论文标题
安全指数通过方案总和编程合成
Safety Index Synthesis via Sum-of-Squares Programming
论文作者
论文摘要
控制系统通常需要满足严格的安全要求。安全指数提供了一种评估系统安全水平并得出所得安全控制政策的方便方法。但是，在控制范围内设计安全指数功能是困难的，需要大量的专家知识。本文提出了一个框架，用于使用平方符号编程为通用控制系统合成安全指数。我们的方法是表明，确保安全控制对安全设置边界的非空置性等同于当地的多种积极问题。然后，我们证明了这个问题等于通过代数几何形状的Pitivstellensatz进行编程。我们验证了具有不同自由度和地面车辆的机器人臂上的拟议方法。结果表明，合成的安全指数可确保安全性，即使在高维机器人系统中，我们的方法也有效。
Control systems often need to satisfy strict safety requirements. Safety index provides a handy way to evaluate the safety level of the system and derive the resulting safe control policies. However, designing safety index functions under control limits is difficult and requires a great amount of expert knowledge. This paper proposes a framework for synthesizing the safety index for general control systems using sum-of-squares programming. Our approach is to show that ensuring the non-emptiness of safe control on the safe set boundary is equivalent to a local manifold positiveness problem. We then prove that this problem is equivalent to sum-of-squares programming via the Positivstellensatz of algebraic geometry. We validate the proposed method on robot arms with different degrees of freedom and ground vehicles. The results show that the synthesized safety index guarantees safety and our method is effective even in high-dimensional robot systems.
