Mission Design for Unmanned Aerial Vehicles using Hybrid Probabilistic Logic Programs

TL;DR

ProMis, a system architecture for probabilistic mission design, links the data available from various static and dynamic data sources with legal text and operator requirements by following principles of formal verification and probabilistic modeling and enables the combination of low-level perception and high-level rules in AAM to infer validity over the UAV's state-space.

Abstract

Advanced Air Mobility (AAM) is a growing field that demands a deep understanding of legal, spatial and temporal concepts in navigation. Hence, any implementation of AAM is forced to deal with the inherent uncertainties of human-inhabited spaces. Enabling growth and innovation requires the creation of a system for safe and robust mission design, i.e., the way we formalize intentions and decide their execution as trajectories for the Unmanned Aerial Vehicle (UAV). Although legal frameworks have emerged to govern urban air spaces, their full integration into the decision process of autonomous agents and operators remains an open task. In this work we present ProMis, a system architecture for probabilistic mission design. It links the data available from various static and dynamic data sources with legal text and operator requirements by following principles of formal verification and probabilistic modeling. Hereby, ProMis enables the combination of low-level perception and high-level rules in AAM to infer validity over the UAV's state-space. To this end, we employ Hybrid Probabilistic Logic Programs (HPLP) as a unifying, intermediate representation between perception and action-taking. Furthermore, we present methods to connect ProMis with crowd-sourced map data by generating HPLP atoms that represent spatial relations in a probabilistic fashion. Our claims of the utility and generality of ProMis are supported by experiments on a diverse set of scenarios and a discussion of the computational demands associated with probabilistic missions.

Figures (8)

• Figure 1: Adaptable mission design with ProMis: Probabilistic Mission Landscapes (PML) express the probability of a First-Order Logic model being satisfied over the navigation area. Each picture shows a different constraint and, on the bottom-right, a conjunction of all others. Cyan locations indicate a high probability of satisfying all constraints.
• Figure 2: The Probabilistic Mission (ProMis) system architecture: Static and dynamic data sources are transformed by the Probabilistic Clause Modules (PCM) into continuous and categorical distributions. Then, the Hybrid Probabilistic Logic Program (HPLP) Assembler writes the retrieved location dependent parameters as distributional clauses and combines the hereby formed HPLP with predefined laws and constraints. Given the parameters of the mission, tiled inference over the agent's navigation space results in a Probabilistic Mission Landscape (PML) that can then be looped back to be stored, used for action planning or as advanced mission analysis tool for the operator.
• Figure 3: Probabilistic Clause Modules express uncertainties in geospatial data: Here, a road network was queried from crowd-sourced data and random maps have been generated according to our uncertainty in the individual map features. For each location in the agent's navigation frame the parameters (a) and (b) of a normal distribution, modeling the distance to the closest road, are computed. From the cumulative distribution function of $\mathcal{N}(\mu, \sigma^2)$, or more generally via sampling, we can obtain the probability of a regulatory constraint being met, e.g., keeping a distance of over 30 meters (c). The color range transitions from red (low) to blue (high). Finally, (d) shows the probability of a location in the agent's navigation space being occupied by buildings. For visual clarity, the color range is inverse compared to the first three.
• Figure 4: Probabilistic knowledge within the final HPLP $\mathcal{P}$ in the form of distributional, spatial atoms. Here, distance and over are generated relations and applied to each location in the agent's discretized navigation space. To keep the universe small, all features of a common type are aggregated into a single reference object, e.g., "building".
• Figure 5: Simplified laws and constraints for the operation of an UAV. While the operator usually has to decide on-site whether and how they can maneuver their UAV, ProMis models and automates this decision. Probabilistic inference over the navigation space utilizing this model and extracted distributional knowledge of the environment yields a PML $\mathcal{L}$ for mission design.