Scalable and Approximation-free Symbolic Control for Unknown Euler-Lagrange Systems
Ratnangshu Das, Shubham Sawarkar, Pushpak Jagtap
TL;DR
The paper tackles the challenge of enforcing temporal-logic specifications on Euler-Lagrange systems with unknown dynamics and disturbances, where traditional symbolic control struggles with scalability and continuous-time guarantees. It introduces Virtual Confinement Zones (VCZs), a moving $n$-D safety region with center dynamics $\\dot{\boldsymbol{\xi}} = u$, and delegates high-level synthesis to a simple VCZ center model while enforcing a closed-form, model-free confinement controller for the true EL system. A modified specification $\\phi_\\lambda$ is used to guarantee that if the VCZ center satisfies $\\phi_\\lambda$ and the real trajectory remains inside the VCZ, then the original specification $\\phi$ is satisfied in continuous time; the approach includes feasibility analysis and a trade-off between conservatism and efficiency. Case studies on a pendulum, a 4D SCARA manipulator, and an 8D multi-agent system show substantial reductions in computation time and memory compared to traditional SCOTS-based symbolic control, with hardware experiments underscoring practical viability and scalability.
Abstract
We propose a novel symbolic control framework for enforcing temporal logic specifications in Euler-Lagrange systems that addresses the key limitations of traditional abstraction-based approaches. Unlike existing methods that require exact system models and provide guarantees only at discrete sampling instants, our approach relies only on bounds on system parameters and input constraints, and ensures correctness for the full continuous-time trajectory. The framework combines scalable abstraction of a simplified virtual system with a closed-form, model-free controller that guarantees trajectories satisfy the original specification while respecting input bounds and remaining robust to unknown but bounded disturbances. We provide feasibility conditions for the construction of confinement regions and analyze the trade-off between efficiency and conservatism. Case studies on pendulum dynamics, a two-link manipulator, and multi-agent systems, including hardware experiments, demonstrate that the proposed approach ensures both correctness and safety while significantly reducing computational time and memory requirements. These results highlight its scalability and practicality for real-world robotic systems where precise models are unavailable and continuous-time guarantees are essential.