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Research Papers

# Multi-Agent Autonomous Surveillance: A Framework Based on Stochastic Reachability and Hierarchical Task Allocation

[+] Author and Article Information
Nikolaos Kariotoglou

Automatic Control Laboratory,
Department of Electrical and
Information Engineering,
ETH Zurich,
Physikstrasse 3,
Zurich 8092, Switzerland
e-mail: karioto@control.ee.ethz.ch

Davide M. Raimondo

Identification and Control of
Dynamic Systems Laboratory,
Dipartimento di Ingegneria Industriale
e dell'Informazione,
Università degli Studi di Pavia,
Via Ferrata 1,
Pavia 27100, Italy
e-mail: davide.raimondo@unipv.it

Sean J. Summers

Automatic Control Laboratory,
Department of Electrical and
Information Engineering,
ETH Zurich,
Physikstrasse 3,
Zurich 8092, Switzerland
e-mail: ssummers@control.ee.ethz.ch

John Lygeros

Automatic Control Laboratory,
Department of Electrical and
Information Engineering,
ETH Zurich,
Physikstrasse 3,
Zurich 8092, Switzerland
e-mail: jlygeros@control.ee.ethz.ch

Even though we model the evader dynamics in $R3$ (where the third dimension is orientation) in the reach-avoid formulation we only need the location of the center to calculate γe(y) (see Eq. (10)) and hence the covering functions.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 29, 2014; final manuscript received September 15, 2014; published online October 21, 2014. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 137(3), 031008 (Oct 21, 2014) (14 pages) Paper No: DS-14-1037; doi: 10.1115/1.4028589 History: Received January 29, 2014; Revised September 15, 2014

## Abstract

We develop and implement a framework to address autonomous surveillance problems with a collection of pan-tilt (PT) cameras. Using tools from stochastic reachability with random sets, we formulate the problems of target acquisition, target tracking, and acquisition while tracking as reach-avoid dynamic programs for Markov decision processes (MDPs). It is well known that solution methods for MDP problems based on dynamic programming (DP), implemented by state space gridding, suffer from the curse of dimensionality. This becomes a major limitation when one considers a network of PT cameras. To deal with larger problems we propose a hierarchical task allocation mechanism that allows cameras to calculate reach-avoid objectives independently while achieving tasks collectively. We evaluate the proposed algorithms experimentally on a setup involving industrial PT cameras and mobile robots as targets.

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## Figures

Fig. 2

Reach-avoid indicator function values for different state trajectories. (a) Indicator functions for the square trajectory in Fig. 1. (b) Indicator functions for the circle trajectory in Fig. 1, and (c) indicator functions for the diamond trajectory in Fig. 1.

Fig. 1

An example of three system trajectories starting at x0. The reach-avoid probability is the expected value of a sum-multiplicative cost of indicator functions over the different trajectories.

Fig. 3

Maps between spaces. (a) The FOV projection on the ground plane. (b) Visualization of the transformation maps between the different spaces. The dotted line on space Y corresponds to a realization of the evader process while the dotted circles on G are the mapping through γe.

Fig. 4

Visualization of the multicamera network. The flat circles correspond to potential evaders

Fig. 5

Auxiliary state machine

Fig. 7

Comparison of the total complexity. The y-axis is in logarithmic scale. The diamond line approaches the square one as m increases

Fig. 6

Block diagram of the task allocator

Fig. 8

View of the experimental setup

Fig. 15

Total percentage of time spent in each of the states {S00, S01, S10, S11} of P under different choices of hierarchies H. The subscript d denotes experiments where we decoupled the area of coverage of cameras. This is simple to implement by setting the columns of each camera's B matrix in Eq. (10) to 0.

Fig. 9

Estimated distribution of the evader process

Fig. 10

Camera kernel movement for u∧=up

Fig. 12

Camera configuration

Fig. 13

An example of reach-avoid probabilities reported by the two cameras at a specific time instance

Fig. 14

Effect of horizon length

Fig. 11

Tracking trajectories under different initial conditions and parameters

Fig. 16

Objective allocation for the two cameras for different horizon lengths

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