人工势场法势场可视化

### 人工势场法势场可视化的实现方法

#### 使用Python进行势场可视化

为了更好地理解并展示人工势场法的工作原理，可以通过编程语言如Python来创建势场的可视化效果。Matplotlib库是一个非常适合用于绘制二维图形的选择。

首先定义吸引场和排斥场函数：

import numpy as np
import matplotlib.pyplot as plt

def attractive_field(x, y, goal_x, goal_y, k_att):
    dist = np.sqrt((goal_x - x)**2 + (goal_y - y)**2)
    f_x = k_att * (x - goal_x)
    f_y = k_att * (y - goal_y)
    return f_x, f_y, dist

def repulsive_field(x, y, obstacle_list, k_rep, r_obstacle):
    sum_f_x = 0.0
    sum_f_y = 0.0
    
    for ox, oy, size in obstacle_list:
        dx = x - ox
        dy = y - oy
        dist = max(np.sqrt(dx**2 + dy**2), 0.1)  
        
        if dist <= r_obstacle:
            fx = k_rep * ((1.0 / dist - 1.0 / r_obstacle) * (dx / dist ** 2))
            fy = k_rep * ((1.0 / dist - 1.0 / r_obstacle) * (dy / dist ** 2))
            
            sum_f_x += fx
            sum_f_y += fy
            
    return sum_f_x, sum_f_y

接着编写一个函数用来计算总力并将结果绘制成图像：

def plot_potential_field(goal, obstacles, grid_size=0.5, k_att=1.0, k_rep=3.0, r_obstacle=7.0):
    min_x, min_y = -10, -10
    max_x, max_y = 10, 10
    x_coords, y_coords = np.meshgrid(
        np.arange(min_x, max_x, grid_size),
        np.arange(min_y, max_y, grid_size))

    fig, ax = plt.subplots()
    
    u = np.zeros_like(x_coords)
    v = np.zeros_like(y_coords)

    for i in range(len(u)):
        for j in range(len(v)):
            att_fx, att_fy, _ = attractive_field(x_coords[i][j], y_coords[i][j], goal[0], goal[1], k_att)
            rep_fx, rep_fy = repulsive_field(x_coords[i][j], y_coords[i][j], obstacles, k_rep, r_obstacle)
            
            total_force_x = att_fx + rep_fx
            total_force_y = att_fy + rep_fy
                
            u[i][j] = total_force_x
            v[i][j] = total_force_y

    q = ax.quiver(x_coords, y_coords, u, v, units='xy', scale=1/0.2)
    ax.plot([goal[0]], [goal[1]], "xr", markersize=8)
    for obs in obstacles:
        circle = plt.Circle((obs[0], obs[1]), radius=obs[2]+r_obstacle*0.9, color="black", fill=False)
        ax.add_patch(circle)
        circle = plt.Circle((obs[0], obs[1]), radius=obs[2], color="red")
        ax.add_patch(circle)

    ax.set_xlim([min_x, max_x])
    ax.set_ylim([min_y, max_y])

    plt.xlabel('X')
    plt.ylabel('Y')
    plt.title('Potential Field Visualization')

plot_potential_field((-5,-5),( [(4, 4, 1)]))  # Example with one obstacle at position (4,4) and a target point (-5,-5).
plt.show()

这段代码展示了如何通过矢量图表示各个位置上的合力方向[^1]。这有助于直观地观察到不同区域内的移动趋势——靠近目标的地方会显示出指向目标的力量；而接近障碍物的位置则会有远离这些障碍的趋势。