{"ID":2831023,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08248","arxiv_id":"2512.08248","title":"Learning Spatiotemporal Tubes for Temporal Reach-Avoid-Stay Tasks using Physics-Informed Neural Networks","abstract":"This paper presents a Spatiotemporal Tube (STT)-based control framework for general control-affine MIMO nonlinear pure-feedback systems with unknown dynamics to satisfy prescribed time reach-avoid-stay tasks under external disturbances. The STT is defined as a time-varying ball, whose center and radius are jointly approximated by a Physics-Informed Neural Network (PINN). The constraints governing the STT are first formulated as loss functions of the PINN, and a training algorithm is proposed to minimize the overall violation. The PINN being trained on certain collocation points, we propose a Lipschitz-based validity condition to formally verify that the learned PINN satisfies the conditions over the continuous time horizon. Building on the learned STT representation, an approximation-free closed-form controller is defined to guarantee satisfaction of the T-RAS specification. Finally, the effectiveness and scalability of the framework are validated through two case studies involving a mobile robot and an aerial vehicle navigating through cluttered environments.","short_abstract":"This paper presents a Spatiotemporal Tube (STT)-based control framework for general control-affine MIMO nonlinear pure-feedback systems with unknown dynamics to satisfy prescribed time reach-avoid-stay tasks under external disturbances. The STT is defined as a time-varying ball, whose center and radius are jointly appr...","url_abs":"https://arxiv.org/abs/2512.08248","url_pdf":"https://arxiv.org/pdf/2512.08248v1","authors":"[\"Ahan Basu\",\"Ratnangshu Das\",\"Pushpak Jagtap\"]","published":"2025-12-09T05:08:52Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false}