Spatiotemporal Tubes based Controller Synthesis against Omega-Regular Specifications for Unknown Systems
Ratnangshu Das, Aiman Aatif Bayezeed, Pushpak Jagtap
TL;DR
The paper addresses synthesis of approximation-free, closed-form controllers for unknown nonlinear MIMO systems to enforce $\omega$-regular specifications recognized by non-deterministic Büchi automata (NBA). It introduces a discretization-free, spatiotemporal tubes (STT) framework that decomposes NBA specifications into a sequence of reach-avoid tasks, solves each task with a closed-form RA controller, and stitches them into a hybrid policy that provably satisfies the NBA language. The approach extends to general strict-feedback MIMO systems with unknown dynamics, relaxing restrictive obstacle-position assumptions and providing a scalable, real-time capable solution demonstrated on a 2R manipulator and an omnidirectional mobile robot. This work advances formal control by delivering an approximation-free, hybrid control synthesis method for complex, infinite-horizon specifications with unknown dynamics, enabling robust autonomous behavior under omega-regular constraints.
Abstract
This paper provides a discretization-free solution to the synthesis of approx-imation-free closed-form controllers for unknown nonlinear systems to enforce complex properties expressed by $ω$-regular languages, as recognized by Non-deterministic Büchi Automata (NBA). In order to solve this problem, we first decompose NBA into a sequence of reach-avoid problems, which are solved using the Spatiotemporal Tubes (STT) approach. Controllers for each reach-avoid task are then integrated into a hybrid policy that ensures the fulfillment of the desired $ω$-regular properties. We validate our method through omnidirectional robot navigation and manipulator control case studies.