Quantify Free-Space Loss from Robust Barrier Tightening

Quantify the reduction in free space between two obstacles caused by robust control barrier function tightening for a disturbed, input-bounded robot, particularly when the feasibility margin is small.

Background

Robust barrier constraints add a disturbance-dependent margin to the nominal safety constraint. The paper notes that this tightening consumes control authority precisely near the boundary of feasibility, where available maneuvering authority is already limited. It identifies as unresolved both the associated feasibility difficulty and the extent to which the tightening narrows or eliminates passages between obstacles.

References

Robust tightening therefore poses two challenges. It consumes control authority precisely where the feasibility margin is smallest, a difficulty that leaves open, and the extent to which it reduces the free space between two obstacles has not yet been quantified.

— Safe Unicycle Navigation Among Multiple Obstacles Under Bounded Disturbances: A Learning-Augmented CLF-CBF Approach (Extended Version)  (2610.17916 - Singh et al., 13 Oct 2026) in Section 1, Introduction, subsection “Disturbance”