J. Hespanha, H. J. Kim, and S. Sastry, "Multiple-agent probabilistic pursuit-evasion games," in In Proc. of the 38th Conf. on Decision and Contr, 1999, pp. 2432--2437.  Home/Search   Document Details and Download   Summary   Related Articles   Check

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J.P. Hespanha, H.J. Kim, and S.S. Sastry. Multiple-agent probabilistic pursuit-evasion games. In IEEE Int. Conf. on Decision and Control, pages 2432--2437, 1999.

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J. P. Hespanha, H. J. Kim and S. Sastry. Multiple-Agent Probabilistic Pursuit-Evasion Games, Proceedings of the 38th IEEE Conference of Decision and Control, 3, 2432-2437, 1999.

....E g [T # ] T # 1 , with # as in (6) Lemma 1 shows that for a pursuit policy which is persistent on the average, the probability of capturing the evaders in finite time is equal to one. Moreover, Lemma 1 gives a simple upper bound on the expected capture time. The following lemma (proved in [24]) gives a su#cient condition for a policy to be persistent on the average. Lemma 2: Let fnd t , be the set of all sequences of measurements of length t, associated with an evader not being found up to time t. A su#cient condition for a pursuit policy g to be persistent on the average with ....

J. Hespanha, J. Kim, and S. Sastry, "Multiple-agent probabilistic pursuit-evasion games," Tech. Rep., Dept. of EECS, University of California at Berkeley, March 1999.

....hand, most of the literature in pursuit evasion games, see e.g. 3] 4] 5] 6] 7] assumes worst case motion for the evaders and an accurate map of the environment. In practice, this results in overly conservative pursuit policies applied to inaccurate maps built from noisy measurements. In [8] the pursuit evasion game and map building problems are combined in a single probabilistic framework. The basic scenario considers multiple pursuers trying to capture a single randomly moving evader. In [9] we extended the scenario to consider multiple evaders and proposed a simple vision based ....

.... as the random function g : g(Y t ) # u(t 1) u 1 (t 1) u np (t 1) 5) We measure the performance of a specific pursuit policy g by the expected capture time E g [T # ] # E[T # g = g] Since the dependence of E g [T # ] on the pursuit policy g is in general very complex [8], instead of finding the optimal policy that minimizes E g [T # ] we look for e#ciently computable sub optimal policies with good performance. To this end, we first introduce the notion of a persistent pursuit policy [8] and show that it guarantees a certain degree of success for the pursuers. ....

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J. Hespanha, J. Kim, and S. Sastry, "Multiple-agent probabilistic pursuit-evasion games," in Proc. of 38th IEEE Conf. on Decision and Control, 1999, vol. 3, pp. 2432--2437.

....of the environment. In practice, this results in overly conservative pursuit policies if applied to inaccurate maps built from noisy measurements. Figure 1: UAV UGV Pursuit Evasion Game Recently, the pursuit evasion game and map building problems have been combined in a probabilistic framework [5], which avoids the conservativeness in herent to the classical worst case approaches and takes into account inaccuracies in sensor information. The basic setup considers multiple pursuers trying to cap ture a single evader undergoing random motion. In [5] it is shown that, under certain ....

....combined in a probabilistic framework [5] which avoids the conservativeness in herent to the classical worst case approaches and takes into account inaccuracies in sensor information. The basic setup considers multiple pursuers trying to cap ture a single evader undergoing random motion. In [5] it is shown that, under certain assumptions, there exists a persistent pursuit policy that guarantees that the evader can be captured in finite time with proba bility one. In [11, 12] the basic scenario is extended to consider supervisory agents, such as a helicopter, that can estimate the ....

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J. Hespanha, H. Kim, and S. Sastry. Multiple-agent probabilistic pursuit-evasion games. In Proc. of 38th IEEE CDC, pages 2432-2437, Dec. 1999.

....any searching agent and gv(xu) vp(1 p)2n3(1 n)4, k, k2, ks and k4 being, respectively, the number of false positives, true negatives, false negatives, and true positives. In the simulations below, we use 5 p, d Z) 0,0) 5(0,0) 1 8p, with p [0,1 8] We adopt the algo rithms in [6] implementing at low computational cost the greedy control in both the cases of constrained and unconstrained motions. Figure 2 refers to the case when p = 1 20, ns = 3, and T = 30. The plot on the left side represents cost (3) kove 50, kc 10) as a function of the threshold. The cost is ....

J.P. Hespanha, H.J. Kim, and S. Sastry. Multiple-agent probabilistic pursuit-evasion games. In Proc. of the 38th Conf. on Decision and Contr., December 1999.

....[1] On the other hand, most of the PEG literature, see e.g. 5] considers worst case motion for the evaders and assumes an accurate map of the environment. In practice, this results in overly conservative pursuit policies if applied to inaccurate maps built from noisy measurements. In [2] we combined pursuit evasion games and map building in a single probabilistic framework which avoids the conservativeness inherent to the classical worst case approaches and takes into account inaccurate sensing. We also proved the existence of a persistent pursuit policy which guarantees to ....

....of an architecture for multi agent coordination and control. Section 4 presents the simulation and experimental results, and Section 5 concludes the paper. 2 Pursuit Evasion Scenario This section describes the theoretic foundations for the PEG scenario following the frameworks described in [2, 8], and a vision based detection algorithm [11] 2.1 Probabilistic Framework Consider a finite two dimensional environment X with n c cells that contain an unknown number of fixed obstacles. x p # X (x e # X ) is the set of cells occupied by the n p pursuers (n e evaders) For each t # ....

[Article contains additional citation context not shown here]

J. Hespanha, H.J. Kim, and S. Sastry. Multiple-agent probabilistic pursuit-evasion games. In Proc. of 38th IEEE CDC, pages 2432--2437, Dec. 1999.

....is adopted for theone s# 3 nonzero s#3 games# Exis#) #d of a Nas h equilibrium s# lutionis proven andthes implifications which make thes olution computationally feas ible us#ed linear programming (LP) are explained. This paper extends the probabilis#N approach to purs#x)d(3 as#) games foundin [10]. In this reference, the pur s#ers# team s# ill adopts a greedy policy that maximizes the probability of finding the evader at the next time ins#d nt, but the evaderis not actively avoiding to be captured. The paper is organizedas follows . In Section 2, the purs#rd NN as#2 n game is des#4 ....

J. P. Hespanha, H. J. Kim, and S. Sastry, "Multipleagent probabilistic pursuit-evasion games," in Proc.ofthe 38 th Conf. on Decision and Contr., Dec. 1999.

....logic for switching between modes. The greedy control applied within each mode consists in directing at each time instant t the agents to the locations that maximize the probability of finding the evader at the next time instant, conditional to the information collected up to time t. In [21], it is shown how this greedy control can be implemented at low computational cost in both the cases of constrained and unconstrained motions. As for the switching logic, the pursuer switches from the search to the handle mode either when the maximum of the conditional probability of finding the ....

J. P. Hespanha, H. J. Kim, and S. Sastry, "Multiple-agent probabilistic pursuit-evasion games," in Proc. of the 38th Conf. on Decision and Contr., pp. 2432--2437, Dec. 1999.

....is adopted for the one step nonzero sum games. Existence of a Nash equilibrium solution is proven and the simplifications which make the solution computationally feasible using linear programming (LP) are explained. This paper extends the probabilistic approach to pursuit evasion games found in [10]. In this reference, the pursuers team still adopts a greedy policy that maximizes the probability of finding the evader at the next time instant, but the evader is not actively avoiding to be captured. The paper is organized as follows. In Section 2, the pursuit evasion game is described using ....

J. P. Hespanha, H. J. Kim, and S. Sastry, "Multipleagent probabilistic pursuit-evasion games," in Proc. of the 38 th Conf. on Decision and Contr., Dec. 1999.

....is adopted for the one step nonzero sum games. Existence of a Nash equilibrium solution is proven and the simpli cations which make the solution computationally feasible using linear programming (LP) are explained. This paper extends the probabilistic approach to pursuit evasion games found in [10]. In this reference, the pursuers team still adopts a greedy policy that maximizes the probability of nding the evader at the next time instant, but the evader is not actively avoiding to be captured. The paper is organized as follows. In Section 2, the pursuit evasion game is described using ....

J. P. Hespanha, H. J. Kim, and S. Sastry, \Multipleagent probabilistic pursuit-evasion games," in Proc. of the 38 th Conf. on Decision and Contr., Dec. 1999.

....deviation with respect to the Nash equilibrium policy. Existence of a Nash equilibrium solution is proved and the simpli cations which make the solution computationally feasible using linear programming are explained. This paper extends the probabilistic approach to pursuit evasion games found in [22]. In this reference, the pursuers team adopts a greedy policy that consists of moving towards the locations that maximize the probability of nding the evader at the next time instant. The evader, however, is not actively avoiding to be captured and, in fact, a model of its motion is supposed to ....

J. P. Hespanha, H. J. Kim, and S. Sastry, \Multiple-agent probabilistic pursuit-evasion games," in Proc. of the 38th Conf. on Decision and Contr., pp. 2432-2437, Dec. 1999.

....policies are proposed for simple multi pursuers singleevader games with inaccurate observations and obstacles. Simulation results are shown in Section 5 for a two dimensional pursuit game and Section 6 contains some concluding remarks and directions for future research. The reader is referred to [9] for the proofs of some of the results presented here. Notation: We denote by( Omega ; F ; P) the relevant probability space with Omega the set of all possible events related to the pursuit evasion game, F a family of subsets of Omega forming a oe algebra, and P : F [0; 1] a probability ....

....first time instant in T at which one of the evaders is found, if none is found in finite time we set T = 1. T can be regarded as a random variable with values in T : T [ f 1g. We denote by F g : T [0; 1] its distribution function, i.e. F g (t) P g (T t) One can show [9] that F g (t) 1 Gamma t Y =1 Gamma 1 Gamma f g ( Delta ; t 2 T ; 2) where, for each t 2 T , f g (t) denotes the conditional probability of finding an evader at time t, given that none was found up to that time, i.e. f g (t) P g (T = t j T t) Moreover, when ....

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J. P. Hespanha, H. J. Kim, and S. Sastry. Multiple-agent probabilistic pursuit-evasion games. Technical report, Dept. Electrical Eng. & Comp. Science, University of California at Berkeley, Mar. 1999.

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J. Hespanha, H. J. Kim, and S. Sastry, "Multiple-agent probabilistic pursuit-evasion games," in In Proc. of the 38th Conf. on Decision and Contr, 1999, pp. 2432--2437.

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J. Hespanha, H. J. Kim, and S. Sastry, "Multiple-agent probabilistic pursuit-evasion games," in In Proc. of the 38th Conf. on Decision and Contr, 1999, pp. 2432--2437.

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J. Hespanha, H. Kim, and S. Sastry, "Multiple-agent probabilistic pursuit-evasion games," in Proceedings of the 38th Conf. on Decision and Control, Phoenix, AZ, December 1999, pp. 2432--2437.

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J. P. Hespanha, H. J. Kim, and S. Sastry, "Multipleagent probabilistic pursuit-evasion games." in IEEE Conference on Decision and Control, vol. 3, 1999, pp. 2432--2437.

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J. Hespanha, H. Kim, and S. Sastry, "Multiple-agent probabilistic pursuit-evasion games," in Proceedings of the 38th Conf. on Decision and Control, Phoenix, AZ, December 1999, pp. 2432--2437.

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J. Hespanha, H. Kim, and S. Sastry. Multipleagent probabilistic pursuit-evasion games. In IEEE CDC, December 1999.

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