36 research outputs found
Guarding a Non-Maneuverable Translating Line with an Attached Defender
In this paper we consider a target-guarding differential game where the
defender must protect a linearly translating line-segment by intercepting an
attacker who tries to reach it. In contrast to common target-guarding problems,
we assume that the defender is attached to the target and moves along with it.
This assumption affects the defenders' maximum speed in inertial frame, which
depends on the target's direction of motion. Zero-sum differential game of
degree for both the attacker-win and defender-win scenarios are studied, where
the payoff is defined to be the distance between the two agents at the time of
game termination. We derive the equilibrium strategies and the Value function
by leveraging the solution for the infinite-length target scenario. The
zero-level set of this Value function provides the barrier surface that divides
the state space into defender-win and attacker-win regions. We present
simulation results to demonstrate the theoretical results.Comment: 8 pages, 8 figures. arXiv admin note: text overlap with
arXiv:2207.0409
Dynamic network analysis of a target defense differential game with limited observations
In this paper, we study a Target-Attacker-Defender (TAD) differential game
involving one attacker, one target and multiple defenders. We consider two
variations where (a) the attacker and the target have unlimited observation
range and the defenders are visibility constrained (b) only the attacker has
unlimited observation range and the remaining players are visibility
constrained. We model the players' interactions as a dynamic game with
asymmetric information. Here, the visibility constraints of the players induce
a visibility network which encapsulates the visibility information during the
evolution of the game. Based on this observation, we introduce network adapted
feedback or implementable strategies for visibility constrained players. Using
inverse game theory approach we obtain network adapted feedback Nash
equilibrium strategies. We introduce a consistency criterion for selecting a
subset (or refinement) of network adapted feedback Nash strategies, and provide
an optimization based approach for computing them. Finally, we illustrate our
results with numerical experiments.Comment: 8 figure
The Barrier Surface in the Cooperative Football Differential Game
This paper considers the blocking or football pursuit-evasion differential
game. Two pursuers cooperate and try to capture the ball carrying evader as far
as possible from the goal line. The evader wishes to be as close as possible to
the goal line at the time of capture and, if possible, reach the line. In this
paper the solution of the game of kind is provided: The Barrier surface that
partitions the state space into two winning sets, one for the pursuer team and
one for the evader, is constructed. Under optimal play, the winning team is
determined by evaluating the associated Barrier function.Comment: 5 pages, 1 figur
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
Air Force Institute of Technology Research Report 2020
This Research Report presents the FY20 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs). Interested individuals may discuss ideas for new research collaborations, potential CRADAs, or research proposals with individual faculty using the contact information in this document
Satellite proximate interception vector guidance based on differential games
This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire (CW) equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exo-atmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations. Keywords: Differential games, Saddle solution, Satellite interception, Time-to-go estimation, Zero effort miss trajector
Air Force Institute of Technology Research Report 2018
This Research Report presents the FY18 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs). Interested individuals may discuss ideas for new research collaborations, potential CRADAs, or research proposals with individual faculty using the contact information in this document
Contributions To Pursuit-Evasion Game Theory.
This dissertation studies adversarial conflicts among a group of agents moving in the plane, possibly among obstacles, where some agents are pursuers and others are evaders. The goal of the pursuers is to capture the evaders, where capture requires a pursuer to be either co-located with an evader, or in close proximity. The goal of the evaders is to avoid capture. These scenarios, where different groups compete to accomplish conflicting goals, are referred to as pursuit-evasion games, and the agents are called players.
Games featuring one pursuer and one evader are analyzed using dominance, where a point in the plane is said to be dominated by a player if that player is able to reach the point before the opposing players, regardless of the opposing players' actions. Two generalizations of the Apollonius circle are provided. One solves games with environments containing obstacles, and the other provides an alternative solution method for the Homicidal Chauffeur game. Optimal pursuit and evasion strategies based on dominance are provided.
One benefit of dominance analysis is that it extends to games with many players. Two foundational games are studied; one features multiple pursuers against a single evader, and the other features a single pursuer against multiple evaders. Both are solved using dominance through a reduction to single pursuer, single evader games. Another game featuring competing teams of pursuers is introduced, where an evader cooperates with friendly pursuers to rendezvous before being captured by adversaries.
Next, the assumption of complete and perfect information is relaxed, and uncertainties in player speeds, player positions, obstacle locations, and cost functions are studied. The sensitivity of the dominance boundary to perturbations in parameters is provided, and probabilistic dominance is introduced. The effect of information is studied by comparing solutions of games with perfect information to games with uncertainty. Finally, a pursuit law is developed that requires minimal information and highlights a limitation of dominance regions.
These contributions extend pursuit-evasion game theory to a number of games that have not previously been solved, and in some cases, the solutions presented are more amenable to implementation than previous methods.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120650/1/dwoyler_1.pd