Robust Multi-Agent Safety via Tube-Based Tightened Exponential Barrier Functions

TL;DR

This paper introduces a formal framework for designing safe controllers for nonlinear multi-agent systems with disturbances, using a constraint tightening approach based on robust invariant tubes and exponential barrier functions.

Contribution

It develops a novel method that couples robust error feedback with nominal planning to ensure safety in multi-agent systems under disturbances.

Findings

The method guarantees safety for disturbed systems via tightened constraints.

Implementation within a distributed MPC scheme demonstrates practical effectiveness.

The approach applies to systems in Brunovsky canonical form with arbitrary dynamics.

Abstract

This paper presents a constructive framework for synthesizing provably safe controllers for nonlinear multi-agent systems subject to bounded disturbances. The methodology applies to systems representable in Brunovsky canonical form, accommodating arbitrary-order dynamics in multi-dimensional spaces. The central contribution is a method of constraint tightening that formally couples robust error feedback with nominal trajectory planning. The key insight is that the design of an ancillary feedback law, which confines state errors to a robust positively invariant (RPI) tube, simultaneously provides the exact information needed to ensure the safety of the nominal plan. Specifically, the geometry of the resulting RPI tube is leveraged via its support function to derive state-dependent safety margins. These margins are then used to systematically tighten the high relative-degree exponential control barrier function (eCBF) constraints imposed on the nominal planner. This integrated synthesis guarantees that any nominal trajectory satisfying the tightened constraints corresponds to a provably safe trajectory for the true, disturbed system. We demonstrate the practical utility of this formal synthesis method by implementing the planner within a distributed Model Predictive Control (MPC) scheme, which optimizes performance while inheriting the robust safety guarantees.