Actuator-Aware Spatiotemporal Tube Synthesis for Temporal Reach-Avoid-Stay Tasks
Authors: Keshab Patra, K Madhava Krishna
Organizations: Robotics Research Center, International Institute of Information Technology - Hyderabad Hyderabad, Telangana, India
Abstract
This work proposes an actuator-aware spatiotemporal tube (STT) synthesis framework to accomplish temporal reach-avoid-stay (T-RAS) tasks for an unknown nonlinear multi-input and multi-output (MIMO) system under actuator constraints. Existing STT synthesis methods address actuator saturation after the tube generation either through repeated online re-optimization or controller redesign. Instead, the proposed framework incorporates actuator constraints directly into the tube synthesis process. The STT centerline and width are parameterized using Bernstein polynomial basis functions, whose convex-hull property enables sample-free enforcement of geometric and derivative constraints. By analyzing the worst-case closed-loop error dynamics of an approximation-free prescribed performance controller (PPC) used for STT tracking, we derive a linear actuator feasibility constraint. The constraints are embedded directly in terms of the tubes' Bernstein control points into the STT synthesis optimization for actuator-feasible tube generation, eliminating the need for online re-optimization or controller redesign. A simulation study on an omnidirectional mobile robot performing a T-RAS task shows that the proposed framework adheres to the prescribed actuator limits throughout the task and reduces required control effort by approximately 50% compared with an existing STT synthesis method.
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.
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.
We present STT-LfD, a unified Learning from Demonstration (LfD) framework that integrates motion learning with control for unknown Euler-Lagrange systems. Unlike traditional decoupled approaches that track a fixed reference, the proposed method treats demonstrations as a data-driven safety specification. Using heteroscedastic Gaussian Processes, STT-LfD learns Spatiotemporal Tubes (STTs) as an intent envelope that capture time-varying precision requirements of a task. A closed-form feedback controller then enforces these learned constraints while respecting actuator limits, without requiring explicit system identification. The approach preserves the temporal structure of demonstrations, remains computationally efficient, and avoids explicit system identification. Hardware experiments on a mobile robot and a 7-DOF manipulator show that it outperforms baselines in robustness to disturbances and computational speed.