Real-Time Spatiotemporal Tubes for Dynamic Unsafe Sets
Ratnangshu Das, Siddhartha Upadhyay, Pushpak Jagtap
TL;DR
The paper tackles safe, prescribed-time control for nonlinear systems with unknown dynamics navigating dynamic environments. It introduces a real-time, spherical spatiotemporal tube (STT) whose center and radius adapt online based on sensory input, paired with a closed-form, model-free controller to keep the system within the evolving tube. Formal guarantees ensure obstacle avoidance and on-time target reach, validated through simulations and hardware experiments on a 2D mobile robot and a 3D quadrotor. The work demonstrates real-time efficiency, scalability to dense obstacle fields, and favorable comparisons to baseline methods, while acknowledging offline STT synthesis drawbacks and outlining directions for integration with global planning. Overall, it provides a practical framework for real-time safety-critical control in uncertain, dynamic settings.
Abstract
This paper presents a real-time control framework for nonlinear pure-feedback systems with unknown dynamics to satisfy reach-avoid-stay tasks within a prescribed time in dynamic environments. To achieve this, we introduce a real-time spatiotemporal tube (STT) framework. An STT is defined as a time-varying ball in the state space whose center and radius adapt online using only real-time sensory input. A closed-form, approximation-free control law is then derived to constrain the system output within the STT, ensuring safety and task satisfaction. We provide formal guarantees for obstacle avoidance and on-time task completion. The effectiveness and scalability of the framework are demonstrated through simulations and hardware experiments on a mobile robot and an aerial vehicle, navigating in cluttered dynamic environments.