Simulating differential games with improved fidelity to better inform cooperative & adversarial two vehicle UAV flight

Abstract

Automatic determination of an areal vehicle's strategy rests on accurate simulation and forecasting to inform control decisions. As system dynamics affect the outcomes, when two or more vehicles interact finding the best strategy to take may be considered a differential game. While traditionally modelled using ideal kinematics, the effect on, and the variation of, the optimal strategy based on simulating realistic dynamics is investigated. A derivation for the optimal strategies of the players in ‘regular’ regions of the state space is completed. Two simulators were developed to compare game terminal results to the theoretical predictions. A MATLAB simulator with ideal player kinematics was the first simulator formed. Then, a high-fidelity simulator, using Microsoft's AirSim project was implemented. This involved configuring AirSim to run using software commands only, and extending the functionality to allow for the simulation of two separately-controlled drones. A trivial differential game with two agile players, termed Pedestrian Tag (PT), was used to identify the accuracy of time-to-capture predictions. The MATLAB simulator was found to match the model prediction, whereas the AirSim simulator required more gameplay time than predicted to achieve capture. For a Homicidal Chauffeur (HC) game, the MATLAB simulator results were consistent with the theoretical predictions. However, multiple outcomes of trials contrasted the predicted terminal results for the high-fidelity simulator. The results indicate that modelling the players to have ideal kinematics does not correctly predict the outcome of a pursuit-evasion game with full/realistic dynamics. Although some deviation from the model assumptions was introduced due to implementation constraints, the primary factor was concluded to be the realistic velocities of the drone agents due to unaccounted dynamics such as inertia and drag. Future research topics prompted by this work include applying the simulation to more differential games, and comparing against player strategies developed from other methods.