Optimal minimax pursuit evasion on a Manhattan grid

Krishnamoorthy, K.; Darbha, Swaroop; Khargonekar, Pramod P.; Casbeer, David W.; Chandler, P.; Pachter, Meir

doi:10.1109/acc.2013.6580360

Cited by 22 publications

(14 citation statements)

References 11 publications

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“…But we are encouraged by the fact that the condition provided herein does faithfully recover the optimal min-max (capture time) pursuit policy for the example problem above. Indeed, we have verified this empirically for bigger grids as well by comparing our policy (for 3 rows and number of columns, 3 to 6) with the optimal min-max pursuit policy developed in [16]. …”

Section: Manhattan Grid Examplementioning

confidence: 99%

“…By writing the Bellman Equation as in (19), the measurement z, effectively, parameterizes the action space of the evader. Notice that the capture time (19) can be computed recursively along with the guaranteed capture sets (14)- (17). The worst case minimum-time control is given by:…”

Section: ) Ifmentioning

confidence: 99%

“…In addition, we also compute the pursuit policy that gives (worst-case) minimum time capture, among all policies that satisfy the sufficient condition. In related work [16], [17], where the road network is restricted to a Manhattan grid, the optimal min-max time to capture (and the corresponding pursuit policy) is provided for both single and two UAVs pursuing an evader. Indeed, we use the Manhattan grid as an example problem in this work to illustrate our solution method.…”

Section: Introductionmentioning

confidence: 99%

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Moving ground target isolation by a UAV using predicted observations

Casbeer

Krishnamoorthy²,

Chandler

et al. 2014

53rd IEEE Conference on Decision and Control

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Abstract-An interesting variant of the cops and robbers pursuit-evasion problem is presented. The motivation for the problem comes from the need to monitor a network of roads leading to a protected area. In this paper, an unmanned aerial vehicle (UAV) is searching for a slower moving ground vehicle on a road network that has been out-fitted with unattended ground sensors (UGSs). The UGSs are communication constrained and can only relay observations of the ground vehicle when the UAV visits them. Furthermore, the UAV does not have on-board capability to detect and identify the evader and therefore must investigate the UGSs to learn the evader's location. This scenario leads the UAV's control actions to depend on partial information. A sufficient condition for guaranteed isolation of the intruder is provided along with the corresponding pursuit policy. Since the policy is non-unique, we select a policy that provides the least time to capture among all policies with the guarantee.

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Section: Manhattan Grid Examplementioning

confidence: 99%

Section: ) Ifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Moving ground target isolation by a UAV using predicted observations

Casbeer

Krishnamoorthy²,

Chandler

et al. 2014

53rd IEEE Conference on Decision and Control

Self Cite

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“…Sufficient conditions for guaranteed capture on a simple network with a finite number of nodes in discrete time have been developed [9]. Optimal control of pursuers isolating a slower moving evader on a Manhattan grid road network has been studied and the corresponding strategies have been given [10], [11].…”

Section: Introductionmentioning

confidence: 99%

“…Endeavors on closely related UGS-based intruder isolation problems are carried out in [9], [10], [11], yet limited to some special cases, where simple networks, such as finite grids and a special Manhattan grid road network, are considered in discrete time. Sufficient conditions for guaranteed capture on a simple network with a finite number of nodes in discrete time have been developed [9].…”

Section: Introductionmentioning

confidence: 99%

Continuous-time intruder isolation using Unattended Ground Sensors on graphs

Chen

Kalyanam²,

Zhang

et al. 2014

2014 American Control Conference

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This paper studies the continuous-time intruder isolation problem on a general road network graph under delayed information scenario. Several Unattended Ground Sensors (UGSs) are pre-installed along certain edges of the graph for detecting intruder motion and recording the detection time. Measurements of a UGS can only be obtained when the UAV is within its communication range. The goal of this paper is to find the optimal path for the UAV to follow in order to capture the intruder within the shortest time, based on the delayed information from the visited UGSs. We propose an unfolding strategy to transform the road network graph to a decision tree incorporating delayed measurement information. Based on the decision tree, both optimal and suboptimal min-max solutions are developed. Several interesting properties of the corresponding optimal value function are also derived. Numerical simulations based on a real road network are presented to demonstrate the effectiveness of the proposed strategies.

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