Virtual Target Selection for a Multiple-Pursuer Multiple-Evader Scenario

This paper considers an M-pursuer N-evader scenario involving virtual targets. The virtual targets serve as an intermediary target for the pursuers, allowing the pursuers to delay their final assignment to the evaders. However, upon reaching the virtual target, the pursuers must decide which evader to capture. It is assumed that there are more pursuers than evaders and that the pursuers are faster than the evaders. The objective is two-part: first, assign each pursuer to a virtual target and evader such that the pursuer team's energy is minimized, and second, choose the virtual targets' locations for this minimization problem. The approach taken is to consider the Apollonius geometry between each pursuer's virtual target location and each evader. Using the constructed Apollonius circles, the pursuer's travel distance and maneuver at a virtual target are obtained. These metrics serve as a gauge for the total energy required to capture a particular evader and are used to solve the joint virtual target selection and pursuer-evader assignment problem. This paper provides a mathematical definition of this problem, the solution approach taken, and an example.Comment: AIAA SciTech 2024 Preprin

Surveillance of a Faster Fixed-Course Target

The maximum surveillance of a target which is holding course is considered, wherein an observer vehicle aims to maximize the time that a faster target remains within a fixed-range of the observer. This entails two coupled phases: an approach phase and observation phase. In the approach phase, the observer strives to make contact with the faster target, such that in the observation phase, the observer is able to maximize the time where the target remains within range. Using Pontryagin's Minimum Principle, the optimal control laws for the observer are found in closed-form. Example scenarios highlight various aspects of the engagement.Comment: 12 pages, 8 figure

Noise Aware Path Planning and Power Management of Hybrid Fuel UAVs

Hybrid fuel Unmanned Aerial Vehicles (UAV), through their combination of multiple energy sources, offer several advantages over the standard single fuel source configuration, the primary one being increased range and efficiency. Multiple power or fuel sources also allow the distinct pitfalls of each source to be mitigated while exploiting the advantages within the mission or path planning. We consider here a UAV equipped with a combustion engine-generator and battery pack as energy sources. We consider the path planning and power-management of this platform in a noise-aware manner. To solve the path planning problem, we first present the Mixed Integer Linear Program (MILP) formulation of the problem. We then present and analyze a label-correcting algorithm, for which a pseudo-polynomial running time is proven. Results of extensive numerical testing are presented which analyze the performance and scalability of the labeling algorithm for various graph structures, problem parameters, and search heuristics. It is shown that the algorithm can solve instances on graphs as large as twenty thousand nodes in only a few seconds.Comment: 11 pages, 12 figure

Behavioral Problems In The Utilization Of New Technology To Control Caries: Patients And Provider Readiness And Motivation

New research developments frequently are neither adopted by providers nor utilized by patients. This dual problem of impacting the behaviors of providers and patients presents a challenge. This paper will present behavioral theories and technologies that can be utilized to impact both provider and patient behaviors

Aircraft Defense Differential Game with Non-Zero Capture Radius

An aircraft defense differential game is analyzed where a Target aircraft and a Defender missile team up to defeat an Attacker missile. The Attacker pursues the (slower) Target which evades the Attacker with the help of the Defender, which is endowed with a non-zero capture radius. The Target and the Defender cooperate in a way that the Defender intercepts the Attacker before the latter reaches the Target. The payoff functional is the distance between the Target and the Attacker at the interception time which the Attacker strives to minimize and the Target/Defender team strives to maximize. The work in this paper generalizes existing results to consider a non-zero capture radius as opposed to the limiting case of point capture. Abstract © IFA

A Geometric Approach for the Cooperative Two-Pursuer One-Evader Differential Game

This paper revisits Isaacs’ two cutters and fugitive ship differential game where two faster pursuers cooperate to capture a slower evader in minimum time; the three players have simple motion. The evader, knowing that is being pursued by two cooperative pursuers, tries to maximize the capture time. A solution of this differential game is determined based on the Hamiltonian formulation and based on the geometric properties of the game. Additionally, this solution is verified by analyzing the properties of the obtained candidate Value function