Probabilistic Mission Design for Neuro-Symbolic Unmanned Aircraft Systems

TL;DR

This paper tackles the challenge of BVLOS UAS navigation in dynamic, legally constrained, and uncertain environments by introducing Probabilistic Mission Design (ProMis), a neuro-symbolic framework that integrates uncertain geospatial data and neural perception with Hybrid Probabilistic Logic Programs to reason about legality. ProMis produces Probabilistic Mission Landscapes (PML), scalar fields that quantify the likelihood that local regulations and operator constraints are satisfied across the agent's state space, enabling interpretable planning and regulatory adaptation. The approach fuses neuro-symbolic spatial relations derived from crowd-sourced maps and neural perception (e.g., ChangeFormer) with LLM-enabled prompting to generate ProMis code, and demonstrates runtime and sampling strategies to make the method practical. Key contributions include a formal architecture for multi-modal inputs, a vocabulary of probabilistic spatial relations, integration with HPLP, and an open-source implementation, highlighting ProMis as a scalable path toward regulation-aware, explainable UAS navigation in AAM.

Abstract

Advanced Air Mobility (AAM) is a growing field that demands accurate and trustworthy models of legal concepts and restrictions for navigating Unmanned Aircraft Systems (UAS). In addition, any implementation of AAM needs to face the challenges posed by inherently dynamic and uncertain human-inhabited spaces robustly. Nevertheless, the employment of UAS beyond visual line of sight (BVLOS) is an endearing task that promises to significantly enhance today's logistics and emergency response capabilities. Hence, we propose Probabilistic Mission Design (ProMis), a novel neuro-symbolic approach to navigating UAS within legal frameworks. ProMis is an interpretable and adaptable system architecture that links uncertain geospatial data and noisy perception with declarative, Hybrid Probabilistic Logic Programs (HPLP) to reason over the agent's state space and its legality. To inform planning with legal restrictions and uncertainty in mind, ProMis yields Probabilistic Mission Landscapes (PML). These scalar fields quantify the belief that the HPLP is satisfied across the agent's state space. Extending prior work on ProMis' reasoning capabilities and computational characteristics, we show its integration with potent machine learning models such as Large Language Models (LLM) and Transformer-based vision models. Hence, our experiments underpin the application of ProMis with multi-modal input data and how our method applies to many AAM scenarios.

Figures (12)

• Figure 1: Probabilistic Mission Landscapes: Through ProMis, each point in the agent's state space is associated with an independent and identically distributed (i.i.d.) probability of satisfying the modeled navigation constraints under uncertainty (from high probability in blue to low in red). Due to the independence of each point, samples can be computed in parallel and interpolated into a scalar field.
• Figure 2: The Probabilistic Mission (ProMis) system architecture: Probabilistic Clause Modules map the agent' provided environment data from statistical (see Section \ref{['sec:nesy_relations']}) and neural (see Section \ref{['sec:neural_relations']}) models into continuous and categorical distributions over the agent's navigation space. Combined with the mission rules encoded by an operator or via an LLM, a Hybrid Probabilistic Logic Program is built to infer the satisfying state space as a Probabilistic Mission Landscape.
• Figure 3: Sampling spatial relations from uncertain maps: With an expectation of a feature's true location (black road segment) and the respective error parameters, one can generate map variations (gray road segments) to estimate the parameters, e.g., of the distance $d$ from a reference point $\mathbf{x}$.
• Figure 4: Hybrid probabilistic spatial relations from statistical evaluation: We show the mean (a) and variance (b) of distance(X, road). Through integration, one obtains the probability of a regulatory constraint being satisfied, e.g., keeping a distance of over $15m$ to roads (c). Finally, (d) shows P(over(X, building)), which as a categorical distribution can be directly taken from the estimated parameters. By associating the parameters with points in state-space, they are translated into HPLP clauses as in Listing \ref{['listing:spatial_relations']}. Colors have been made transparent to reveal the map data employed as background knowledge.
• Figure 5: Hybrid probabilistic spatial relation from neural sensing: Before (a) and after (b), images taken by a satellite provide the input for the ChangeFormer, resulting in the parameters of change(X) (c) after training the model on ground-truth data (d). By associating the prediction with points in state-space, it is translated into HPLP clauses as in Listing \ref{['listing:spatial_relations']}. Note how the ChangeFormer is, on the one hand, not perfect and missed some of the construction sites in the west, but, on the other hand, identified a building that is not part of OpenStreetMap at the time of writing (center-top).