The adaptive tracking state-feedback control for underactuated mechanical systems with outputs characterized by global relative degree equal to two is addressed. A new control technique called virtual control is proposed. Fictitious control inputs and outputs are introduced to achieve full actuation: the key step is to find the reference signals for the fictitious outputs so that the resulting virtual adaptive controls are zero. The adaptive control of an underactuated three-link walking robot with unknown torso mass is designed according to the proposed control strategy. Simulations show that adaptation is crucial for stable walking.

中文翻译：

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相对度数为2的欠驱动机械系统的自适应跟踪控制

提出了一种针对欠驱动机械系统的自适应跟踪状态反馈控制，其输出特征为全局相对度等于2。提出了一种称为虚拟控制的新控制技术。引入虚拟控制输入和输出以实现完全致动：关键步骤是找到虚拟输出的参考信号，以使生成的虚拟自适应控制为零。根据所提出的控制策略，设计了具有未知躯干质量的欠驱动三连杆步行机器人的自适应控制。仿真表明，适应对于稳定的步行至关重要。