Privacy Preserving Mechanisms for Coordinating Airspace Usage in Advanced Air Mobility

TL;DR

This work tackles privacy-preserving allocation of capacity-constrained airspace for dynamically arriving Advanced Air Mobility (AAM) vehicles with heterogeneous private valuations. It formulates airspace as a time-extended graph $ ilde{ ilde{ ilde{ ilde{ ilde{ ilde{G}}}}}$ with horizon $T$ and region-specific capacities, and introduces an artificial currency, the air-credits, to support a market-based allocation via receding-horizon auctions. A fractional-competitive equilibrium $(ar{oldsymbol{x}}^ abla,oldsymbol{p}^ abla)$ is shown to exist and be computable as a fixed point of a budget-adjusted welfare problem, enabling a distributed ADMM-based inner loop to approximate prices without exposing private valuations. The authors then derive an integral allocation from the fractional equilibrium by ranking vehicles according to their fractional allocations and allocating along the rank, ensuring capacity constraints are respected; this two-step algorithm is validated on a Toulouse drone-delivery dataset and a Northern California vertiport scenario, demonstrating effective throughput, low market-clearing error, and privacy preservation.

Abstract

Advanced Air Mobility (AAM) operations are expected to transform air transportation while challenging current air traffic management practices. By introducing a novel market-based mechanism, we address the problem of on-demand allocation of capacity-constrained airspace to AAM vehicles with heterogeneous and private valuations. We model airspace and air infrastructure as a collection of contiguous regions with constraints on the number of vehicles that simultaneously enter, stay, or exit each region. Vehicles request access to the airspace with trajectories spanning multiple regions at different times. We use the graph structure of our airspace model to formulate the allocation problem as a path allocation problem on a time-extended graph. To ensure the cost information of AAM vehicles remains private, we introduce a novel mechanism that allocates each vehicle a budget of "air-credits" and anonymously charges prices for traversing the edges of the time-extended graph. We seek to compute a competitive equilibrium that ensures that: (i) capacity constraints are satisfied, (ii) a strictly positive resource price implies that the sector capacity is fully utilized, and (iii) the allocation is integral and optimal for each AAM vehicle given current prices, without requiring access to individual vehicle utilities. However, a competitive equilibrium with integral allocations may not always exist. We provide sufficient conditions for the existence and computation of a fractional-competitive equilibrium, where allocations can be fractional. Building on these theoretical insights, we propose a distributed, iterative, two-step algorithm that: 1) computes a fractional competitive equilibrium, and 2) derives an integral allocation from this equilibrium. We validate the effectiveness of our approach in allocating trajectories for two emerging urban air mobility services: drone delivery and air taxis.

Figures (11)

• Figure 1: Model of airspace as a set of contiguous regions, each having arrival, departure, and transit constraints. Some regions are at the cruising altitude, while others encompass vertiport/launch pads.
• Figure 2: A time-trajectory of a drone delivering a package in an urban setting. The drone starts from the launch pad $\textsf{V1}$ (Sector 1) and needs to drop a package in Sector 5 before returning. Here, we have shown a simple trajectory that moves between regions in one time-step, but in general, such trajectories can remain in any region for multiple time-steps.
• Figure 3: A schematic depiction of the receding horizon approach.
• Figure 4: Flowchart of Algorithm \ref{['algo:1']}, illustrating the processes executed independently by the SP and AAM vehicles, as well as the steps computed within the inner and outer loops.
• Figure 5: Flowchart of Algorithm \ref{['algo:2']}, illustrating the ranking system and the removal of over-demanded edges.

Theorems & Definitions (15)

• Definition 2.1: Time-extended Graph
• Definition 4.1
• Definition 4.2
• Proposition 4.3
• Lemma 4.4
• Proposition 4.5
• Remark 4.6
• Remark 5.1
• Remark 5.2
• Remark 5.3