基于解析法的四轴SCARA机器人正逆运动学代码

一、正运动学实现（C++）

#include <cmath>
#include <array>struct Pose {double x, y, z;  // 末端位姿double yaw;      // 末端偏航角
};// DH参数定义（示例值）
const double L1 = 0.2;  // 基座到J2连杆长度
const double L2 = 0.3;  // J2到J3连杆长度
const double L3 = 0.15; // J3垂直移动行程// 正运动学计算
Pose forwardKinematics(double theta1, double theta2, double d3, double theta4) {Pose pose;// 平面位置计算pose.x = L1 * cos(theta1) + L2 * cos(theta1 + theta2);pose.y = L1 * sin(theta1) + L2 * sin(theta1 + theta2);pose.z = d3;  // 垂直方向位移// 姿态计算double yaw = theta1 + theta2 + theta4;pose.yaw = yaw;return pose;
}

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二、逆运动学实现（C++）

#include <array>
#include <cmath>// 逆运动学求解（带奇异点检测）
bool inverseKinematics(const Pose& target, double& theta1, double& theta2, double& d3, double& theta4) {// 奇异点检测（工作空间边界）double r = std::sqrt(target.x * target.x + target.y * target.y);if(r > (L1 + L2) || r < std::abs(L1 - L2)) {return false;  // 超出工作空间}// 关节角度计算（几何法）double k1 = L1 + L2 * cos(target.yaw);double k2 = L2 * sin(target.yaw);// 计算θ2（两解）double cos_theta2 = (target.x*k1 + target.y*k2) / (r*(L1*L1 + L2*L2 + 2*L1*L2*cos(target.yaw)));double sin_theta2 = (target.y*k1 - target.x*k2) / (r*(L1*L1 + L2*L2 + 2*L1*L2*cos(target.yaw)));double theta2_1 = std::atan2(sin_theta2, cos_theta2);double theta2_2 = theta2_1 + M_PI;  // 第二解// 选择最近解（根据当前关节状态优化）double current_theta2 = 0.0;  // 假设当前角度为0double delta1 = std::abs(theta2_1 - current_theta2);double delta2 = std::abs(theta2_2 - current_theta2);double selected_theta2 = (delta1 < delta2) ? theta2_1 : theta2_2;// 计算θ1theta1 = std::atan2(target.y, target.x) - std::atan2(L2 * sin(selected_theta2), L1 + L2 * cos(selected_theta2));// 计算d3d3 = target.z;// 计算θ4theta4 = target.yaw - theta1 - selected_theta2;return true;
}

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三、工程优化策略

1. 关节限位处理

// 关节角度约束（示例范围）
const double theta_min[4] = {-M_PI/2, -M_PI/2, 0.0, -M_PI};
const double theta_max[4] = {M_PI/2, M_PI/2, 0.5*M_PI, M_PI};// 角度约束函数
void clampAngles(double& angle, double min_val, double max_val) {while(angle > max_val) angle -= 2*M_PI;while(angle < min_val) angle += 2*M_PI;angle = std::max(min_val, std::min(max_val, angle));
}

2. 多解选择策略

// 多解生成与选择
std::array<double, 4> getMultipleSolutions(const Pose& target) {std::array<double, 4> solutions;// 生成θ2的两个解double k1 = L1 + L2 * cos(target.yaw);double k2 = L2 * sin(target.yaw);double cos_theta2 = (target.x*k1 + target.y*k2) / (r*(L1*L1 + L2*L2 + 2*L1*L2*cos(target.yaw)));double sin_theta2 = (target.y*k1 - target.x*k2) / (r*(L1*L1 + L2*L2 + 2*L1*L2*cos(target.yaw)));double theta2_1 = std::atan2(sin_theta2, cos_theta2);double theta2_2 = theta2_1 + M_PI;// 选择最优解（基于最小能量）double current_theta2 = 0.0;  // 假设当前角度double delta1 = std::abs(theta2_1 - current_theta2);double delta2 = std::abs(theta2_2 - current_theta2);solutions[1] = (delta1 < delta2) ? theta2_1 : theta2_2;solutions[3] = (delta1 < delta2) ? theta2_2 : theta2_1;  // 对称解return solutions;
}

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四、完整控制流程

int main() {// 目标位姿（示例）Pose target = {0.5, 0.3, 0.2, M_PI/4};// 逆解计算double theta1, theta2, d3, theta4;if(!inverseKinematics(target, theta1, theta2, d3, theta4)) {std::cerr << "目标点超出工作空间！" << std::endl;return -1;}// 角度约束处理clampAngles(theta1, theta_min[0], theta_max[0]);clampAngles(theta2, theta_min[1], theta_max[1]);clampAngles(d3, theta_min[2], theta_max[2]);clampAngles(theta4, theta_min[3], theta_max[3]);// 正解验证Pose actual = forwardKinematics(theta1, theta2, d3, theta4);std::cout << "位置误差: (" << target.x - actual.x << ", " << target.y - actual.y << ", " << target.z - actual.z << ")" << std::endl;return 0;
}

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五、测试验证方法

void testWorkspace() {// 生成工作空间网格点for(double x = -0.5; x <= 0.5; x += 0.1) {for(double y = -0.4; y <= 0.4; y += 0.1) {Pose target = {x, y, 0.1, 0.0};double theta1, theta2, d3, theta4;bool success = inverseKinematics(target, theta1, theta2, d3, theta4);std::cout << "点("<< x << ","<< y << ") 可达: " << (success ? "是" : "否") << std::endl;}}
}

参考代码 4轴scara机器人的正逆解代码 www.youwenfan.com/contentcnh/56976.html

六、扩展功能实现

1. 三维空间扩展

// 添加俯仰角控制
struct Pose3D {double x, y, z;double yaw, pitch;  // 新增俯仰角
};// 修改正运动学方程
pose3D forwardKinematics3D(double theta1, double theta2, double d3, double theta4, double theta5) {// 增加俯仰角计算double pitch = theta5;// ... 其他计算
}

2. 动力学补偿

// 添加重力补偿项
void gravityCompensation(double& torque1, double& torque2) {static const double m = 1.2;  // 末端质量static const double g = 9.81;torque1 += m * g * L1 * sin(theta1);torque2 += m * g * (L1 * sin(theta1) + L2 * sin(theta1 + theta2));
}

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七、参考文献

1. SCARA机器人正运动学公式推导
2. 解析法逆解实现细节
3. 工业级运动控制实现方案
4. 多解选择策略与优化

建议结合具体机械结构参数调整DH参数，并通过实际标定优化模型精度。对于实时控制系统，推荐使用C++实现并配合实时操作系统（RTOS）。