John-Paul Clarke

Yutian Pang, Andrew Paul Kendall, John-Paul Clarke

Mission-critical operations of highly maneuverable Remotely Piloted Aircraft Systems (RPAS) require reliable communication to ensure safe integration into existing airspace. Understanding system-level performance under stochastic communication conditions is essential for estimating mission success and assessing operational risks. This study quantifies the impact of communication latency and complete signal loss on the mission completion performance of a highly maneuverable RPAS. The mission is defined as a static waypoint tracking task in three-dimensional airspace. We first derive mathematical formulations for key reliability metrics within the Required Communication Performance (RCP) framework. These stochastic communication factors, including latency and availability, are then incorporated into flight control simulations to evaluate system behavior. Extensive multiprocessing Monte Carlo simulations are conducted using high-performance computing to generate mission success rate and mission completion time envelopes. Results show significant degradation in flight performance as communication latency increases or availability decreases, which directly reduces the system stability margin. To better characterize this relationship, we introduce a new reliability metric, communicability, which integrates three key RCP metrics and provides insight into the maximum tolerable latency for flight control. The proposed framework informs RPAS design by revealing trade-offs between communication capability and flight control performance. The code used in this study is publicly available at this \href{https://github.com/YutianPangASU/comm-dynamics}{repository}.

Vlad Popescu, John-Paul B. Clarke, Karen M. Feigh et al.

A method to quantify the probabilistic controller taskload inherent to maintaining aircraft adherence to 4-D trajectories within flow corridors is presented. An Ornstein-Uhlenbeck model of the aircraft motion and a Poisson model of the flow scheduling are introduced along with reasonable numerical values of the model parameters. Analytic expressions are derived for the taskload probability density functions for basic functional elements of the flow structure. Monte Carlo simulations are performed for these basic functional elements and the controller taskload probabilities are exhibited.

Mirmojtaba Gharibi, John-Paul Clarke

We provide a general and malleable heuristic for the air conflict resolution problem. This heuristic is based on a new neighborhood structure for searching the solution space of trajectories and flight-levels. Using unsupervised learning, the core idea of our heuristic is to cluster the conflict points and disperse them in various flight levels. Our first algorithm is called Cluster & Disperse and in each iteration it assigns the most problematic flights in each cluster to another flight-level. In effect, we shuffle them between the flight-levels until we achieve a well-balanced configuration. The Cluster & Disperse algorithm then uses any horizontal plane conflict resolution algorithm as a subroutine to solve these well-balanced instances. Nevertheless, we develop a novel algorithm for the horizontal plane based on a similar idea. That is we cluster and disperse the conflict points spatially in the same flight level using the gradient descent and a social force. We use a novel maneuver making flights travel on an arc instead of a straight path which is based on the aviation routine of the Radius to Fix legs. Our algorithms can handle a high density of flights within a reasonable computation time. We put their performance in context with some notable algorithms from the literature. Being a general framework, a particular strength of the Cluster & Disperse is its malleability in allowing various constraints regarding the aircraft or the environment to be integrated with ease. This is in contrast to the models for instance based on mixed integer programming.

Fanruiqi Zeng, Zaiwei Chen, John-Paul Clarke et al.

Unmanned aerial vehicles or drones are becoming increasingly popular due to their low cost and high mobility. In this paper we address the routing and coordination of a drone-truck pairing where the drone travels to multiple locations to perform specified observation tasks and rendezvous periodically with the truck to swap its batteries. We refer to this as the Nested-Vehicle Routing Problem (Nested-VRP) and develop a Mixed Integer Quadratically Constrained Programming (MIQCP) formulation with critical operational constraints, including drone battery capacity and synchronization of both vehicles during scheduled rendezvous. An enhancement of the MIQCP model for the Nested-VRP is achieved by deriving the equivalent Mixed Integer Linear Programming (MILP) formulation as well as leveraging lifting and Reformulation-Linearization techniques to strengthen the subtour elimination constraints of the drone. Given the NP-hard nature of the Nested-VRP, we further propose an efficient neighborhood search (NS) heuristic where we generate and improve on a good initial solution by iteratively solving the Nested-VRP on a local scale. We provide comparisons of both the exact approaches based on MIQCP or its enhanced formulations and NS heuristic methods with a relaxation lower bound in the cases of small and large problem sizes, and present the results of a computational study to show the effectiveness of the MIQCP model and its variants as well as the efficiency of the NS heuristic, including for a real-life instance with 631 locations. We envision that this framework will facilitate the planning and operations of combined drone-truck missions.

Zaiwei Chen, Sheng Zhang, Thinh T. Doan et al.

Motivated by applications in reinforcement learning (RL), we study a nonlinear stochastic approximation (SA) algorithm under Markovian noise, and establish its finite-sample convergence bounds under various stepsizes. Specifically, we show that when using constant stepsize (i.e., $α_k\equiv α$), the algorithm achieves exponential fast convergence to a neighborhood (with radius $O(α\log(1/α))$) around the desired limit point. When using diminishing stepsizes with appropriate decay rate, the algorithm converges with rate $O(\log(k)/k)$. Our proof is based on Lyapunov drift arguments, and to handle the Markovian noise, we exploit the fast mixing of the underlying Markov chain. To demonstrate the generality of our theoretical results on Markovian SA, we use it to derive the finite-sample bounds of the popular $Q$-learning with linear function approximation algorithm, under a condition on the behavior policy. Importantly, we do not need to make the assumption that the samples are i.i.d., and do not require an artificial projection step in the algorithm to maintain the boundedness of the iterates. Numerical simulations corroborate our theoretical results.

Sang Hyun Kim, Eric Feron, John-Paul Clarke et al.

Passengers' experience is becoming a key metric to evaluate the air transportation system's performance. Efficient and robust tools to handle airport operations are needed along with a better understanding of passengers' interests and concerns. Among various airport operations, this paper studies airport gate scheduling for improved passengers' experience. Three objectives accounting for passengers, aircraft, and operation are presented. Trade-offs between these objectives are analyzed, and a balancing objective function is proposed. The results show that the balanced objective can improve the efficiency of traffic flow in passenger terminals and on ramps, as well as the robustness of gate operations.