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：安全性在机器人任务中至关重要。基于能量函数的方法已被引入以解决该问题。为确保在控制权限限制下的安全性，我们需要设计一种能够在所有系统状态下实现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。进而可针对该低维模型综合能量函数，以确保持续可行性。所得安全控制器可直接迁移至具有相同抽象的其他系统，例如当机械臂抓取不同工具时。该方法的有效性通过在7自由度机械臂（14维状态）的仿真与真实实验中得以验证。我们的方法始终能找到可行控制，并在5个不同系统的500次试验中实现了零安全违规。