Adversarially Robust Geometric Safety Certificates for Nonholonomic Robots Against Maneuvering Obstacles

Chandan Kumar Sah; Bazeela Banday; Jishnu Keshavan

cs.ROSep 29, 2026

Adversarially Robust Geometric Safety Certificates for Nonholonomic Robots Against Maneuvering Obstacles

Authors: Chandan Kumar Sah, Bazeela Banday, Jishnu Keshavan

Organizations: Department of Mechanical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India

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.

Figures & tables

Parameter	Value	Source / Reason
$\ell_{r}$	$0.20$ m	Rear-axle length
$a_{\max}$	$5.0$ m s -2	Longitudinal acceleration limit
$\beta_{\max}$	$0.28$ rad	Slip-angle limit
$v_{\max}$	$3.5$ m s -1	Maximum speed
$v_{\mathrm{des}}$	$2.5$ m s -1	Cruise reference speed
$r$	$1.0$ m	Combined safety radius

TABLE I : Simulation parameters inherited from [ 8 , Table I] . Bold entries are specific to the adversarial extension.

Fig. 4 : Buffer Soft AR-DPCBF navigation timelapse ( $\min_{t}h^{*}=+0.21$ ). The unsafe sets are drawn with their exact $\{h=0\}$ (orange) and $\{h^{*}=0\}$ (green) boundaries; the green set is the uniformly wider adversarial widening. The proactive buffer keeps the robot outside the contracted set throughout.

Fig. 8 : (a) Pooled collision (solid) and barrier-violation (hatched) rates across six dense conditions ( $N=15$ , $600$ paired trials). (b) Empirical validation of Theorem 10 : colour indicates the fraction of boundary states satisfying the worst-case Nagumo condition. The region above the dashed line, $c_{\min}=\kappa$ , is certified as uniformly maintainable, while the empirical feasibility cliff occurs beyond this threshold.

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