Learning Spatiotemporal Tubes for Full Class of Signal Temporal Logic Tasks for Control of Unknown Systems under Input Constraints

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.

SafeDMPs: Integrating Formal Safety with DMPs for Adaptive HRI

Robots operating in human-centric environments must be both robust to disturbances and provably safe from collisions. Achieving these properties simultaneously and efficiently remains a central challenge. While Dynamic Movement Primitives (DMPs) offer inherent stability and generalization from single demonstrations, they lack formal safety guarantees. Conversely, formal methods like Control Barrier Functions (CBFs) provide provable safety but often rely on computationally expensive, real-time optimization, hindering their use in high-frequency control. This paper introduces SafeDMPs, a novel framework that resolves this trade-off. We integrate the closed-form efficiency and dynamic robustness of DMPs with a provably safe, non-optimization-based control law derived from Spatio-Temporal Tubes (STTs). This synergy allows us to generate motions that are not only robust to perturbations and adaptable to new goals, but also guaranteed to avoid static and dynamic obstacles. Our approach achieves a closed-form solution for a problem that traditionally requires online optimization. Experimental results on a 7-DOF robot manipulator demonstrate that SafeDMPs is orders of magnitude faster and more accurate than optimization-based baselines, making it an ideal solution for real-time, safe, and collaborative robotics.