Learning Spatiotemporal Tubes for Full Class of Signal Temporal Logic Tasks for Control of Unknown Systems under Input Constraints
This work addresses the problem of safe control for unknown nonlinear systems with input constraints to satisfy complex temporal logic specifications, which is important for autonomous systems but the approach is incremental as it combines existing ideas (PINNs, STL, tube-based control) in a new way.
This paper develops a spatiotemporal tube (STT) control framework for unknown Euler-Lagrange systems under input constraints to satisfy Signal Temporal Logic (STL) tasks. The method uses physics-informed neural networks to parameterize tubes and a closed-form control law to keep trajectories inside them, validated on multiple case studies.
This paper presents a Spatiotemporal Tube (STT)-based control framework for general unknown nonlinear Euler-Lagrange (EL) systems subject to input constraints, with the objective of satisfying Signal Temporal Logic (STL) specifications, where confinement of the system trajectory within the STT guarantees the satisfaction of the corresponding STL task. For both single and multi-agent scenarios, the STT corresponding to each agent is modeled as a time-varying ball, whose center and radius are jointly parameterized using a physics-informed neural network (PINN). The robustness metric associated with the STL specification corresponding to the agents is incorporated into the training process as a loss function, enabling the learned tube to encode task-level temporal requirements. For a multi-agent scenario, we introduce an additional robustness metric corresponding to the global task, which, when satisfied, ensures the tubes do not collide with each other. To ensure that the system trajectory remains within the learned STT and thereby satisfies the local and global STL specifications, we propose a control strategy that explicitly accounts for input constraints. In particular, a closed-form control law is developed to keep the trajectory inside the tube while regulating the motion of the tube by enforcing bounds on its evolution depending on the input constraints of the system. The proposed approach has been validated over several case studies.