Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers
01 Dec 2011-pp 4835-4840
TL;DR: This paper studies a game of multiple pursuers cooperating to capture a single evader in a bounded, convex, polytope in the plane, and presents a decentralized control scheme based on the Voronoi partion of the game domain, where the pursuers jointly minimize the area of the evader's Vor onoi cell.
Abstract: Pursuit-evasion games are an important problem in robotics and control, but games with many players are difficult to analyze and solve. This paper studies a game of multiple pursuers cooperating to capture a single evader in a bounded, convex, polytope in the plane. We present a decentralized control scheme based on the Voronoi partion of the game domain, where the pursuers jointly minimize the area of the evader's Voronoi cell. We prove that capturing the evader is guaranteed under this scheme regardless of the evader's actions, and show simulation results demonstrating the pursuit strategy.
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Posted Content•
TL;DR: This paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies which are adaptive, distributed, asynchronous, and verifiably correct.
Abstract: This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.
2,198 citations
TL;DR: This work presents a decentralized, real-time algorithm for cooperative pursuit of a single evader by multiple pursuers in bounded, simply-connected planar domains based on minimizing the area of the generalized Voronoi partition of the evader.
127 citations
Cites background from "Guaranteed decentralized pursuit-ev..."
...By Lemma 4 and Lemma 5 in [17], one of the following conditions must be true at any given time:...
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...Convex domain simulations can be found in [17]....
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...The directional derivatives can be computed by the following lemma, whose proof can be found in [17]....
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...Some elements of the results for convex domains and equal speeds were first presented in [17]....
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01 Apr 2017
TL;DR: A decentralized version of this policy applicable in two-dimensional (2-D) and 3-D environments is presented, and it is shown in multiple simulations that it outperforms other decentralized multipursuer heuristics.
Abstract: We propose a distributed algorithm for the cooperative pursuit of multiple evaders using multiple pursuers in a bounded convex environment. The algorithm is suitable for intercepting rogue drones in protected airspace, among other applications. The pursuers do not know the evaders' policy, but by using a global “area-minimization” strategy based on a Voronoi tessellation of the environment, we guarantee the capture of all evaders in finite time. We present a decentralized version of this policy applicable in two-dimensional (2-D) and 3-D environments, and show in multiple simulations that it outperforms other decentralized multipursuer heuristics. Experiments with both autonomous and human-controlled robots were conducted to demonstrate the practicality of the approach. Specifically, human-controlled evaders are not able to avoid capture with the algorithm.
92 citations
Cites background or methods from "Guaranteed decentralized pursuit-ev..."
...Our pursuit strategy is inspired by the area-minimization policy in [1]–[3] for pursuers chasing one evader in a 2D environment....
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...First, we extend the results of [1]–[3] to environments of arbitrary dimension, making it practical for aerial robots in 3D environments....
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...propose an “area-minimization” policy that reduces the safe-reachable area of the evader to guarantee capture in the plane [1]–[3]....
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TL;DR: This paper provides a complete, closed form solution of the active target defense differential game; synthesize closed-loop state feedback optimal strategies for the agents and obtain the Value function of the game.
Abstract: This paper is concerned with a scenario of active target defense modeled as a zero-sum differential game. The differential game theory as developed by Isaacs provides the correct framework for the analysis of pursuit-evasion conflicts and the design of optimal strategies for the players involved in the game. This paper considers an Attacker missile pursuing a Target aircraft protected by a Defender missile which aims at intercepting the Attacker before the latter reaches the Target aircraft. A differential game is formulated where the two opposing players/teams try to minimize/maximize the distance between the Target and the Attacker at the time of interception of the Attacker by the Defender and such time indicates the termination of the game. The Attacker aims to minimize the terminal distance between itself and the Target at the moment of its interception by the Defender. The opposing player/team consists of two cooperating agents: The Target and the Defender. These two agents cooperate in order to accomplish the two objectives: Guarantee interception of the Attacker by the Defender and maximize the terminal Target-Attacker separation. In this paper, we provide a complete, closed form solution of the active target defense differential game; we synthesize closed-loop state feedback optimal strategies for the agents and obtain the Value function of the game. We characterize the Target's escape set and show that the Value function is continuous and continuously differentiable over the Target's escape set, and that it satisfies the Hamilton–Jacobi–Isaacs equation everywhere in this set.
72 citations
Cites background from "Guaranteed decentralized pursuit-ev..."
...These scenarios are typically considered in the context of dynamic games [1] and [2]....
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TL;DR: The idea of Apollonius circle is used to develop an escape strategy for the high speed evader, resolving the shortfalls in the existing work and establishing the efficacy of the escape strategy using simulation results.
Abstract: In this paper, we address pursuit-evasion games of high speed evader involving multiple pursuers and a single evader with holonomic constraints in an open domain. The existing work on this problem discussed the required formation and capture strategy for a group of pursuers. However, the formulation has mathematical errors and has raised concerns over the validity of the developed capture strategy. This paper uses the idea of Apollonius circle to develop an escape strategy for the high speed evader, resolving the shortfalls in the existing work. The strategy is built on a concept of perfectly encircled formation and the conditions required to construct the same are presented. The escape strategy contains two steps. Firstly, the evader employs a strategy that forces a gap in the formation against all the admissible strategies of a group of pursuers. In the second step, it uses this gap to escape. The strategy considers both direct and indirect gaps in the formations. The indirect gap is encountered when a group of three or four pursuers is employed to capture. The efficacy of the escape strategy is established using simulation results.
70 citations
References
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Book•
01 Jan 1982
TL;DR: In this paper, the authors present a general formulation of non-cooperative finite games: N-Person nonzero-sum games, Pursuit-Evasion games, and Stackelberg Equilibria of infinite dynamic games.
Abstract: Preface to the classics edition Preface to the second edition 1. Introduction and motivation Part I: 2. Noncooperative Finite Games: two-person zero-aum 3. Noncooperative finite games: N-Person nonzero-sum 4. Static noncooperative Infinite Games Part II: 5. General Formulation of Infinite Dynamic Games 6. Nash and Saddle-Point Equilibria of Infinite Dynamic Games 7. Stackelberg Equilibria of Infinite Dynamic Games 8. Pursuit-Evasion Games Appendix A: Mathematical Review Appendix B: Some notions of probability theory Appendix C: Fixed point theorems Bibliography Table: Corollaries, Definitions, Examples, Lemmas, Propositions, remarks and theorems Index.
4,471 citations
07 Aug 2002
TL;DR: In this paper, the authors describe decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks, which are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies.
Abstract: This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.
2,445 citations
Posted Content•
TL;DR: This paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies which are adaptive, distributed, asynchronous, and verifiably correct.
Abstract: This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.
2,198 citations
"Guaranteed decentralized pursuit-ev..." refers methods in this paper
...Voronoi decomposition has also been extensively used in distributed and decentralized control of multiple agents in surveillance and coverage tasks, where cooperative actions result from the influence of shared Voronoi boundaries [17]....
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TL;DR: An algorithm for computing the set of reachable states of a continuous dynamic game based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation.
Abstract: We describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation. While alternative techniques for computing the reachable set have been proposed, the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters. Because the time-dependent equation's solution is continuous and defined throughout the state space, methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions. A numerical implementation of our formulation is described and has been released on the web. Its correctness is verified through a two vehicle, three dimensional collision avoidance example for which an analytic solution is available.
1,107 citations
"Guaranteed decentralized pursuit-ev..." refers methods in this paper
...A large body of work based on this approach has since appeared, with solutions ranging from the method of characteristics [2], [3] to numerical solutions of related Hamilton-Jacobi equations [4], [5]....
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