Reeds_Shepp.py

import math
import matplotlib.pyplot as plt
import numpy as np

show_animation = True


class Path:

    def __init__(self):
        self.lengths = []
        self.ctypes = []
        self.L = 0.0
        self.x = []
        self.y = []
        self.yaw = []
        self.directions = []


def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
    """
    Plot arrow
    """

    if not isinstance(x, float):
        for (ix, iy, iyaw) in zip(x, y, yaw):
            plot_arrow(ix, iy, iyaw)
    else:
        plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
                  fc=fc, ec=ec, head_width=width, head_length=width)
        plt.plot(x, y)


def mod2pi(x):
    v = np.mod(x, 2.0 * math.pi)
    if v < -math.pi:
        v += 2.0 * math.pi
    else:
        if v > math.pi:
            v -= 2.0 * math.pi
    return v


def straight_left_straight(x, y, phi):
    phi = mod2pi(phi)
    if y > 0.0 and 0.0 < phi < math.pi * 0.99:
        xd = - y / math.tan(phi) + x
        t = xd - math.tan(phi / 2.0)
        u = phi
        v = math.sqrt((x - xd) ** 2 + y ** 2) - math.tan(phi / 2.0)
        return True, t, u, v
    elif y < 0.0 < phi < math.pi * 0.99:
        xd = - y / math.tan(phi) + x
        t = xd - math.tan(phi / 2.0)
        u = phi
        v = -math.sqrt((x - xd) ** 2 + y ** 2) - math.tan(phi / 2.0)
        return True, t, u, v

    return False, 0.0, 0.0, 0.0


def set_path(paths, lengths, ctypes):
    path = Path()
    path.ctypes = ctypes
    path.lengths = lengths

    # check same path exist
    for tpath in paths:
        typeissame = (tpath.ctypes == path.ctypes)
        if typeissame:
            if sum(tpath.lengths) - sum(path.lengths) <= 0.01:
                return paths  # not insert path

    path.L = sum([abs(i) for i in lengths])

    # Base.Test.@test path.L >= 0.01
    if path.L >= 0.01:
        paths.append(path)

    return paths


def straight_curve_straight(x, y, phi, paths):
    flag, t, u, v = straight_left_straight(x, y, phi)
    if flag:
        paths = set_path(paths, [t, u, v], ["S", "L", "S"])

    flag, t, u, v = straight_left_straight(x, -y, -phi)
    if flag:
        paths = set_path(paths, [t, u, v], ["S", "R", "S"])

    return paths


def polar(x, y):
    r = math.sqrt(x ** 2 + y ** 2)
    theta = math.atan2(y, x)
    return r, theta


def left_straight_left(x, y, phi):
    u, t = polar(x - math.sin(phi), y - 1.0 + math.cos(phi))
    if t >= 0.0:
        v = mod2pi(phi - t)
        if v >= 0.0:
            return True, t, u, v

    return False, 0.0, 0.0, 0.0


def left_right_left(x, y, phi):
    u1, t1 = polar(x - math.sin(phi), y - 1.0 + math.cos(phi))

    if u1 <= 4.0:
        u = -2.0 * math.asin(0.25 * u1)
        t = mod2pi(t1 + 0.5 * u + math.pi)
        v = mod2pi(phi - t + u)

        if t >= 0.0 >= u:
            return True, t, u, v

    return False, 0.0, 0.0, 0.0


def curve_curve_curve(x, y, phi, paths):
    flag, t, u, v = left_right_left(x, y, phi)
    if flag:
        paths = set_path(paths, [t, u, v], ["L", "R", "L"])

    flag, t, u, v = left_right_left(-x, y, -phi)
    if flag:
        paths = set_path(paths, [-t, -u, -v], ["L", "R", "L"])

    flag, t, u, v = left_right_left(x, -y, -phi)
    if flag:
        paths = set_path(paths, [t, u, v], ["R", "L", "R"])

    flag, t, u, v = left_right_left(-x, -y, phi)
    if flag:
        paths = set_path(paths, [-t, -u, -v], ["R", "L", "R"])

    # backwards
    xb = x * math.cos(phi) + y * math.sin(phi)
    yb = x * math.sin(phi) - y * math.cos(phi)

    flag, t, u, v = left_right_left(xb, yb, phi)
    if flag:
        paths = set_path(paths, [v, u, t], ["L", "R", "L"])

    flag, t, u, v = left_right_left(-xb, yb, -phi)
    if flag:
        paths = set_path(paths, [-v, -u, -t], ["L", "R", "L"])

    flag, t, u, v = left_right_left(xb, -yb, -phi)
    if flag:
        paths = set_path(paths, [v, u, t], ["R", "L", "R"])

    flag, t, u, v = left_right_left(-xb, -yb, phi)
    if flag:
        paths = set_path(paths, [-v, -u, -t], ["R", "L", "R"])

    return paths


def curve_straight_curve(x, y, phi, paths):
    flag, t, u, v = left_straight_left(x, y, phi)
    if flag:
        paths = set_path(paths, [t, u, v], ["L", "S", "L"])

    flag, t, u, v = left_straight_left(-x, y, -phi)
    if flag:
        paths = set_path(paths, [-t, -u, -v], ["L", "S", "L"])

    flag, t, u, v = left_straight_left(x, -y, -phi)
    if flag:
        paths = set_path(paths, [t, u, v], ["R", "S", "R"])

    flag, t, u, v = left_straight_left(-x, -y, phi)
    if flag:
        paths = set_path(paths, [-t, -u, -v], ["R", "S", "R"])

    flag, t, u, v = left_straight_right(x, y, phi)
    if flag:
        paths = set_path(paths, [t, u, v], ["L", "S", "R"])

    flag, t, u, v = left_straight_right(-x, y, -phi)
    if flag:
        paths = set_path(paths, [-t, -u, -v], ["L", "S", "R"])

    flag, t, u, v = left_straight_right(x, -y, -phi)
    if flag:
        paths = set_path(paths, [t, u, v], ["R", "S", "L"])

    flag, t, u, v = left_straight_right(-x, -y, phi)
    if flag:
        paths = set_path(paths, [-t, -u, -v], ["R", "S", "L"])

    return paths


def left_straight_right(x, y, phi):
    u1, t1 = polar(x + math.sin(phi), y - 1.0 - math.cos(phi))
    u1 = u1 ** 2
    if u1 >= 4.0:
        u = math.sqrt(u1 - 4.0)
        theta = math.atan2(2.0, u)
        t = mod2pi(t1 + theta)
        v = mod2pi(t - phi)

        if t >= 0.0 and v >= 0.0:
            return True, t, u, v

    return False, 0.0, 0.0, 0.0


def generate_path(q0, q1, max_curvature):
    dx = q1[0] - q0[0]
    dy = q1[1] - q0[1]
    dth = q1[2] - q0[2]
    c = math.cos(q0[2])
    s = math.sin(q0[2])
    x = (c * dx + s * dy) * max_curvature
    y = (-s * dx + c * dy) * max_curvature

    paths = []
    paths = straight_curve_straight(x, y, dth, paths)
    paths = curve_straight_curve(x, y, dth, paths)
    paths = curve_curve_curve(x, y, dth, paths)

    return paths


def interpolate(ind, length, mode, max_curvature, origin_x, origin_y, origin_yaw, path_x, path_y, path_yaw, directions):
    if mode == "S":
        path_x[ind] = origin_x + length / max_curvature * math.cos(origin_yaw)
        path_y[ind] = origin_y + length / max_curvature * math.sin(origin_yaw)
        path_yaw[ind] = origin_yaw
    else:  # curve
        ldx = math.sin(length) / max_curvature
        ldy = 0.0
        if mode == "L":  # left turn
            ldy = (1.0 - math.cos(length)) / max_curvature
        elif mode == "R":  # right turn
            ldy = (1.0 - math.cos(length)) / -max_curvature
        gdx = math.cos(-origin_yaw) * ldx + math.sin(-origin_yaw) * ldy
        gdy = -math.sin(-origin_yaw) * ldx + math.cos(-origin_yaw) * ldy
        path_x[ind] = origin_x + gdx
        path_y[ind] = origin_y + gdy

    if mode == "L":  # left turn
        path_yaw[ind] = origin_yaw + length
    elif mode == "R":  # right turn
        path_yaw[ind] = origin_yaw - length

    if length > 0.0:
        directions[ind] = 1
    else:
        directions[ind] = -1

    return path_x, path_y, path_yaw, directions


def generate_local_course(total_length, lengths, mode, max_curvature, step_size):
    n_point = math.trunc(total_length / step_size) + len(lengths) + 4

    px = [0.0 for _ in range(n_point)]
    py = [0.0 for _ in range(n_point)]
    pyaw = [0.0 for _ in range(n_point)]
    directions = [0.0 for _ in range(n_point)]
    ind = 1

    if lengths[0] > 0.0:
        directions[0] = 1
    else:
        directions[0] = -1

    ll = 0.0

    for (m, l, i) in zip(mode, lengths, range(len(mode))):
        if l > 0.0:
            d = step_size
        else:
            d = -step_size

        # set origin state
        ox, oy, oyaw = px[ind], py[ind], pyaw[ind]

        ind -= 1
        if i >= 1 and (lengths[i - 1] * lengths[i]) > 0:
            pd = - d - ll
        else:
            pd = d - ll

        while abs(pd) <= abs(l):
            ind += 1
            px, py, pyaw, directions = interpolate(
                ind, pd, m, max_curvature, ox, oy, oyaw, px, py, pyaw, directions)
            pd += d

        ll = l - pd - d  # calc remain length

        ind += 1
        px, py, pyaw, directions = interpolate(
            ind, l, m, max_curvature, ox, oy, oyaw, px, py, pyaw, directions)

    # remove unused data
    while px[-1] == 0.0:
        px.pop()
        py.pop()
        pyaw.pop()
        directions.pop()

    return px, py, pyaw, directions


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


def calc_paths(sx, sy, syaw, gx, gy, gyaw, maxc, step_size):
    q0 = [sx, sy, syaw]
    q1 = [gx, gy, gyaw]

    paths = generate_path(q0, q1, maxc)
    for path in paths:
        x, y, yaw, directions = generate_local_course(
            path.L, path.lengths, path.ctypes, maxc, step_size * maxc)

        # convert global coordinate
        path.x = [math.cos(-q0[2]) * ix + math.sin(-q0[2])
                  * iy + q0[0] for (ix, iy) in zip(x, y)]
        path.y = [-math.sin(-q0[2]) * ix + math.cos(-q0[2])
                  * iy + q0[1] for (ix, iy) in zip(x, y)]
        path.yaw = [pi_2_pi(iyaw + q0[2]) for iyaw in yaw]
        path.directions = directions
        path.lengths = [length / maxc for length in path.lengths]
        path.L = path.L / maxc

    return paths


def reeds_shepp_path_planning(sx, sy, syaw,
                              gx, gy, gyaw, maxc, step_size=0.2):
    paths = calc_paths(sx, sy, syaw, gx, gy, gyaw, maxc, step_size)

    if not paths:
        return None, None, None, None, None

    minL = float("Inf")
    best_path_index = -1
    for i, _ in enumerate(paths):
        if paths[i].L <= minL:
            minL = paths[i].L
            best_path_index = i

    bpath = paths[best_path_index]

    return bpath.x, bpath.y, bpath.yaw, bpath.ctypes, bpath.lengths


def main():
    print("Reeds Shepp path planner sample start!!")

    start_x = -1.0  # [m]
    start_y = -4.0  # [m]
    start_yaw = np.deg2rad(-20.0)  # [rad]

    end_x = 5.0  # [m]
    end_y = 5.0  # [m]
    end_yaw = np.deg2rad(25.0)  # [rad]

    curvature = 1.0
    step_size = 0.1

    px, py, pyaw, mode, clen = reeds_shepp_path_planning(
        start_x, start_y, start_yaw, end_x, end_y, end_yaw, curvature, step_size)

    if show_animation:  # pragma: no cover
        plt.cla()
        plt.plot(px, py, label="final course " + str(mode))

        # plotting
        plot_arrow(start_x, start_y, start_yaw)
        plot_arrow(end_x, end_y, end_yaw)

        plt.legend()
        plt.grid(True)
        plt.axis("equal")
        plt.show()

    if not px:
        assert False, "No path"


if __name__ == '__main__':
    main()