二乗和最適化と動的計画法による到達回避問題の解法
Reach-Avoid Problems via Sum-of-Squares Optimization and Dynamic Programming
多項式系の到達回避問題に対し、二乗和最適化と動的計画法を組み合わせて到達と回避の保証を維持する保守的な解法を提案し、計算スケーラビリティを実証した論文。
著者: Benoit Landry, Mo Chen, Scott Hemley, Marco Pavone
分類: eess.SY, cs.RO, cs.SY, math.OC
原文アブストラクト
Reach-avoid problems involve driving a system to a set of desirable configurations while keeping it away from undesirable ones. Providing mathematical guarantees for such scenarios is challenging but have numerous potential practical applications. Due to the challenges, analysis of reach-avoid problems involves making trade-offs between generality of system dynamics, generality of problem setups, optimality of solutions, and computational complexity. In this paper, we combine sum-of-squares optimization and dynamic programming to address the reach-avoid problem, and provide a conservative solution that maintains reaching and avoidance guarantees. Our method is applicable to polynomial system dynamics and to general problem setups, and is more computationally scalable than previous related methods. Through a numerical example involving two single integrators, we validate our proposed theory and compare our method to Hamilton-Jacobi reachability. Having validated our theory, we demonstrate the computational scalability of our method by computing the reach-avoid set of a system involving two kinematic cars.
