2024年“华数杯”数学竞赛A题 | 代码&技术文档（论文）

机器臂关节角路径的优化设计

问题一

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代码

• Matlab

clc
clear
% 参数定义
a = [0, 300, 1200, 300, 0, 0];
alpha = [0, -90, 0, -90, -90, -90];
d = [600, 0, 0, 1200, 0, 0];
theta_min = [-160, -150, -200, -180, -120, -180];
theta_max = [160, 15, 80, 180, 120, 180];
P_target = [1500, 1200, 200]; % 目标位置
lambda = 1; % 权重因子

% 初始种群生成
population_size = 100;
num_generations = 100;
crossover_rate = 0.8;
mutation_rate = 0.1;

% 随机生成初始种群
population = zeros(population_size, 6);
for i = 1:population_size
    for j = 1:6
        population(i, j) = theta_min(j) + (theta_max(j) - theta_min(j)) * rand;
    end
end

% 遗传算法主程序
for generation = 1:num_generations
    % 适应度计算
    fitness_values = zeros(population_size, 1);
    for i = 1:population_size
        fitness_values(i) = fitness(population(i, :), P_target);
    end
    
    % 将适应度值转换为非负值
    min_fitness = min(fitness_values);
    fitness_va