Input-Constrained Spatiotemporal Tubes for Safe Navigation of Unknown Euler-Lagrange Systems in Dynamic Environments

2026-07-09

AI Summary

This work addresses the challenge of safe navigation in dynamic environments for systems with unknown dynamics and actuator input constraints. It proposes a novel real-time control framework that, for the first time, explicitly embeds input constraints into the design of an extended spatio-temporal tube (STT). By integrating finite-time reachability analysis with a control authority matching mechanism, the approach rigorously guarantees that Euler–Lagrange systems satisfy reachability, obstacle avoidance, and dwell-time specifications within a finite horizon—without requiring an explicit system model or online optimization—while always respecting actuator limits. The method features offline-verifiable feasibility conditions and has been validated through simulations on mobile robots, quadrotors, and spacecraft, as well as hardware experiments demonstrating safe, constraint-compliant navigation.

Abstract

Safe navigation in dynamic environments is challenging when system dynamics are unknown and actuator inputs are limited. Existing methods either rely on accurate models, require online optimization, or do not explicitly account for input constraints. This paper presents a real-time control framework for unknown Euler-Lagrange systems that guarantees finite-time reach-avoid-stay (FT-RAS) specifications while respecting actuator limits. We extend the spatiotemporal tube (STT) framework by incorporating input constraints into the controller design and derive offline-verifiable feasibility conditions that relate the available control authority to the tube design and uncertainty bounds. The resulting framework is approximation-free and computationally efficient, making it suitable for real-time implementation. The proposed approach is validated through simulations on a mobile robot, a quadrotor, and a spacecraft, together with hardware experiments on a mobile robot, demonstrating safe navigation while satisfying actuator constraints.

Problem

• safe navigation
• unknown dynamics
• input constraints
• dynamic environments
• Euler-Lagrange systems

Innovation

• spatiotemporal tubes
• input-constrained control
• unknown Euler-Lagrange systems
• finite-time reach-avoid-stay
• real-time safety guarantees