Safety is critical in robotic tasks. Energy function based methods have been introduced to address the problem. To ensure safety in the presence of control limits, we need to design an energy function that results in persistently feasible safe control at all system states. However, designing such an energy function for high-dimensional nonlinear systems remains challenging. Considering the fact that there are redundant dynamics in high dimensional systems with respect to the safety specifications, this paper proposes a novel approach called abstract safe control. We propose a system abstraction method that enables the design of energy functions on a low-dimensional model. Then we can synthesize the energy function with respect to the low-dimensional model to ensure persistent feasibility. The resulting safe controller can be directly transferred to other systems with the same abstraction, e.g., when a robot arm holds different tools. The proposed approach is demonstrated on a 7-DoF robot arm (14 states) both in simulation and real-world. Our method always finds feasible control and achieves zero safety violations in 500 trials on 5 different systems.

翻译：安全性是机器人任务中的关键问题。基于能量函数的方法已被引入以解决该问题。为确保在存在控制约束时的安全性，我们需要设计一种能够在所有系统状态下产生持续可行安全控制的能量函数。然而，为高维非线性系统设计此类能量函数仍具有挑战性。考虑到高维系统中存在与安全规范相关的冗余动力学特性，本文提出了一种称为抽象安全控制的新方法。我们提出了一种系统抽象方法，使得能够在低维模型上设计能量函数。随后，我们可以针对低维模型综合能量函数，以确保持续可行性。由此产生的安全控制器可直接迁移至具有相同抽象的其他系统，例如当机器人手臂抓持不同工具时。所提方法在7自由度机器人手臂（14个状态）的仿真与真实实验中均得到验证。我们的方法在5种不同系统的500次试验中总能找到可行控制，且实现了零安全违规。