Newest papers

Temporal Difference Learning of Probabilistic Reach-Avoid Value Functions

Elias Fontanari, Pietro Noah Crestaz, Matteo Saveriano, Andrea Del Prete · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28106 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

避免攻击的集合,定义了可以完成任务的状态,同时避免不安全的区域,是部署机器人在受干扰和不确定性环境的基本工具,以及运行时任务可行性监测,允许预测一个状态是否安全,并将导致任务的成功完成。经典汉密尔顿 - 雅各布的可行性(HJR)和其最近的神经扩展(例如,利普希茨连续任务可行性学习,DeepReach)对攻击进行对抗,计算出在最坏的情况下避免攻击的状态。这保证了安全性,但在扰乱时会产生过于保守的集合,而不是对抗的,并且可能还需要预先知道或指定攻击。我们建议在显示某些基于Hopper的可行性时,我们能够达到更为保守

Machine translation (Meta M2M100); the English original follows.

Abstract

Reach-avoid sets, defining the states from which a task can be completed while avoiding unsafe regions, are fundamental tools for deploying robots in environments subject to disturbances and uncertainty, as well as for runtime task-feasibility monitoring, allowing prediction of whether a state is safe and will lead to successful task completion. Classical Hamilton-Jacobi Reachability (HJR) and its recent neural extensions (e.g., Lipschitz Continuous Reachability Learning, DeepReach) treat disturbances adversarially, computing the reach-avoid set under worst-case disturbances from a bounded set. This guarantees safety but can yield overly conservative sets when disturbances are stochastic rather than adversarial, and additionally requires the disturbance set to be known or specified in advance. We propose Probabilistic reach-avoid Value Function (PVF), a self-supervised method, applicable to black-box systems, for computing reach-avoid sets as the states with a certain reach-avoid probability under stochastic, potentially unbounded disturbances. We evaluate our approach against HJR-based baselines on systems of increasing complexity, up to a Hopper locomotion task, and show that our probabilistic sets are less conservative and more accurate than adversarial HJR sets when disturbances are non-adversarial.

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Topics: Probabilistic logic, Reachability, Set (abstract data type), Bounded function, Task (project management), Computer science

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