Kp / Kd 参数说明

在仿真 (Isaac Gym)

PD 控制器：

\[\tau = K_p e_p + K_d e_v\]

• \(K_p\)：刚度
• \(K_d\)：阻尼
• \(e_p\)：位置误差
• \(e_v\)：速度误差

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在真实机器人执行器

PID 控制器：

\[I = P_p P_v e_p + P_v e_v\]

\[\tau' = g I K_t = g(P_p P_v K_t e_p + P_v K_t e_v)\]

• \(P_p\)：位置环比例参数
• \(P_v\)：速度环比例参数
• \(g\)：齿轮比
• \(K_t\)：扭矩常数

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Sim-to-Real 参数对齐关系

当满足 \(\tau = \tau'\) 时，仿真与实机参数的对应关系如下：

\[K_p = g P_p P_v K_t\]

\[K_d = g P_v K_t\]

由此推导出实机配置参数：

\[P_v = \frac{K_d}{K_t \cdot g}\]

\[P_p = \frac{K_p}{K_d}\]

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关节逻辑代码片段

void RealRobot::computeJointPdParams() {
  joint_Kp_s = joint_Kp_;
  joint_Kd_s = joint_Kd_;

  for (int i = 0; i < robot_dof_nums_; i++) {
    if (bAdam_u_) {
      // Adam-U 逻辑
      joint_Kp_(i) = joint_Kp_(i) / joint_Kd_(i);
      joint_Kd_(i) = joint_Kd_(i) / PConfig::getInstance().kdScale()(i);
    } else {
      // Adam 逻辑：踝关节特殊处理
      if (i == kAnkleJoint1 || i == kAnkleJoint2) {
        joint_Kp_(i) = joint_Kp_(i - 1);
        joint_Kd_(i) = joint_Kd_(i - 1);
      } else {
        joint_Kp_(i) = joint_Kp_(i) / joint_Kd_(i);
        joint_Kd_(i) = joint_Kd_(i) / PConfig::getInstance().kdScale()(i);
      }
    }
  }

  std::cout << "joint_Kp: " << joint_Kp_.transpose() << std::endl;
  std::cout << "joint_Kd: " << joint_Kd_.transpose() << std::endl;
}