Date of Award

3-2025

Document Type

Thesis

Degree Name

Master of Science in Electrical Engineering

Department

Department of Electrical and Computer Engineering

First Advisor

Meir Pachter, PhD

Abstract

This paper is concerned with a co-planar pursuit-evasion scenario where two Pursuers (P) are after an Evader (E). The players are holonomic/can turn on a dime and their speeds, VP and VE, are constant, but the evader is faster than the pursuers, that is, the speed ratio parameter μ =  VE/VP > 1. The Pursuers are endowed with a circular capture disc whose radius l > 0. A differential game (DG) with three states and one parameter is addressed through geometric and analytical methods where a partial solution is outlined and visualized. The game is split into two phases, non-contact and contact. Where inside the non-contact phase the optimal control feedback strategy found for all players is collision course (CC). Then when simulated some states are biased for P where E is captured early along the CC trajectories. Upon E’s contact with P’s capture disc, the game continues to find an optimal feedback strategy to include E circumnavigating the contacted capture disc until entrenchment by both Pursuers. The optimal control for the contacted P is assumed pure-pursuit (PP), and the other P control is solved sub-optimally in closed form, then optimally using Isaac’s method, resulting in retrograde dynamics driven by a series of nonlinear PDE’s. The optimal opposing P control as expected results in faster capture times, compared against the sub-optimal control. When implemented together both controls can be combined using a switching method in simulation that is primary affected with a margin-of-error (MoE) variable, requiring some feedback strategy adaptations. The results sustain Lozano’s conclusions in [1] that a control switching strategy is required for the complete solution in this 2P1E (Two-Pursuers One- Evader) DG.

AFIT Designator

AFIT-ENG-MS-25-M-033

Comments

An embargo was observed for posting this thesis on AFIT Scholar. 
Approved for public release, distribution unlimited. PA case number 88ABW-2026-0460.

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