lqr_pid.py

import numpy as np
import math
import matplotlib.pyplot as plt
from rrt_plan import *
import math
import sys
import matplotlib.pyplot as plt
import numpy as np
import scipy.linalg as la
import pathlib

# === Parameters =====

# LQR parameter
lqr_Q = np.eye(5)
lqr_R = np.eye(2)
dt = 0.1  # time tick[s]
L = 0.5  # Wheel base of the vehicle [m]
max_steer = np.deg2rad(45.0)  # maximum steering angle[rad]

show_animation = True


class State:

    def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
        self.x = x
        self.y = y
        self.yaw = yaw
        self.v = v


def update(state, a, delta):

    if delta >= max_steer:
        delta = max_steer
    if delta <= - max_steer:
        delta = - max_steer

    state.x = state.x + state.v * math.cos(state.yaw) * dt
    state.y = state.y + state.v * math.sin(state.yaw) * dt
    state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
    state.v = state.v + a * dt

    return state


def pi_2_pi(angle):
    return (angle + math.pi) % (2 * math.pi) - math.pi


def solve_dare(A, B, Q, R):
    """
    solve a discrete time_Algebraic Riccati equation (DARE)
    """
    x = Q
    x_next = Q
    max_iter = 150
    eps = 0.01

    for i in range(max_iter):
        x_next = A.T @ x @ A - A.T @ x @ B @ \
                 la.inv(R + B.T @ x @ B) @ B.T @ x @ A + Q
        if (abs(x_next - x)).max() < eps:
            break
        x = x_next

    return x_next


def dlqr(A, B, Q, R):
    """Solve the discrete time lqr controller.
    x[k+1] = A x[k] + B u[k]
    cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
    # ref Bertsekas, p.151
    """

    # first, try to solve the ricatti equation
    X = solve_dare(A, B, Q, R)

    # compute the LQR gain
    K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)

    eig_result = la.eig(A - B @ K)

    return K, X, eig_result[0]


def lqr_speed_steering_control(state, cx, cy, cyaw, ck, pe, pth_e, sp, Q, R):
    ind, e = calc_nearest_index(state, cx, cy, cyaw)

    tv = sp[ind]

    k = ck[ind]
    v = state.v
    th_e = pi_2_pi(state.yaw - cyaw[ind])

    # A = [1.0, dt, 0.0, 0.0, 0.0
    #      0.0, 0.0, v, 0.0, 0.0]
    #      0.0, 0.0, 1.0, dt, 0.0]
    #      0.0, 0.0, 0.0, 0.0, 0.0]
    #      0.0, 0.0, 0.0, 0.0, 1.0]
    A = np.zeros((5, 5))
    A[0, 0] = 1.0
    A[0, 1] = dt
    A[1, 2] = v
    A[2, 2] = 1.0
    A[2, 3] = dt
    A[4, 4] = 1.0

    # B = [0.0, 0.0
    #     0.0, 0.0
    #     0.0, 0.0
    #     v/L, 0.0
    #     0.0, dt]
    B = np.zeros((5, 2))
    B[3, 0] = v / L
    B[4, 1] = dt

    K, _, _ = dlqr(A, B, Q, R)

    # state vector
    # x = [e, dot_e, th_e, dot_th_e, delta_v]
    # e: lateral distance to the path
    # dot_e: derivative of e
    # th_e: angle difference to the path
    # dot_th_e: derivative of th_e
    # delta_v: difference between current speed and target speed
    x = np.zeros((5, 1))
    x[0, 0] = e
    x[1, 0] = (e - pe) / dt
    x[2, 0] = th_e
    x[3, 0] = (th_e - pth_e) / dt
    x[4, 0] = v - tv

    # input vector
    # u = [delta, accel]
    # delta: steering angle
    # accel: acceleration
    ustar = -K @ x

    # calc steering input
    ff = math.atan2(L * k, 1)  # feedforward steering angle
    fb = pi_2_pi(ustar[0, 0])  # feedback steering angle
    delta = ff + fb

    # calc accel input
    accel = ustar[1, 0]

    return delta, ind, e, th_e, accel


def calc_nearest_index(state, cx, cy, cyaw):
    dx = [state.x - icx for icx in cx]
    dy = [state.y - icy for icy in cy]

    d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]

    mind = min(d)

    ind = d.index(mind)

    mind = math.sqrt(mind)

    dxl = cx[ind] - state.x
    dyl = cy[ind] - state.y

    angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
    if angle < 0:
        mind *= -1

    return ind, mind


def calc_speed_profile(cyaw, target_speed):
    speed_profile = [target_speed] * len(cyaw)

    direction = 1.0

    # Set stop point
    for i in range(len(cyaw) - 1):
        dyaw = abs(cyaw[i + 1] - cyaw[i])
        switch = math.pi / 4.0 <= dyaw < math.pi / 2.0

        if switch:
            direction *= -1

        if direction != 1.0:
            speed_profile[i] = - target_speed
        else:
            speed_profile[i] = target_speed

        if switch:
            speed_profile[i] = 0.0

    # speed down
    for i in range(40):
        speed_profile[-i] = target_speed / (50 - i)
        if speed_profile[-i] <= 1.0 / 3.6:
            speed_profile[-i] = 1.0 / 3.6

    return speed_profile


def main():
    print("LQR steering control tracking start!!")
    # ax = [0.0, 6.0, 12.5, 10.0, 17.5, 20.0, 25.0]
    # ay = [0.0, -3.0, -5.0, 6.5, 3.0, 0.0, 0.0]
    # goal = [ax[-1], ay[-1]]
    obstacle_list = [
    (5, 5, 1)
    ]  # [x,y,size(radius)]

    fov_r=0.5
    x_path=[]
    y_path=[]

    # Set Initial parameters
    rrt_star = RRTStar(
        start=[0, 0],
        goal=[6, 10],
        rand_area=[-2, 15],
        obstacle_list=obstacle_list,
        expand_dis=1,
        robot_radius=0.8)
    path = rrt_star.planning(animation=True)

    if path is None:
        print("Cannot find path")
    else:
        # print("found path!!")
        affan = 0

        # Draw final path
        
        if show_animation:
            rrt_star.draw_graph()
            iter=0
            for (x,y) in path:
                if iter: 
                    x_path.append(x)
                    y_path.append(y)
                iter=1
            plt.plot(x_path, y_path, 'r--')
            plt.grid(True)

    # plt.show()
    ax=x_path
    ay=y_path
    goal = [ax[-1], ay[-1]]
        # Define dt time, create controller, define start and goal points
        # In every iteration, get an action from PID and make the action,
        # after that, sleep for dt. Repeat that loop until reaching the goal state.
        
        


    cyaw=[]
    cx=[]
    cy=[]
    cx1, cy1, cyaw1, ck, s = calc_spline_course(
            ax, ay, ds=0.1)
    cx= [round(num, 1) for num in cx1]
    cy= [round(num, 1) for num in cy1]
    cyaw= [round(num, 1) for num in cyaw1]
    # print(len(cx1))
    # print(len(cyaw1))
    # for i in range(len(cx1)):
    #     if i == (len(cx1) -1):
    #         cx.append(cx1[i])
    #         cy.append(cy1[i])
    #         cyaw.append(cyaw1[i])
    #         break;

    #     if i%3 == 0:
    #         cx.append(cx1[i])
    #         cy.append(cy1[i])
    #         cyaw.append(cyaw1[i] )

    target_speed = 10.0 / 3.6  # simulation parameter km/h -> m/s

    sp = calc_speed_profile(cyaw, target_speed)

    t, x, y, yaw, v = do_simulation(cx, cy, cyaw, ck, sp, goal)

    if show_animation:  # pragma: no cover
        plt.close()
        plt.subplots(1)
        plt.plot(ax, ay, "xb", label="waypoints")
        plt.plot(cx, cy, "-r", label="target course")
        plt.plot(x, y, "-g", label="tracking")
        plt.grid(True)
        plt.axis("equal")
        plt.xlabel("x[m]")
        plt.ylabel("y[m]")
        plt.legend()

        plt.subplots(1)
        plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
        plt.grid(True)
        plt.legend()
        plt.xlabel("line length[m]")
        plt.ylabel("yaw angle[deg]")

        plt.subplots(1)
        plt.plot(s, ck, "-r", label="curvature")
        plt.grid(True)
        plt.legend()
        plt.xlabel("line length[m]")
        plt.ylabel("curvature [1/m]")

        plt.show()
if __name__ == '__main__':
    main()