基于粒子群算法的机械臂“3-5-3”时间轨迹优化代码

以下是一个基于粒子群算法的机械臂“3-5-3”时间轨迹优化的 Python 代码示例：

import numpy as np

# 定义机械臂轨迹优化问题的参数
num_particles = 50  # 粒子数
max_iterations = 100  # 最大迭代次数
c1 = 2  # 自我认知常数
c2 = 2  # 社会认知常数
w = 0.7  # 惯性权重
max_velocity = 5  # 最大速度
max_acceleration = 5  # 最大加速度
num_joints = 3  # 关节数
num_waypoints = 5  # 轨迹中路点数

# 定义机械臂运动学模型和运动控制器
def forward_kinematics(q):
    # 计算机械臂末端位姿
    # ...
    return pose

def inverse_kinematics(pose):
    # 计算机械臂关节角度
    # ...
    return q

def motion_controller(q, qd, qdd):
    # 控制机械臂关节运动
    # ...
    return q, qd, qdd

# 定义适应度函数
def fitness_function(q_traj):
    # 计算机械臂轨迹的总时间
    # ...
    return fitness_value

# 初始化粒子群和全局最优解
particles = np.zeros((num_particles, num_joints, num_waypoints))
velocities = np.zeros((num_particles, num_joints, num_waypoints))
best_positions = particles.copy()
best_fitness_values = np.ones(num_particles) * np.inf
global_best_position = np.zeros((num_joints, num_waypoints))
global_best_fitness_value = np.inf

# 初始化粒子群和全局最优解的位置和速度
for i in range(num_particles):
    for j in range(num_joints):
        for k in range(num_waypoints):
            particles[i, j, k] = np.random.uniform(-np.pi, np.pi)
            velocities[i, j, k] = np.random.uniform(-max_velocity, max_velocity)
    fitness_value = fitness_function(particles[i])
    if fitness_value < best_fitness_values[i]:
        best_positions[i] = particles[i].copy()
        best_fitness_values[i] = fitness_value
    if fitness_value < global_best_fitness_value:
        global_best_position = particles[i].copy()
        global_best_fitness_value = fitness_value

# 迭代更新粒子群的位置和速度
for iter in range(max_iterations):
    for i in range(num_particles):
        # 更新速度
        velocities[i] = w * velocities[i] \
            + c1 * np.random.rand() * (best_positions[i] - particles[i]) \
            + c2 * np.random.rand() * (global_best_position - particles[i])
        velocities[i] = np.clip(velocities[i], -max_velocity, max_velocity)

        # 更新位置
        particles[i] = particles[i] + velocities[i]
        particles[i] = np.clip(particles[i], -np.pi, np.pi)

        # 计算适应度值
        fitness_value = fitness_function(particles[i])

        # 更新个体最优解和全局最优解
        if fitness_value < best_fitness_values[i]:
            best_positions[i] = particles[i].copy()
            best_fitness_values[i] = fitness_value
        if fitness_value < global_best_fitness_value:
            global_best_position = particles[i].copy()
            global_best_fitness_value = fitness_value

# 输出最优解
q_traj = global_best_position.reshape(num_joints, num_waypoints)
print("Optimal trajectory:")
print(q_traj)

需要根据具体的机械臂运动学模型和运动控制器来实现 `forward_kinematics`、`inverse_kinematics` 和 `motion_controller` 函数，并根据具体的优化问题来实现 `fitness_function` 函数。