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Research Papers

A Partitioning Scheme for a Switched Feedback Control Law in Two Agent Pursuit-Evasion Scenarios

[+] Author and Article Information
Brian J. Goode

 Vibration and Acoustics Laboratory, Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061bjgoode@vt.edu

Andrew J. Kurdila

 Center for Intelligent Material, Systems and Structures, Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061kurdila@vt.edu

Michael J. Roan

 Vibration and Acoustics Laboratory, Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061mroan@vt.edu

There are several methods of integrating the vector field to determine the state trajectories. For simple planar cases, the authors use a visual inspection.

J. Dyn. Sys., Meas., Control 134(1), 011025 (Dec 06, 2011) (11 pages) doi:10.1115/1.4004767 History: Received November 17, 2010; Accepted June 01, 2011; Published December 06, 2011; Online December 06, 2011

A switched feedback control law is derived for an autonomous pursuing agent that attempts to intercept an evading agent whose dynamics are initially unknown. The model of the pursuer’s dynamics is known perfectly, and the evader is modeled as a disturbance. A new method is presented to efficiently update the pursuer’s control law as measurements of the parameters that govern the evader’s dynamics are received. Using a graph theoretical approach, the control law updates are limited to specific partitions of the state space, which eliminate many unneeded calculations. Results show increases in the time efficiency of the update calculations compared to traditional control law generation methods with a minimal loss in accuracy. An 11.6% overall decrease in calculation time over traditional methods and a 1% error rate compared to the true solution is achieved when solving the homicidal chauffeur game. We show how actual gains in time efficiency depend on the specific application of the controller and the size of the state space grid approximation. Both the theoretical development and implementation of the switched feedback controller are discussed.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

The reduced coordinates, x, are fixed with respect to the pursuer’s forward velocity

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Figure 2

V*(x) for the time-optimal homicidal chauffeur

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Figure 3

The phase plot shows states where trajectories are prevented from entering T due to the finite horizon objective

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Figure 4

Flowchart for verifying Theorem 1

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Figure 5

The block diagram of the switched control system

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Figure 6

Construction of the initial control partitions

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Figure 7

Illustration of Algorithm 2 on the plane

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Figure 8

Initial partitioning scheme of the homicidal chauffeur. The shaded region is the assumed region where the evader can traverse to an undesired partition.

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Figure 9

Flowchart for control updates

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Figure 10

The time (s) is plotted as a function of the speed ratio, γ, and turning radius, r

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Figure 11

The effect of the accuracy of the solution as the grid size is increased

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