二乗和計画による安全指数の合成
Safety Index Synthesis via Sum-of-Squares Programming
制御系の安全指数を二乗和計画で自動合成する枠組みを提案し、ロボットアームや車両で有効性を検証した。
著者: Weiye Zhao, Tairan He, Tianhao Wei, Simin Liu, Changliu Liu
分類: cs.RO
原文アブストラクト
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.
