### 实现 Gipps 跟驰模型 为了在 Python 中实现 Gipps 车辆跟驰模型并绘制相应的定时空间图或轨迹图，可以采用如下方法： #### 1. 安装必要的库 首先需要安装一些常用的科学计算和绘图库。可以通过 pip 来完成这些依赖项的安装。 ```bash pip install numpy matplotlib scipy pandas ``` #### 2. 编写核心算法逻辑 下面是一个简单的 Python 版本的 Gipps 模型实现示例，该版本适用于单车道环形道路场景下的车辆动态行为模拟[^1]。 ```python import numpy as np import matplotlib.pyplot as plt class Vehicle: def __init__(self, v0=30 / 3.6, a_max=1.5, b_comf=2.0, s_min=2.0, T_safe=1.5): self.v = v0 # 初始速度 (m/s) self.x = 0 # 初始位置 (m) self.a_max = a_max # 加速度上限 (m/s²) self.b_comf = b_comf # 减速舒适度下限 (m/s²) self.s_min = s_min # 最小安全距离 (m) self.T_safe = T_safe # 时间头位 (s) def gipps_model(lead_vehicle, follow_vehicle, delta_t=0.1): """ 计算跟随车的速度更新 """ # 前方车辆状态 lead_v = lead_vehicle.v lead_x = lead_vehicle.x # 后方车辆状态 fol_v = follow_vehicle.v fol_x = follow_vehicle.x # 计算两车间距 gap = lead_x - fol_x - 4.0 # 减去车身长度估计值 # 根据Gipps模型公式调整加减速决策 desired_gap = follow_vehicle.s_min + max( 0, fol_v * follow_vehicle.T_safe + (fol_v * (fol_v - lead_v)) / (2 * np.sqrt(follow_vehicle.a_max * follow_vehicle.b_comf)) ) if gap >= desired_gap and fol_v < lead_v: new_speed = min(fol_v + follow_vehicle.a_max * delta_t, lead_v) elif gap < desired_gap or fol_v > lead_v: deceleration_needed = ((fol_v ** 2) - (lead_v ** 2)) / ( 2 * (gap - follow_vehicle.s_min)) if abs(deceleration_needed) <= follow_vehicle.b_comf: new_speed = np.sqrt(max(0, lead_v ** 2 + 2 * deceleration_needed * (gap-follow_vehicle.s_min))) else: new_speed = max(0, fol_v - follow_vehicle.b_comf * delta_t) else: new_speed = fol_v return new_speed # 初始化车队列 vehicles = [Vehicle() for _ in range(5)] # 创建五辆车组成的队列 for i in range(len(vehicles)-1): vehicles[i].v *= 0.9**(i+1) time_steps = int(60/delta_t)+1 # 总时间步数设为一分钟 positions_history = [[] for _ in vehicles] for t in range(time_steps): positions_at_time_step = [] for idx, vehicle in enumerate(vehicles[::-1]): prev_pos = vehicle.x if idx != len(vehicles)-1: next_vehicle = vehicles[-idx-2] vehicle.v = gipps_model(next_vehicle, vehicle, delta_t) vehicle.x += vehicle.v * delta_t positions_at_time_step.append(vehicle.x) for veh_idx, pos in zip(range(len(positions_history)), reversed(positions_at_time_step)): positions_history[veh_idx].append(pos) plt.figure(figsize=(8, 6)) for hist in positions_history: plt.plot(np.linspace(0, time_steps*delta_t, num=len(hist)), hist) plt.title('Space-Time Diagram of Vehicles Following Behavior') plt.xlabel('Time(s)') plt.ylabel('Position(m)') plt.grid(True) plt.show() ``` 此代码片段定义了一个 `Vehicle` 类用于表示单个车辆对象，并实现了基本版的 Gipps 模型函数来决定每一步中各辆车应采取的动作。最后部分展示了如何记录一段时间内的所有车辆的位置变化情况以便于后续作图展示。 请注意这只是一个非常基础的例子，在实际应用时可能还需要考虑更多的因素如随机扰动、更复杂的初始条件设定等以提高仿真的准确性[^2]。