人工场势法路径规划三维代码

以下是一个简单的三维人工势场法路径规划的示例代码：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 障碍物的位置和半径
obstacle_pos = np.array([[-5, 5, 5], [5, -5, 5], [5, 5, -5]])
obstacle_r = np.array([2, 2, 2])

# 目标点和起始点
goal_pos = np.array([10, 10, 10])
start_pos = np.array([-10, -10, -10])

# 路径规划的参数
alpha = 100  # 斥力系数
beta = 0.1  # 引力系数
delta_t = 0.1  # 时间步长
max_iter = 500  # 最大迭代次数
epsilon = 0.1  # 判断是否到达目标点的阈值

def get_potential_field(pos):
    """
    计算当前位置的势场
    """
    # 引力项
    F_att = -beta * (pos - goal_pos)
    
    # 斥力项
    F_rep = np.zeros(3)
    for i in range(len(obstacle_pos)):
        dist = np.linalg.norm(pos - obstacle_pos[i])
        if dist < obstacle_r[i]:
            F_rep += alpha * ((1 / dist) - (1 / obstacle_r[i])) * ((pos - obstacle_pos[i]) / (dist ** 3))
    
    return F_att + F_rep

def path_planning():
    """
    路径规划
    """
    pos = start_pos
    path = [pos]
    for i in range(max_iter):
        # 计算当前位置的势场
        F = get_potential_field(pos)
        
        # 更新位置
        pos = pos + delta_t * F
        
        # 将新的位置加入路径中
        path.append(pos)
        
        # 判断是否到达目标点
        if np.linalg.norm(pos - goal_pos) < epsilon:
            print("到达目标点！")
            break
    
    return np.array(path)

# 生成网格点
x = np.linspace(-15, 15, 30)
y = np.linspace(-15, 15, 30)
z = np.linspace(-15, 15, 30)
X, Y, Z = np.meshgrid(x, y, z)

# 计算各个网格点的势场
F_X, F_Y, F_Z = np.zeros_like(X), np.zeros_like(Y), np.zeros_like(Z)
for i in range(len(x)):
    for j in range(len(y)):
        for k in range(len(z)):
            F = get_potential_field(np.array([x[i], y[j], z[k]]))
            F_X[i,j,k], F_Y[i,j,k], F_Z[i,j,k] = F[0], F[1], F[2]

# 绘制势场图
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.quiver(X, Y, Z, F_X, F_Y, F_Z, length=0.5, normalize=True, cmap='viridis')
ax.scatter(obstacle_pos[:,0], obstacle_pos[:,1], obstacle_pos[:,2], c='r', marker='o')
ax.scatter(goal_pos[0], goal_pos[1], goal_pos[2], c='g', marker='o')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_xlim(-15, 15)
ax.set_ylim(-15, 15)
ax.set_zlim(-15, 15)
plt.show()

# 路径规划
path = path_planning()

# 绘制路径
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(path[:,0], path[:,1], path[:,2], 'b')
ax.scatter(obstacle_pos[:,0], obstacle_pos[:,1], obstacle_pos[:,2], c='r', marker='o')
ax.scatter(goal_pos[0], goal_pos[1], goal_pos[2], c='g', marker='o')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_xlim(-15, 15)
ax.set_ylim(-15, 15)
ax.set_zlim(-15, 15)
plt.show()

在这个代码中，我们使用了一个简单的三维场景，包含了三个球形障碍物和一个起点和终点。使用人工势场法，我们计算每个点的势场，然后根据势场的改变来更新机器人的位置，从而规划出一条到达目标点的路径。我们还绘制了势场图和路径图以展示路径规划的结果。