Steering with Contingencies: Combinatorial Stabilization and Reach-Avoid Filters

TL;DR

This paper introduces control filters for autonomous systems that ensure stability and safe diversion to multiple targets, using combinatorial optimization and reach-avoid sets to handle contingency requirements efficiently.

Contribution

It formalizes combinatorial stabilization and reach-avoid filters, enabling real-time safe switching among multiple targets with minimal constraints.

Findings

Filters require only p+1 constraints, avoiding combinatorial blow-up.

Framework demonstrated on examples ensuring steering with contingency.

Enables safe diversion and target switching in autonomous navigation.

Abstract

In applications such as autonomous landing and navigation, it is often desirable to steer toward a target while retaining the ability to divert to at least $r$ (out of $p$) alternative sites if conditions change. In this work, we formalize this combinatorial contingency requirement and develop tractable control filters for enforcement. Combinatorial stabilization requires asymptotic stability of a selected equilibrium while ensuring the trajectory remains within the safe region of attraction of at least $r$-out-of-$p$ candidates. To enforce this requirement, we use control Lyapunov functions (CLFs) to construct regions of attraction, which are combined combinatorially within an optimization-based filter. Combinatorial targeting extends this framework to finite-horizon problems using Hamilton-Jacobi backward reach-avoid sets, accommodating shrinking reachable regions due to finite horizons or resource depletion. In both formulations, the resulting combinatorial stability filter and combinatorial reach-avoid filter require only $p+1$ constraints, preventing combinatorial blow-up and enabling safe real-time switching between targets. The framework is demonstrated on two examples where the filters ensure steering with contingency and enable safe diversion.