aiqbench analysis
This research introduces a novel geometric certificate that ensures safe navigation for nonholonomic robots against actively maneuvering obstacles by directly integrating worst-case obstacle dynamics into the safe-set geometry. By exploiting structural properties of line-of-sight certificates, the method reduces complex differential games to direct capability comparisons, significantly lowering computational costs compared to standard robust control barrier function approaches. The proposed framework establishes sufficient conditions for forward invariance even when obstacle capabilities are unknown, offering a practical path toward collision-free operation in dense environments without relying on generic disturbance assumptions.
Adversarially Robust Geometric Safety Certificates for Nonholonomic Robots Against Maneuvering Obstacles
arXiv:2609.37126v1 Announce Type: new Abstract: Safe navigation against obstacles that can actively maneuver within bounded capabilities remains challenging: robust control barrier function methods typically treat obstacle actions as generic disturbances, while differential-game approaches are computationally expensive for online navigation. We propose an adversarially robust geometric certificate that accounts for the worst-case effect of admissible obstacle maneuvers directly in the safe-set geometry through a closed-form contraction of the certificate parameters. The construction exploits a structural property of line-of-sight (LoS) certificates: the robot and obstacle actions enter the certificate through a common state-dependent geometric gain. This gain cancels in the worst-case comparison, reducing the differential game to a direct comparison between obstacle maneuvering capability and the weaker of the robot's longitudinal and steering authorities. Instantiated on the parabolic certificate, the construction yields Adversarially Robust Dynamic Parabolic Control Barrier Functions (AR-DPCBF), for which we establish sufficient conditions for forward invariance of the contracted safe set against all admissible obstacle maneuvers under kinematic bicycle dynamics with bounded inputs. When the obstacle capability is unknown, a sliding-window estimator supplies a high-probability upper bound, allowing the guarantee to be retained with the corresponding coverage probability. We further formulate soft and buffered variants to recover feasibility in dense environments. Simulations across obstacle capabilities, densities, and capability mismatch show substantial reductions in barrier violations and collisions and demonstrate that pointwise robustification of the barrier derivative cannot substitute for contraction of its geometry.
Abstract:Safe navigation against obstacles that can actively maneuver within bounded capabilities remains challenging: robust control barrier function methods typically treat obstacle actions as generic disturbances, while differential-game approaches are computationally expensive for online navigation. We propose an adversarially robust geometric certificate that accounts for the worst-case effect of admissible obstacle maneuvers directly in the safe-set geometry through a closed-form contraction of the certificate parameters. The construction exploits a structural property of line-of-sight (LoS) certificates: the robot and obstacle actions enter the certificate through a common state-dependent geometric gain. This gain cancels in the worst-case comparison, reducing the differential game to a direct comparison between obstacle maneuvering capability and the weaker of the robot's longitudinal and steering authorities. Instantiated on the parabolic certificate, the construction yields Adversarially Robust Dynamic Parabolic Control Barrier Functions (AR-DPCBF), for which we establish sufficient conditions for forward invariance of the contracted safe set against all admissible obstacle maneuvers under kinematic bicycle dynamics with bounded inputs. When the obstacle capability is unknown, a sliding-window estimator supplies a high-probability upper bound, allowing the guarantee to be retained with the corresponding coverage probability. We further formulate soft and buffered variants to recover feasibility in dense environments. Simulations across obstacle capabilities, densities, and capability mismatch show substantial reductions in barrier violations and collisions and demonstrate that pointwise robustification of the barrier derivative cannot substitute for contraction of its geometry.
Robotics (cs.RO); Multiagent Systems (cs.MA)
arXiv:2609.37126 [cs.RO]
(or arXiv:2609.37126v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2609.37126 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 325 words
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