三个差速无人车通过领航-跟随编队，基于滑模控制器，python代码

以下是基于滑模控制器的三个差速无人车领航-跟随编队的Python代码示例：

import numpy as np
import matplotlib.pyplot as plt

# 定义滑模控制器
def sliding_control(x, xd, lambda_):
    u = -lambda_ * np.sign(x - xd)
    return u

# 定义差速无人车类
class DifferentialDriveVehicle:
    def __init__(self, x, y, theta, L, v_min, v_max, w_min, w_max):
        self.x = x
        self.y = y
        self.theta = theta
        self.L = L
        self.v_min = v_min
        self.v_max = v_max
        self.w_min = w_min
        self.w_max = w_max

    def update_pose(self, v, w, dt):
        self.x += v * np.cos(self.theta) * dt
        self.y += v * np.sin(self.theta) * dt
        self.theta += w * dt

    def get_pose(self):
        return self.x, self.y, self.theta

    def control(self, x, y, theta, k1, k2, k3):
        # 计算控制输入
        dx = x - self.x
        dy = y - self.y
        rho = np.sqrt(dx**2 + dy**2)
        alpha = np.arctan2(dy, dx) - self.theta
        alpha = np.arctan2(np.sin(alpha), np.cos(alpha))
        beta = -self.theta - alpha + theta
        beta = np.arctan2(np.sin(beta), np.cos(beta))
        v = k1 * rho * np.cos(alpha)
        w = k2 * alpha + k3 * beta

        # 对速度和角速度进行限制
        v = np.clip(v, self.v_min, self.v_max)
        w = np.clip(w, self.w_min, self.w_max)

        # 对差速无人车进行控制
        vl = v - self.L/2 * w
        vr = v + self.L/2 * w
        return vl, vr

# 初始化三个差速无人车
vehicle1 = DifferentialDriveVehicle(0, 0, 0, 0.5, -1, 1, -2, 2)
vehicle2 = DifferentialDriveVehicle(2, 0, 0, 0.5, -1, 1, -2, 2)
vehicle3 = DifferentialDriveVehicle(4, 0, 0, 0.5, -1, 1, -2, 2)

# 定义领航-跟随编队的目标轨迹
T = np.linspace(0, 10, 100)
X = np.sin(T)
Y = np.cos(T)

# 设置滑模控制器参数
lambda_ = 1
epsilon = 1e-5

# 进行仿真
dt = 0.1
for i in range(len(T)):
    # 计算领航-跟随编队的目标姿态
    if i+1 < len(T):
        x_d, y_d = X[i+1], Y[i+1]
    else:
        x_d, y_d = X[-1], Y[-1]
    theta_d = np.arctan2(y_d - Y[i], x_d - X[i])

    # 对三个差速无人车进行控制
    vl1, vr1 = vehicle1.control(X[i], Y[i], theta_d, 1, 2, 1)
    vl2, vr2 = vehicle2.control(vehicle1.x, vehicle1.y, vehicle1.theta, 1, 2, 1)
    vl3, vr3 = vehicle3.control(vehicle2.x, vehicle2.y, vehicle2.theta, 1, 2, 1)

    # 计算滑模控制器控制输入
    u1 = sliding_control(vehicle1.x - vehicle2.x, epsilon, lambda_)
    u2 = sliding_control(vehicle2.x - vehicle3.x, epsilon, lambda_)

    # 对差速无人车进行控制
    vehicle1.update_pose((vl1 + u1)/2, (vr1 + u1)/2, dt)
    vehicle2.update_pose((vl2 + u2)/2, (vr2 + u2)/2, dt)
    vehicle3.update_pose((vl3 + u2)/2, (vr3 + u2)/2, dt)

    # 绘制差速无人车轨迹
    plt.plot(vehicle1.x, vehicle1.y, 'bo')
    plt.plot(vehicle2.x, vehicle2.y, 'go')
    plt.plot(vehicle3.x, vehicle3.y, 'ro')

# 绘制目标轨迹
plt.plot(X, Y, 'k--')
plt.axis('equal')
plt.show()

在上述代码中，我们首先定义了滑模控制器函数`sliding_control()`，然后定义了差速无人车类`DifferentialDriveVehicle`，包括其位置、姿态、车轮间距、速度和角速度限制等属性，以及控制函数`control()`，用于计算控制输入。接着，我们初始化了三个差速无人车，并定义了领航-跟随编队的目标轨迹。在仿真过程中，我们首先计算领航-跟随编队的目标姿态，然后对三个差速无人车进行控制，计算出滑模控制器的控制输入，再进行差速无人车的控制，最后绘制差速无人车的轨迹。