Adversarially Robust Geometric Safety Certificates for Nonholonomic Robots Against Maneuvering Obstacles

2026-09-29

AI Summary

This study addresses the computational expense and real-time limitations of traditional robust control for nonholonomic robots navigating against actively maneuvering adversarial obstacles. We propose an Adversarially Robust Distance Policy Control Barrier Function (AR-DPCBF) that exploits the geometric gain structure of line-of-sight certificates to reduce differential games to capability comparisons. By analytically shrinking certificate parameters in closed form to account for worst-case obstacle maneuvers, this approach overcomes the limitations of conventional pointwise robustification. Integrated with sliding-window estimation and soft-constraint buffering mechanisms, the framework enables efficient online navigation in dense environments. Simulations demonstrate that the proposed method significantly reduces barrier violations and collision rates, validating its advantage in providing high-probability safety guarantees across diverse obstacle capabilities.

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.

Problem

• safe navigation
• adversarially robust
• nonholonomic robots
• maneuvering obstacles
• control barrier functions

Innovation

• Adversarially Robust Control Barrier Functions
• Geometric Safety Certificates
• Nonholonomic Robots
• Differential Games
• Dynamic Parabolic CBF