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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。
DWA算法主要分三步:
流程图如下:
以下代码参考:
# 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]])
这个动态窗口就是机器人在当前状态下能达到的速度 v v v和转速 ω \omega 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
对动态窗口采样,得到 N × M N\times M N×M组 [ v i j , ω i j ] ∣ i < N , j < M [v_{ij},\omega_{ij}]|i<N,j<M [vij,ωij]∣i<N,j<M,并计算 v = v i j , ω = ω i j v=v_{ij},\omega=\omega_{ij} v=vij,ω=ωij时机器人的预测轨迹。接下来计算机器人 v = v i j , ω = ω i j v=v_{ij},\omega=\omega_{ij} v=vij,ω=ωij时的评价函数:
G ( v , ω ) = a 1 ⋅ h e a d i n g ( v , ω ) + a 2 ⋅ d i s t ( v , ω ) + a 3 ⋅ v e l o c i t y ( v , ω ) G(v,\omega)=a_1\cdot heading(v,\omega)+a_2\cdot dist(v,\omega)+a_3\cdot velocity(v,\omega) G(v,ω)=a1⋅heading(v,ω)+a2⋅dist(v,ω)+a3⋅velocity(v,ω)计算机器人处于 v = v i j , ω = ω i j v=v_{ij},\omega=\omega_{ij} v=vij,ω=ωij时的评价函数,得到一系列的代价,代价最小时的 [ v i j , ω i j ] [v_{ij},\omega_{ij}] [vij,ωij]即为最优 [ v , ω ] [v,\omega] [v,ω]
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
根据最优 u = [ v , ω ] u=[v,\omega] u=[v,ω]更新机器人状态
x = motion(x, u, config.dt)
完整代码参见
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