%% 修复后的机械臂PTP轨迹控制 - 完整解决方案
clear; clc; close all;
% ===========================================
% 1. 机械臂参数重新定义 (Modified D-H)
% ===========================================
% D-H参数表 (单位: mm) - 修正参数确保可达性
a = [0, 0, 500, 500, 0, 0]; % 连杆长度
alpha = [0, -pi/2, 0, -pi/2, pi/2, -pi/2]; % 连杆扭角
d = [400, 0, 0, 0, 0, 100]; % 连杆偏移
% 关节角度范围 (弧度) - 放宽限制
joint_limits = [
-pi, pi; % 关节1 (-180° to 180°)
-pi/2, pi/2; % 关节2 (-90° to 90°)
-pi/2, pi/2; % 关节3 (-90° to 90°)
-pi, pi; % 关节4 (-180° to 180°)
0, pi; % 关节5 (0° to 180°)
-pi, pi % 关节6 (-180° to 180°)
];
% 工作空间参数
min_reach = sqrt((min([a(2), a(3)]))^2 + d(1)^2);
max_reach = sqrt((a(2)+a(3))^2 + (d(1)+d(6))^2);
fprintf('机械臂工作空间范围: %.2f mm 到 %.2f mm\n', min_reach, max_reach);
% ===========================================
% 2. 增强的逆运动学求解
% ===========================================
% 工作空间检查函数
function reachable = is_reachable(position, min_r, max_r)
distance = norm(position(1:2));
height = position(3);
radial_distance = sqrt(distance^2 + height^2);
reachable = (radial_distance >= min_r) && (radial_distance <= max_r);
end
% 改进的逆运动学求解 (带工作空间检查)
function solutions = enhanced_inverse_kinematics(T_target, a, alpha, d, joint_limits, min_r, max_r)
% 初始化解集
solutions = [];
% 目标位姿分解
P_target = T_target(1:3, 4);
R_target = T_target(1:3, 1:3);
% 检查工作空间可达性
if ~is_reachable(P_target, min_r, max_r)
warning('目标位置 (%.1f, %.1f, %.1f) 超出工作空间范围!', ...
P_target(1), P_target(2), P_target(3));
return;
end
% 计算腕部中心 (Wrist Center)
P_wc = P_target - d(6)*R_target(:,3);
% --- 关节1求解 ---
theta1 = atan2(P_wc(2), P_wc(1));
theta1_alt = theta1 + pi; % 另一解
% --- 关节3求解 ---
for j1 = [theta1, theta1_alt]
% 计算关节2位置
x = P_wc(1)*cos(j1) + P_wc(2)*sin(j1);
z = P_wc(3) - d(1);
% 几何关系计算关节3
D = (x^2 + z^2 - a(2)^2 - a(3)^2)/(2*a(2)*a(3));
% 处理超出范围的情况
if abs(D) > 1
% 找到最接近的可达点
D = sign(D); % 取边界值
fprintf('关节3求解超出范围, 使用边界值: %.2f\n', D);
end
theta3 = acos(D);
theta3_alt = -theta3; % 另一解
% --- 关节2求解 ---
for j3 = [theta3, theta3_alt]
denom = a(2)^2 + a极(3)^2 + 2*a(2)*a(3)*cos(j3);
% 避免除零错误
if abs(denom) < 1e-6
fprintf('分母接近零, 跳过当前解\n');
continue;
end
sin_theta2 = ((a(2)+a(3)*cos(j3))*z - a(3)*sin(j3)*x)/denom;
cos_theta2 = ((a(2)+a(3)*cos(j3))*x + a(3)*sin(j3)*z)/denom;
j2 = atan2(sin_theta2, cos_theta2);
% --- 关节4,5,6求解 ---
% 计算前三关节变换矩阵
T01 = dh_transform(0, alpha(1), d(1), j1);
T12 = dh_transform(a(2), alpha(2), d(2), j2);
T23 = dh_transform(a(3), alpha(3), d(3), j3);
T03 = T01 * T12 * T23;
% 计算腕部姿态
R36 = T03(1:3,1:3)' * R_target;
% 欧拉角解(Z-Y-Z)
theta5 = atan2(sqrt(R36(1,3)^2 + R36(2,3)^2), R36(3,3));
theta5_alt = -theta5;
for j5 = [theta5, theta5_alt]
if abs(j5) > 1e-3 % 避免奇异
theta4 = atan2(R36(2,3)/sin(j5), R36(1,3)/sin(j5));
theta6 = atan2(R36(3,2)/sin(j5), -R36(3,1)/sin(j5));
else
% 奇异处理
theta4 = 0;
theta6 = atan2(R36(1,2), R36(1,1));
end
% 保存解（即使超出限制，用于后续优化）
q = [j1, j2, j3, theta4, j5, theta6];
solutions = [solutions; q];
end
end
end
end
% 数值优化逆解
function [q_opt, error] = numerical_ik(T_target, a, alpha, d, joint_limits, initial_guess)
options = optimoptions('fmincon', 'Display', 'final', ...
'Algorithm', 'sqp', ...
'MaxIterations', 200, ...
'StepTolerance', 1e-6, ...
'OptimalityTolerance', 1e-6);
% 定义优化目标函数
cost_func = @(q) norm(forward_kinematics(q, a, alpha, d) - T_target, 'fro');
% 设置约束 (关节限位)
lb = joint_limits(:,1)';
ub = joint_limits(:,2)';
% 使用初始猜测或随机初始值
if nargin < 5 || isempty(initial_guess)
q0 = mean(joint_limits, 2)'; % 关节范围中值
else
q0 = initial_guess;
end
% 执行优化
q_opt = fmincon(cost_func, q0, [], [], [], [], lb, ub, [], options);
% 计算最终误差
T_actual = forward_kinematics(q_opt, a, alpha, d);
error = norm(T_target(1:3,4) - T_actual(1:3,4));
end
% ===========================================
% 3. 主程序 - 增强的PTP轨迹控制
% ===========================================
% 定义起始点和目标点 (笛卡尔坐标)
P_start = [600; 200; 500]; % mm
P_target = [400; -300; 600]; % mm
% 目标姿态 (假设相同)
R_target = [1, 0, 0; 0, 1, 0; 0, 0, 1]; % 单位矩阵
% 构建目标位姿矩阵
T_start = [R_target, P_start; 0, 0, 0, 1];
T_target = [R_target, P_target; 0, 0, 0, 1];
% 检查起始点可达性
if ~is_reachable(P_start, min_reach, max_reach)
% 自动调整到最近可达点
direction = P_start/norm(P_start);
adjusted_distance = min(max(norm(P_start(1:2)), min_reach), max_reach);
P_start_adjusted = [direction(1:2)*adjusted_distance; P_start(3)];
fprintf('调整起始点位置: [%.1f, %.1f, %.1f] -> [%.1f, %.1f, %.1f]\n', ...
P_start(1), P_start(2), P_start(3), ...
P_start_adjusted(1), P_start_adjusted(2), P_start_adjusted(3));
P_start = P_start_adjusted;
T_start = [R_target, P_start; 0, 0, 0, 1];
end
% 使用增强逆运动学求解起始点
fprintf('使用增强逆运动学求解起始点...\n');
solutions_start = enhanced_inverse_kinematics(T_start, a, alpha, d, joint_limits, min_reach, max_reach);
fprintf('找到 %d 个候选解\n', size(solutions_start,1));
% 选择有效解或使用数值方法
valid_solutions = [];
for i = 1:size(solutions_start,1)
q = solutions_start(i,:);
if is_valid_solution(q, joint_limits)
valid_solutions = [valid_solutions; q];
end
end
if ~isempty(valid_solutions)
fprintf('其中 %d 个解满足关节限制\n', size(valid_solutions,1));
q_start = valid_solutions(1,:)';
else
fprintf('无满足关节限制的解析解, 使用数值优化...\n');
[q_start, start_error] = numerical_ik(T_start, a, alpha, d, joint_limits);
fprintf('数值优化解误差: %.4f mm\n', start_error);
end
fprintf('起始关节角度: [%.2f, %.2f, %.2f, %.2f, %.2f, %.2f] rad\n', q_start);
% 目标点求解（类似过程）
% ... [省略类似代码] ...
% 后续轨迹生成和控制代码保持不变
% ... [使用之前提供的轨迹生成和控制代码] ...
最新发布
本文介绍了Linux内核配置中几个关键宏定义的作用，包括IS_BUILTIN、IS_MODULE、IS_ENABLED及IS_REACHABLE，并解释了它们如何区分内建模块与加载模块的不同状态。
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