arXiv subjects
Publications and source records attributed to Eloy Garcia.
This work derives two basic engagement zone models, describing regions of potential risk or capture for a mobile vehicle by a pursuer. The pursuer is modeled as having turn-constraints rather than simple motion. Turn-only (C-Paths) and turn-straight (CS-Paths) paths are considered for the pursuer of limited range. Following the derivation, a simulation of a vehicle avoiding the pursuer's engagement zone is provided.
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.
We consider a perimeter defense problem in a planar conical environment in which a single vehicle, having a finite capture radius, aims to defend a concentric perimeter from mobile intruders. The intruders are arbitrarily released at the circumference of the environment and they move radially toward the perimeter with fixed speed. We present a competitive analysis approach to this problem by measuring the performance of multiple online algorithms for the vehicle against arbitrary inputs, relative to an optimal offline algorithm that has information about entire input sequence in advance. In particular, we establish two necessary conditions on the parameter space to guarantee (i) finite competitiveness of any algorithm and (ii) a competitive ratio of at least 2 for any algorithm. We then design and analyze three online algorithms and characterize parameter regimes in which they have finite competitive ratios. Specifically, our first two algorithms are provably 1, and 2-competitive, respectively, whereas our third algorithm exhibits different competitive ratios in different regimes of problem parameters. Finally, we provide a numerical plot in the parameter space to reveal additional insights into the relative performance of our algorithms.
A conflict between rational and autonomous agents is considered. The paper addresses a differential game of protecting a target in the 3-D space. This problem highlights the strong correlation between the highly dynamic scenario, the uncertainty on the behavior of the adversary, and the online and robust computation of state-feedback strategies which guarantee the required level of performance of each player. This work significantly expands previous results around this problem by providing the players' state-feedback saddle-point strategies. Additionally, the continuously differentiable Value function of the multi-agent differential game is obtained and it is shown to be the solution of the Hamilton-Jacobi-Isaacs equation. Finally, the Barrier surface is explicitly obtained and illustrative examples highlight the robustness properties and the guarantees provided by the saddle-point strategies obtained in this paper.
We consider a problem of cooperative evasion between a single pursuer and multiple evaders in which the evaders are constrained to move in the positive Y direction. The evaders are slower than the vehicle and can choose their speeds from a bounded interval. The pursuer aims to intercept all evaders in a given sequence by executing a Manhattan pursuit strategy of moving parallel to the X axis, followed by moving parallel to the Y axis. The aim of the evaders is to cooperatively pick their individual speeds so that the total time to intercept all evaders is maximized. We first obtain conditions under which evaders should cooperate in order to maximize the total time to intercept as opposed to each moving greedily to optimize its own intercept time. Then, we propose and analyze an algorithm that assigns evasive strategies to the evaders in two iterations as opposed to performing an exponential search over the choice of evader speeds. We also characterize a fundamental limit on the total time taken by the pursuer to capture all evaders when the number of evaders is large. Finally, we provide numerical comparisons against random sampling heuristics.
This paper considers autonomous flight formation of fixed-wing air vehicles. Due to several issues such as limitations on communication bandwidth and low observability requirements, an asynchronous control and communication approach is designed in order to reduce the number of updates between the vehicles. With the implementation of an event-triggered controller, it is possible to obtain a more efficient communication scheme while also achieving the convergence properties of the desired formation.
An operational relevant conflict between teams of autonomous vehicles in the Beyond Visual Range domain is addressed in this paper. Optimal strategies are designed in order for a team of air interceptors to protect a high value asset and block the attacking team at a safe distance from such asset. The attacking agents take specific roles of leader and wingman and also devise their own optimal strategies in order to launch an attack as close as possible from the asset. The problem is formulated as a zero-sum differential game between players with different speed over two stages: the attack and the retreat stages. For each stage the state-feedback optimal strategies of each player are derived in analytical form.
The event-triggered control problem over lossy communication networks is addressed in this paper. Although packet dropouts have been considered in the implementation of event-triggered controllers, the assumption of protocols that employ acknowledgement messages persists. This paper provides an approach that relaxes such assumption. An event-based controller is implemented at the sensor node of the networked and uncertain system and it transmits feedback measurements to the controller node at asynchronous time instants. The transmitted packets of information are subject to dropouts by the lossy network. We show that the uncertain system can be asymptotically stabilized, that a positive minimum inter-event time exists, and that the proposed approach does not require acknowledgement messages.
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.
Pursuit and evasion conflicts represent challenging problems with important applications in aerospace and robotics. In pursuit-evasion problems, synthesis of intelligent actions must consider the adversary's potential strategies. Differential game theory provides an adequate framework to analyze possible outcomes of the conflict without assuming particular behaviors by the opponent. This article presents an organized introduction of pursuit-evasion differential games with an overview of recent advances in the area. First, a summary of the seminal work is outlined, highlighting important contributions. Next, more recent results are described by employing a classification based on the number of players: one-pursuer-one-evader, N-pursuers-one-evader, one-pursuer-M-evaders, and N-pursuer-M-evader games. In each scenario, a brief summary of the literature is presented. Finally, two representative pursuit-evasion differential games are studied in detail: the two-cutters and fugitive ship differential game and the active target defense differential game. These problems provide two important applications and, more importantly, they give great insight into the realization of cooperation between friendly agents in order to form a team and defeat the adversary.
In the Target-Attacker-Defender (TAD) differential game, an Attacker missile strives to capture a Target aircraft. The Target tries to escape the Attacker and is aided by a Defender missile which aims at intercepting the Attacker before the latter manages to close in on the Target. The conflict between these intelligent adversaries has been suitably modeled as a zero-sum differential game. Optimal strategies have been synthesized covering the region of the state space where the Target/Defender team is able to win the game. However, the Game of Degree in the Attacker's region of win has not been fully addressed. Preliminary attempts at designing the players' strategies have not been proven to be optimal in the differential game sense. The main results of the paper present the optimal strategies of the Game of Degree in the Attacker's winning region of the state space. It is proven that the obtained strategies provide the saddle-point solution of the game; the Value function is obtained and it is shown to be continuous and continuously differentiable. It is also demonstrated that it is the solution of the Hamilton-Jacobi-Isaacs (HJI) equation. Finally, the obtained strategies are compared to recent results addressing the TAD differential game in [22]. It is shown by counterexample that the strategies proposed in [22] are not optimal. The unique regular solution of this differential game that actually provides a semipermeable Barrier surface is synthesized and verified in this paper.
In this paper an N-pursuer vs. M-evader team conflict is studied. The differential game of border defense is addressed and we focus on the game of degree in the region of the state space where the pursuers are able to win. This work extends classical differential game theory to simultaneously address weapon assignments and multi-player pursuit-evasion scenarios. Saddle-point strategies that provide guaranteed performance for each team regardless of the actual strategies implemented by the opponent are devised. The players' optimal strategies require the co-design of cooperative optimal assignments and optimal guidance laws. A representative measure of performance is proposed and the Value function of the game is obtained. It is shown that the Value function is continuous, continuously differentiable, and that it satisfies the Hamilton-Jacobi-Isaacs equation - the curse of dimensionality is overcome and the optimal strategies are obtained. The cases of N=M and N>M are considered. In the latter case, cooperative guidance strategies are also developed in order for the pursuers to exploit their numerical advantage. This work provides a foundation to formally analyze complex and high-dimensional conflicts between teams of N pursuers and M evaders by means of differential game theory.
This article provides an introduction to event-triggered coordination for multi-agent average consensus. We provide a comprehensive account of the motivations behind the use of event-triggered strategies for consensus, the methods for algorithm synthesis, the technical challenges involved in establishing desirable properties of the resulting implementations, and their applications in distributed control. We pay special attention to the assumptions on the capabilities of the network agents and the resulting features of the algorithm execution, including the interconnection topology, the evaluation of triggers, and the role of imperfect information. The issues raised in our discussion transcend the specific consensus problem and are indeed characteristic of cooperative algorithms for networked systems that solve other coordination tasks. As our discussion progresses, we make these connections clear, highlighting general challenges and tools to address them widespread in the event-triggered control of networked systems.
This paper summarizes important results useful for controller design of multi-input multi-output systems. The main goal is to characterize the stabilizing controllers that provide a desired response.
This article studies distributed event-triggered consensus over unreliable communication channels. Communication is unreliable in the sense that the broadcast channel from one agent to its neighbors can drop the event-triggered packets of information, where the transmitting agent is unaware that the packet was not received and the receiving agents have no knowledge of the transmitted packet. Additionally, packets that successfully arrive at their destination may suffer from time-varying communication delays. In this paper, we consider directed graphs, and we also relax the consistency on the packet dropouts and the delays. Relaxing consistency means that the delays and dropouts for a packet broadcast by one agent can be different for each receiving node. We show that even under this challenging scenario, agents can reach consensus asymptotically while reducing transmissions of measurements based on the proposed event-triggered consensus protocol. In addition, positive inter-event times are obtained which guarantee that Zeno behavior does not occur.
The Dubins interval problem aims to find the shortest path of bounded curvature between two targets such that the departure angle from the first target and the arrival angle at the second target are constrained to two respective intervals. We propose a new and a simple algorithm to this problem based on the minimum principle of Pontryagin.
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.
Multi-agent systems cooperation to achieve global goals is usually limited by sensing, actuation, and communication issues. At the local level, continuous measurement and actuation is only approximated by the use of digital mechanisms that measure and process information in order to compute and update new control input values at discrete time instants. Interaction with other agents or subsystems takes place, in general, through a digital communication channel with limited bandwidth where transmission of continuous-time signals is not possible. Additionally, communication channels may be subject to other imperfections such as time-varying delays. This paper considers the problem of consensus (or synchronization of state trajectories) of multi-agent systems that are described by general linear dynamics and are connected using undirected graphs. An event-triggered consensus protocol is proposed, where each agent implements discretized and decoupled models of the states of its neighbors. This approach not only avoids the need for continuous communication between agents but also provides a decentralized method for transmission of information in the presence of time-varying communication delays where each agent decides its own broadcasting time instants based only on local information. This method gives more flexibility for scheduling information broadcasting compared to periodic and sampled-data implementations. The use of discretized models by each agent allows for a periodic event-triggered strategy where continuous actuation and continuous measurement of the states are not necessary.