arXiv subjects

Ivan Tomasic

Publications and source records attributed to Ivan Tomasic.

9 recordsLinked to original sources

arXiv2026

A Safety-Driven Architectural Framework for Fail-Operational Drone Swarms in Critical Missions

The certification of Unmanned Aerial Vehicle (UAV) swarms for safety-critical operations requires verifiable design assurance. Airworthiness standards demand deterministic reliability, whereas multi-agent coordination algorithms execute non-deterministic models. This paper proposes a mixed-criticality architectural framework that applies SAE ARP4754B methods to swarm reconfiguration. First, a hardware-isolated Safety Monitor functions as a Run-Time Assurance (RTA) gateway, decoupling the flight-critical core from the non-deterministic Swarm Manager. Second, the monitor enforces formal safety contracts based on agent Health Vectors derived systematically from a Functional Hazard Assessment (FHA). Third, the framework propagates these Health Vectors to the collective planner to trigger fail-operational task reallocation, enabling intelligent swarm behaviors without compromising flight-critical isolation. Markov reliability modeling demonstrates that the $10^{-7}$ failures per flight hour Hazardous target is theoretically achievable for our SAIL IV scenario, provided the Safety Monitor meets $C_{monitor}>0.9991$, consistent with DAL B CMD/MON implementations.

eess.SY↗

arXiv2026

Market-Based Replanning for Safety-Critical UAV Swarms in Search and Rescue Missions

Reliable autonomous UAV swarms in Search and Rescue (SAR) missions require fault-tolerant coordination capable of sustaining operations despite agent degradation. This paper introduces the Intelligent Replanning Drone Swarm (IRDS), a distributed coordination architecture designed for resource-constrained environments. The proposed framework employs a Reverse-Auction market mechanism where agents bid to service search sectors based on a distance-weighted cost function, coupled with a geometric consensus protocol for target verification. We evaluate the approach through physics-based simulations (N=8 agents, 8x8 grid) subjected to stochastic fault injection. Results indicate that the swarm autonomously reallocates tasks from failed agents with low latency relative to the total mission duration, maintaining a mission success rate of 93% under 25% workforce degradation. The proposed framework demonstrates a robust, empirically tested method for self-healing aerial robotic coordination.

cs.RO↗

arXiv2026

Scheduling Analysis of UAV Flight Control Workloads on PREEMPT_RT Linux Using a Raspberry Pi 5

Modern UAV architectures increasingly aim to unify high-level autonomy and low-level flight control on a single General-Purpose Operating System (GPOS). However, complex multi-core System-on-Chips (SoCs) introduce significant timing indeterminism due to shared resource contention. This paper performs an architectural analysis of the PREEMPT RT Linux kernel on a Raspberry Pi 5, specifically isolating the impact of kernel activation paths (deferred execution SoftIRQs versus real-time direct activation) on a 250 Hz control loop. Results show that under heavy stress, the standard kernel is unsuitable, exhibiting worst-case latencies exceeding 9 ms. In contrast, PREEMPT RT reduced the worst-case latency by nearly 88 percent to under 225 microseconds, enforcing a direct wake-up path that mitigates OS noise. These findings demonstrate that while PREEMPT RT resolves scheduling variance, the residual jitter on modern SoCs is primarily driven by hardware memory contention.

eess.SY↗

arXiv2024

Hochschild cohomology in toposes

We develop a theory of internal Hochschild cohomology in a ringed topos. We construct it via the internal Hochschild cochain complex, as well as through derived functor/topos cohomology theory, and discuss its relationship to the absolute Hochschild cohomology. By specialising to the topos of difference sets, we obtain a theory of internal difference Hochschild cohomology, and compare it to the absolute Hochschild cohomology through the Grothendieck and hypercohomology spectral sequences. We provide a systematic and detailed treatment of tensor products in suitable toposes in hope to complete the existing literature.

math.CT↗

arXiv2021

Difference Galois theory and dynamics

We develop a Galois theory for difference ring extensions, inspired by Magid's separable Galois theory for ring extensions and by Janelidze's categorical Galois theory. Our difference Galois theorem states that the category of difference ring extensions split by a chosen Galois difference ring extension is classified by actions of the associated difference profinite Galois groupoid. In particular, difference locally étale extensions of a difference ring are classified by its difference profinite fundamental groupoid. The emergence of difference profinite spaces, viewed as discrete dynamical systems in the realm of topological dynamics, leads us to investigate the interaction of difference algebra and symbolic dynamics. As an application of this interaction, we prove the near-rationality of a certain difference zeta function counting solutions of systems of difference algebraic equations over algebraic closures of finite fields with Frobenius.

math.CT↗

arXiv2020

A topos-theoretic view of difference algebra

We view difference algebra as the study of algebraic objects in the topos of difference sets. The methods of topos theory and categorical logic enable us to develop difference homological algebra, identify a solid foundation for difference algebraic geometry, and cohomology theory of difference schemes.

math.AG↗

arXiv2012

Twisted Galois stratification

We prove a direct image theorem stating that the direct image of a Galois formula by a morphism of difference schemes is equivalent to a Galois formula over fields with powers of Frobenius. As a consequence, we obtain an effective quantifier elimination procedure and a precise algebraic-geometric description of definable sets over fields with Frobenii in terms of twisted Galois formulae associated with finite Galois covers of difference schemes.

math.AG↗

arXiv2011

Multiplicity in difference geometry

We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a σ-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.

math.AG↗

arXiv2011

On braided zeta functions

We propose a ribbon braided category approach to zeta-functions in q-deformed geometry. As a proof of concept we compute $ζ_t(C^n)$ where $C^n$ is viewed as the standard representation in the category of modules of $U_q(sl_n)$. We show that the same $ζ_t(C^n)$ is obtained for the $n$-dimensional representation in the category of $U_q(sl_2)$ modules. We show that this implies and is equivalent to the generating function for the decomposition into irreducibles of the symmetric tensor products $S^j(V)$ for $V$ an irreducible representation of $sl_2$. We discuss $ζ_t(C_q(S^2))$ for the standard q-deformed sphere.

math.QA↗