Ro-To-Go! Robust Reactive Control with Signal Temporal Logic

Authors: Roland Ilyes, Lara Brudermüller, Nick Hawes, Bruno Lacerda · ICRA 2026

Licences

Open Access
Paper: CC BY 4.0

Everything below draws on the full paper under its CC BY 4.0 licence; its figure is credited to the authors.

TL;DR

A new STL robustness measure that ignores the already-executed past, computed online by formula progression, so an MPC planner can still prefer safer futures after an early near-miss.

Why it matters

Robots that replan with STL objectives no longer lose all incentive to improve after a past near-violation. Because the measure reduces to ordinary robustness on a progressed formula, past observations are not reprocessed and existing robustness tools and other robustness measures can be reused.

Problem

STL robustness scores a whole trajectory by its most critical point, so in MPC an early close approach to an obstacle caps the score of every later plan. The robot then cannot tell a plan that moves well away from future hazards from one that does not.

Proposed solution

Robustness-to-go changes how predicates are scored: before a chosen time t̂ a predicate counts as +∞ or −∞ depending on whether it held, and after t̂ it is scored as normal robustness. The authors prove it is sound (positive exactly when the formula is satisfied) and that it equals the ordinary robustness of the progressed formula, so at each MPC step the formula is progressed with the latest state and standard robustness tools score only the planning horizon.

Key insights

In feedback control, the most critical point of STL robustness may lie in the past, where the robot can no longer change it
Robustness-to-go from time t̂ equals the robustness of the formula progressed up to t̂, so it depends only on the suffix trajectory
Once an 'eventually' goal is met, it no longer affects the objective, so the robot may leave the goal region; the authors argue past satisfaction cannot be disturbed, so more robustness there is wasted
The measure is orthogonal to averaged robustness measures such as Generalized Mean Robustness and can be combined with them

Main results

Reach-avoid task (100 runs, dynamic environment): success rate 0.91 with Ro-To-Go versus 0.63 with STL robustness
Stay-in-region task (100 runs): success rate 0.99 with Ro-To-Go versus 0.76 with STL robustness
Mean robustness: −0.079 ± 0.574 versus −0.421 ± 0.795 (reach-avoid), 0.601 ± 0.166 versus 0.341 ± 0.344 (stay-in); maximum achievable robustness for reach-avoid is 0.1
Mean minimum distance from the dynamic region in reach-avoid: 0.312 ± 0.217 with Ro-To-Go versus 0.172 ± 0.253 with robustness (units not stated in Table I)
Worked example (Fig. 1): the robustness-based plan comes within 0.13 m of the human, the Ro-To-Go plan within 0.79 m

Limitations

Each MPC step solves a problem that assumes a static environment over the plan, so there are no safety guarantees for the motion plans
Under 'eventually' formulas the behaviour is less robust: the robot leaves the goal once it has been reached
The optimisation-based (NLP) approach it builds on is incomplete and finds local optima
The measure is still local: the most critical point within the planning horizon decides the score
Evaluated only in simulation on a 2D double-integrator robot with random environment motion; no hardware experiments

Field impact

Finalist for the ICRA 2026 Best Paper Award in Automation, with 1 citation. The paper does not release code; it builds on the open-source STLRom library and VP-STO.

Abstract

Signal Temporal Logic (STL) robustness is a common objective for optimal robot control, but its dependence on history limits the robot's decision-making capabilities when used in Model Predictive Control (MPC) approaches. In this work, we introduce Signal Temporal Logic robustness-to-go (Ro-To-Go), a new quantitative semantics for the logic that isolates the contributions of suffix trajectories. We prove its relationship to formula progression for Metric Temporal Logic, and show that the robustness-to-go depends only on the suffix trajectory and progressed formula. We implement robustness-to-go as the objective in an MPC algorithm and use formula progression to efficiently evaluate it online. We test the algorithm in simulation and compare it to MPC using traditional STL robustness. Our experiments show that using robustness-to-go results in a higher success rate.

Open Source Robotics