Active Target Defense Differential Game with a Fast Defender

This paper addresses the active target defense differential game where an Attacker missile pursues a Target aircraft. A Defender missile is fired by the Target's wingman in order to intercept the Attacker before it reaches the aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the distance between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while the Attacker tries to minimize said distance. The results shown here extend previous work. We consider here the case where the Defender is faster than the Attacker. The solution to this differential game provides optimal heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker and it also provides the optimal heading angle for the Attacker to minimize the said distance.Comment: 9 pages, 8 figures. A shorter version of this paper will be presented at the 2015 American Control Conferenc

Escape Regions of the Active Target Defense Differential Game

The active target defense differential game is addressed in this paper. In this differential game an Attacker missile pursues a Target aircraft. The aircraft is however aided by a Defender missile launched by, say, the wingman, to intercept the Attacker before it reaches the Target aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the separation between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while the Attacker simultaneously tries to minimize said distance. This paper focuses on characterizing the set of coordinates such that if the Target's initial position belong to this set then its survival is guaranteed if both the Target and the Defender follow their optimal strategies. Such optimal strategies are presented in this paper as well.Comment: 19 pages, 9 figures. arXiv admin note: text overlap with arXiv:1502.0274

Two-Player Reconnaissance Game with Half-Planar Target and Retreat Regions

This paper is concerned with a variation of a pursuit-evasion game called the Reconnaissance game, in which an Intruder attempts to approach a territory of interest (target region) and return to a safe zone (retreat region) in the presence of a faster Defender. The target and retreat regions are taken to be disjoint closed half-planes. The objective of the Intruder is two-fold: 1) minimize the distance between her position and the target region and 2) escape to the retreat region before being captured by the Defender. The Defender, on the other hand, strives to maximize the same distance and, if possible, capture the Intruder outside the retreat region. The game is decomposed into a series of two subgames: a Target game and an Escape game. A closed-form solution to each subgame, including the Value function and state-feedback saddle-point strategies, is derived separately. Furthermore, winning regions and barrier surfaces are constructed analytically. Numerical simulation results are presented to showcase the efficacy of the proposed solutions

Nonlinear Model Predictive Control Framework For Cooperative Three-Agent Target Defense Game

This paper presents cooperative target defense guidance strategies using nonlinear model predictive control (NMPC) framework for a target-attacker-defender (TAD) game. The TAD game consists of an attacker and a cooperative target-defender pair. The attacker's objective is to capture the target, whereas the target-defender team acts together such that the defender can intercept the attacker and ensure target survival. We assume that the cooperative target-defender pair do not have perfect knowledge of the attacker states, and hence the states are estimated using an Extended Kalman Filter (EKF). The capture analysis based on the Apollonius circles is performed to identify the target survival regions. The efficacy of the NMPC-based solution is evaluated through extensive numerical simulations. The results show that the NMPC-based solution offers robustness to the different unknown attacker models and has better performance than CLOS and A-CLOS based strategies.Comment: 16 page

An Analytic Study of Pursuit Strategies

The Two-on-One pursuit-evasion differential game is revisited where the holonomic players have equal speed, and the two pursuers are endowed with a circular capture range ℓ \u3e 0. Then, the case where the pursuers\u27 capture ranges are unequal, ℓ1 \u3e ℓ2 ≥ 0, is analyzed. In both cases, the state space region where capture is guaranteed is delineated and the optimal feedback strategies are synthesized. Next, pure pursuit is considered whereupon the terminal separation between a pursuer and an equal-speed evader less than the pursuer\u27s capture range ℓ \u3e 0. The case with two pursuers employing pure pursuit is considered, and the conditions for capturability are presented. The pure pursuit strategy is applied to a target-defense scenario and conditions are given that determine if capture of the attacker before he reaches the target is possible. Lastly, three-on-one pursuit-evasion is considered where the three pursuers are initially positioned in a fully symmetric configuration. The evader, situated at the circumcenter of the three pursuers, is slower than the pursuers. We analyze collision course and pure pursuit guidance and provide evidence that conventional strategy for “optimal” evasive maneuver is incorrect

Coordinated Defense Allocation in Reach-Avoid Scenarios with Efficient Online Optimization

In this paper, we present a dual-layer online optimization strategy for defender robots operating in multiplayer reach-avoid games within general convex environments. Our goal is to intercept as many attacker robots as possible without prior knowledge of their strategies. To balance optimality and efficiency, our approach alternates between coordinating defender coalitions against individual attackers and allocating coalitions to attackers based on predicted single-attack coordination outcomes. We develop an online convex programming technique for single-attack defense coordination, which not only allows adaptability to joint states but also identifies the maximal region of initial joint states that guarantees successful attack interception. Our defense allocation algorithm utilizes a hierarchical iterative method to approximate integer linear programs with a monotonicity constraint, reducing computational burden while ensuring enhanced defense performance over time. Extensive simulations conducted in 2D and 3D environments validate the efficacy of our approach in comparison to state-of-the-art approaches, and show its applicability in wheeled mobile robots and quadcopters