动态窗口法(Dynamic Window Approach)概述

DWA是一种基于速度的局部规划器，可计算达到目标所需的机器人的最佳无碰撞速度。

程序实现
DWA算法主要分三步：

计算动态窗口
计算最优 [ v , ω ]
更新机器人状态
流程图如下：

以下代码参考：https://github.com/AtsushiSakai/PythonRobotics

初始化机器人状态、目标位置、障碍物位置

# 初始化机器人状态 [x(m), y(m), yaw(rad), v(m/s), omega(rad/s)]
x = np.array([0.0, 0.0, math.pi / 8.0, 0.0, 0.0])
# 目标位置 [x(m), y(m)]
goal = np.array([gx, gy])
# 障碍物位置 [x(m), y(m)]
ob = np.array([[-1, -1], ...... , [13.0, 13.0]])

获取动态窗口
这个动态窗口就是机器人在当前状态下能达到的速度 v 和转速 ω 范围，受到自身机械特性以及当前状态的影响。

def calc_dynamic_window(x, config):
    """
    calculation dynamic window based on current state x
    """

    # Dynamic window from robot specification
    Vs = [config.min_speed, config.max_speed,
          -config.max_yawrate, config.max_yawrate]

    # Dynamic window from motion model
    Vd = [x[3] - config.max_accel * config.dt,
          x[3] + config.max_accel * config.dt,
          x[4] - config.max_dyawrate * config.dt,
          x[4] + config.max_dyawrate * config.dt]

    #  [vmin, vmax, yaw_rate min, yaw_rate max]
    dw = [max(Vs[0], Vd[0]), min(Vs[1], Vd[1]),
          max(Vs[2], Vd[2]), min(Vs[3], Vd[3])]

    return dw

def calc_control_and_trajectory(x, dw, config, goal, ob):
    """
    calculation final input with dynamic window
    """

    x_init = x[:]
    min_cost = float("inf")
    best_u = [0.0, 0.0]
    best_trajectory = np.array([x])

    # 计算动态窗口内所有的采样样本的代价函数
    for v in np.arange(dw[0], dw[1], config.v_reso):
        for y in np.arange(dw[2], dw[3], config.yawrate_reso):

            trajectory = predict_trajectory(x_init, v, y, config)

            # 计算代价函数
            to_goal_cost = config.to_goal_cost_gain * calc_to_goal_cost(trajectory, goal)
            speed_cost = config.speed_cost_gain * (config.max_speed - trajectory[-1, 3])
            ob_cost = config.obstacle_cost_gain * calc_obstacle_cost(trajectory, ob, config)

            final_cost = to_goal_cost + speed_cost + ob_cost

            # 寻找具有最小代价的样本以及它的轨迹
            if min_cost >= final_cost:
                min_cost = final_cost
                best_u = [v, y]
                best_trajectory = trajectory

    return best_u, best_trajectory

更新状态
根据最优 u = [ v , ω ] 更新机器人状态

x = motion(x, u, config.dt)  

完整代码参见这里