Actuator-Aware Spatiotemporal Tube Synthesis for Temporal Reach-Avoid-Stay Tasks

2026-07-25

AI Summary

This work addresses the time-constrained reach-avoid-stay (T-RAS) task for unknown nonlinear MIMO systems subject to actuator constraints by proposing an actuator-aware spatiotemporal tube (STT) synthesis framework. The approach uniquely embeds actuator limitations directly into the STT generation process, parameterizing both the tube’s centerline and width using Bernstein polynomials. By integrating closed-loop error dynamics governed by approximation-free prescribed performance control, the method formulates linear feasibility constraints. Leveraging the convex hull property of Bernstein bases, it guarantees hard constraint satisfaction without requiring sampling. Simulation results on an omnidirectional mobile robot demonstrate that the proposed framework consistently respects actuator limits throughout the T-RAS mission while reducing control energy consumption by approximately 50% compared to existing methods.

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.

Problem

• actuator constraints
• spatiotemporal tube synthesis
• temporal reach-avoid-stay tasks
• nonlinear MIMO systems
• actuator saturation

Innovation

• actuator-aware
• spatiotemporal tube synthesis
• Bernstein polynomials
• prescribed performance control
• temporal reach-avoid-stay