Python实现车辆换道模型

车辆换道模型主要是用于模拟车辆在多车道道路上的换道行为。下面是一个简单的Python实现，基于IDM和MOBIL模型：

import numpy as np

class Vehicle:
    def __init__(self, x, v, a, d, lane):
        self.x = x # 车辆位置
        self.v = v # 车辆速度
        self.a = a # 车辆加速度
        self.d = d # 车辆长度
        self.lane = lane # 车辆所在车道

class Road:
    def __init__(self, length, lanes):
        self.length = length # 道路长度
        self.lanes = lanes # 车道数
        self.vehicles = [[] for _ in range(lanes)] # 每条车道上的车辆列表

    def add_vehicle(self, vehicle):
        lane = vehicle.lane
        self.vehicles[lane].append(vehicle)

    def remove_vehicle(self, vehicle):
        lane = vehicle.lane
        self.vehicles[lane].remove(vehicle)

    def get_front_vehicle(self, vehicle):
        lane = vehicle.lane
        pos = vehicle.x
        front_pos = self.length
        front_vehicle = None
        for v in self.vehicles[lane]:
            if v != vehicle and v.x > pos and v.x < front_pos:
                front_pos = v.x
                front_vehicle = v
        return front_vehicle, front_pos

def idm_acc(vehicle, front_vehicle, front_pos, delta_t, a_max, b, v_des):
    s_star = vehicle.d + vehicle.v * delta_t + (vehicle.v * (vehicle.v - front_vehicle.v)) / (2 * np.sqrt(a_max * b))
    acc = a_max * (1 - (vehicle.v / v_des)**4 - (s_star / (front_pos - vehicle.d - vehicle.x))**2)
    return acc

def mobil_lane_change(vehicle, front_vehicle, back_vehicle, delta_t, a_max, b, v_des, p, s0):
    if front_vehicle is None:
        return False
    if back_vehicle is None:
        back_pos = -np.inf
    else:
        back_pos = back_vehicle.x
    delta_v = front_vehicle.v - vehicle.v
    s_star = vehicle.d + vehicle.v * delta_t + (vehicle.v * delta_v) / (2 * np.sqrt(a_max * b))
    acc = idm_acc(vehicle, front_vehicle, front_vehicle.x, delta_t, a_max, b, v_des)
    if acc < -b:
        acc = -b
    if vehicle.v + acc * delta_t > v_des:
        acc = (v_des - vehicle.v) / delta_t
    if front_vehicle.x - vehicle.x < s_star:
        return False
    if vehicle.x - back_pos < s0:
        return False
    if np.random.rand() > p:
        return False
    return True

def simulate(road, delta_t, a_max, b, v_des, p, s0):
    for lane in range(road.lanes):
        for vehicle in road.vehicles[lane]:
            front_vehicle, front_pos = road.get_front_vehicle(vehicle)
            back_vehicle, back_pos = None, None
            if len(road.vehicles[lane]) > 1:
                idx = road.vehicles[lane].index(vehicle)
                if idx > 0:
                    back_vehicle = road.vehicles[lane][idx-1]
                    back_pos = back_vehicle.x
            acc = idm_acc(vehicle, front_vehicle, front_pos, delta_t, a_max, b, v_des)
            if mobil_lane_change(vehicle, front_vehicle, back_vehicle, delta_t, a_max, b, v_des, p, s0):
                vehicle.lane = lane - 1
                road.vehicles[lane].remove(vehicle)
                road.vehicles[lane-1].append(vehicle)
                continue
            vehicle.a = acc
            vehicle.v += acc * delta_t
            vehicle.x += vehicle.v * delta_t

假设有一条双车道的道路，长度为1000米，车道宽度为3.5米，最大速度为120 km/h。我们可以按照以下方式模拟车辆行驶：

delta_t = 0.1 # 时间步长
a_max = 3 # 最大加速度 m/s^2
b = 3 # 最大减速度 m/s^2
v_des = 33.33 # 最大速度 m/s
p = 0.5 # 换道概率
s0 = 2 # 最小车距 m

road = Road(length=1000, lanes=2)
for i in range(20):
    x = np.random.rand() * 800 + 100
    v = np.random.rand() * v_des
    a = 0
    d = 5
    lane = 0 if i % 2 == 0 else 1
    vehicle = Vehicle(x, v, a, d, lane)
    road.add_vehicle(vehicle)

for _ in range(1000):
    simulate(road, delta_t, a_max, b, v_des, p, s0)

这里我们先生成20辆随机车辆，然后模拟1000秒的行驶过程。每秒钟调用一次simulate函数，更新每辆车的位置和速度。在simulate函数中，我们先计算车辆的加速度，然后判断是否需要换道，最后更新车辆的位置和速度。