_D = np.array([[0.], [W_D_0], [0.]]) * self.dt
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self.Ad_s.append(Ad)
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self.Bd_s.append(Bd)
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self.W_D_s.append(W_D)
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# return self.Ad_s, self.Bd_s, self.W_D_s
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def search_nearest_point(points, base_point):
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"""
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Parameters
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-----------
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points : numpy.ndarray, shape is (2, N)
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base_point : numpy.ndarray, shape is (2, 1)
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Returns
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-------
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nearest_index :
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nearest_point :
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"""
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distance_mat = np.sqrt(np.sum((points - base_point)**2, axis=0))
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index_min = np.argmin(distance_mat)
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return index_min, points[:, index_min]
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def main():
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# parameters
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dt = 0.01
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simulation_time = 20 # in seconds
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PREDICT_STEP = 30
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iteration_num = int(simulation_time / dt)
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# make simulator with coninuous matrix
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init_xs_lead = np.array([0., 0., math.pi/6, 0.])
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lead_car = WheeledSystem(init_states=init_xs_lead)
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# make system model
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lead_car_system_model = SystemModel()
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# reference
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history_traj_ref = []
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history_angle_ref = []
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traj_ref_xs, traj_ref_ys = make_sample_traj(int(simulation_time/dt))
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traj_ref = np.array([traj_ref_xs, traj_ref_ys])
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# nearest point
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index_min, nearest_point = search_nearest_point(traj_ref, lead_car.xs[:2].reshape(2, 1))
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# get traj's curvature
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NUM_SKIP = 3
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MARGIN = 20
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angles, curvatures = calc_curvatures(traj_ref[:, index_min + MARGIN:index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN], PREDICT_STEP, NUM_SKIP)
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# save traj ref
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history_traj_ref.append(traj_ref[:, index_min + MARGIN:index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN])
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history_angle_ref.append(angles)
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# print(history_traj_ref)
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# input()
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# evaluation function weight
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Q = np.diag([1000000., 10., 1.])
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R = np.diag([0.1])
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# System model update
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V = calc_ideal_vel(traj_ref, dt) # in pratical we should calc from the state
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lead_car_system_model.calc_predict_sytem_model(V, curvatures, PREDICT_STEP)
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# make controller with discreted matrix
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lead_controller = IterativeMpcController(lead_car_system_model, Q, R, PREDICT_STEP,
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dt_input_upper=np.array([1 * dt]), dt_input_lower=np.array([-1 * dt]),
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input_upper=np.array([1.]), input_lower=np.array([-1.]))
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# initialize
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lead_controller.initialize_controller()
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for i in range(iteration_num):
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print("simulation time = {0}".format(i))
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## lead
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# world traj
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lead_states = lead_car.xs
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# nearest point
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index_min, nearest_point = search_nearest_point(traj_ref, lead_car.xs[:2].reshape(2, 1))
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# end check
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if len(traj_ref_ys) <= index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN:
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print("break")
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break
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# get traj's curvature
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angles, curvatures = calc_curvatures(traj_ref[:, index_min+MARGIN:index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN], PREDICT_STEP, NUM_SKIP)
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# save
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history_traj_ref.append(traj_ref[:, index_min + MARGIN:index_min + PREDICT_STEP + 2 * NUM_SKIP + MARGIN])
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history_angle_ref.append(angles)
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# System model update
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V = calc_ideal_vel(traj_ref, dt) # in pratical we should calc from the state
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lead_car_system_model.calc_predict_sytem_model(V, curvatures, PREDICT_STEP)
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# transformation
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# car
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relative_car_position = coordinate_transformation_in_position(lead_states[:2].reshape(2, 1), nearest_point)
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relative_car_position = coordinate_transformation_in_angle(relative_car_position, angles[0])
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relative_car_angle = lead_states[2] - angles[0]
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relative_car_state = np.hstack((relative_car_position[1], relative_car_angle, lead_states[-1]))
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# traj_ref
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relative_traj = coordinate_transformation_in_position(traj_ref[:, index_min:index_min + PREDICT_STEP], nearest_point)
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relative_traj = coordinate_transformation_in_angle(relative_traj, angles[0])
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relative_ref_angle = np.array(angles) - angles[0]
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# make ref
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lead_reference = np.array([[relative_traj[1, -1], relative_ref_angle[-1], 0.] for i in range(PREDICT_STEP)]).flatten()
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print("relative car state = {}".format(relative_car_state))
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print("nearest point = {}".format(nearest_point))
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# input()
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# update system matrix
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lead_controller.update_system_model(lead_car_system_model)
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lead_opt_u, all_opt_u = lead_controller.calc_input(relative_car_state, lead_reference)
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lead_opt_u = np.hstack((np.array([V]), lead_opt_u))
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all_opt_u = np.stack((np.ones(PREDICT_STEP)*V, all_opt_u.flatten()))
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print("opt_u = {}".format(lead_opt_u))
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print("all_opt_u = {}".format(all_opt_u))
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# predict
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lead_car.predict_state(all_opt_u, dt=dt)
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# update
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lead_car.update_state(lead_opt_u, dt=dt)
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# print(lead_car.history_predict_xs)
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# input()
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# figures and animation
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lead_history_states = np.array(lead_car.history_xs)
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lead_history_predict_states = lead_car.history_predict_xs
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"""
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time_history_fig = plt.figure()
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x_fig = time_history_fig.add_subplot(311)
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y_fig = time_history_fig.add_subplot(312)
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theta_fig = time_history_fig.add_subplot(313)
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car_traj_fig = plt.figure()
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traj_fig = car_traj_fig.add_subplot(111)
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traj_fig.set_aspect('equal')
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x_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 0], label="lead")
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x_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 0], label="follow")
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x_fig.set_xlabel("time [s]")
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x_fig.set_ylabel("x")
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x_fig.legend()
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y_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 1], label="lead")
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y_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 1], label="follow")
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y_fig.plot(np.arange(0, simulation_time+0.01, dt), [4. for _ in range(iteration_num+1)], linestyle="dashed")
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y_fig.set_xlabel("time [s]")
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y_fig.set_ylabel("y")
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y_fig.legend()
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theta_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_states[:, 2], label="lead")
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theta_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_states[:, 2], label="follow")
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theta_fig.plot(np.arange(0, simulation_time+0.01, dt), [0. for _ in range(iteration_num+1)], linestyle="dashed")
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theta_fig.set_xlabel("time [s]")
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theta_fig.set_ylabel("theta")
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theta_fig.legend()
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time_history_fig.tight_layout()
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traj_fig.plot(lead_history_states[:, 0], lead_history_states[:, 1], label="lead")
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traj_fig.plot(follow_history_states[:, 0], follow_history_states[:, 1], label="follow")
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traj_fig.set_xlabel("x")
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traj_fig.set_ylabel("y")
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traj_fig.legend()
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plt.show()
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|
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lead_history_us = np.array(lead_controller.history_us)
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follow_history_us = np.array(follow_controller.history_us)
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input_history_fig = plt.figure()
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u_1_fig = input_history_fig.add_subplot(111)
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|
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u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), lead_history_us[:, 0], label="lead")
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u_1_fig.plot(np.arange(0, simulation_time+0.01, dt), follow_history_us[:, 0], label="follow")
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u_1_fig.set_xlabel("time [s]")
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u_1_fig.set_ylabel("u_omega")
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|
|
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input_history_fig.tight_layout()
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plt.show()
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|
"""
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|
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animdrawer = AnimDrawer([lead_history_states, lead_history_predict_states, traj_ref, history_traj_ref, history_angle_ref])
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animdrawer.draw_anim()
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|
|
|
if __name__ == "__main__":
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main() |