**1. Introduction**

Searching strategies for finding targets using appropriate sensing modalities are of great importance in many aspects of life. In the context of national security, there could be a need to find a source of hazardous emissions [1–3]. Similarly, rescue and recovery missions may be tasked with localising a lost piece of equipment that is emitting weak signals [4]. Biological applications include, for example, protein searching for its specific target site on DNA [5], or foraging behaviour of animals in their search for food or a mate [6, 7]. The objective of search research [8] is to develop optimal strategies for localising a target in the shortest time (on average), for a given search volume and sensing characteristics.

The use of autonomous vehicles in dangerous missions, such as finding a source of hazardous emissions, has become widespread [9–11]. Existing approaches to the search and localisation in the context of atmospheric releases can be loosely divided into three categories: up-flow motion methods, concentration gradient-based methods and information gain-based methods, also known as *infotaxis*. Both the up-flow motion methods and the concentration gradient methods are simple, in the sense that they require only a limited level of spatial perception [12]. Their limitations manifest in the presence of turbulent flows, due to the absence of concentration gradients, when the plume typically consists of time-varying

disconnected patches. The information gain-based methods [13] have been developed specifically for searching in turbulent flows. In the absence of a smooth distribution of concentration (e.g., due to turbulence), this strategy directs the searching robot(s) towards the highest information gain. As a theoretically principled approach, where the source-parameter estimation is carried out in the Bayesian framework and the searching platform motion control is based on the information-theoretic principles, the infotaxic (or cognitive) search strategies have attracted a great deal of interest [3, 14–23].

the *i*th robot, whose position at time *k* is<sup>1</sup> **r***<sup>i</sup>*

*DOI: http://dx.doi.org/10.5772/intechopen.86540*

*R η*0*;* **r***<sup>i</sup> k* � � <sup>¼</sup> *<sup>Q</sup>*<sup>0</sup>

*xi <sup>k</sup>* � *X*<sup>0</sup> � �<sup>2</sup> <sup>þ</sup> *<sup>y</sup><sup>i</sup>*

*di <sup>k</sup>* **r**0*;* **r***<sup>i</sup> k* � � <sup>¼</sup>

ℓ *z<sup>i</sup> <sup>k</sup>*j*η*<sup>0</sup> � � <sup>¼</sup> <sup>P</sup> *<sup>z</sup><sup>i</sup>*

**r***i <sup>k</sup>* <sup>¼</sup> *xi <sup>k</sup>; y<sup>i</sup> k*

zero, and *λ* ¼

distributed, i.e.,

Parameter *μ<sup>i</sup>*

reach the sensor at location **r***<sup>i</sup>*

is specified by coordinates:

and angular velocity Ω*<sup>i</sup>*

motion function *β θ<sup>i</sup>*

*δ* ≪ *T<sup>i</sup>*

*π θ<sup>i</sup> t* j*θi <sup>t</sup>*�*<sup>δ</sup>;* **<sup>u</sup>***<sup>i</sup> k* � � <sup>¼</sup> <sup>N</sup> *<sup>θ</sup><sup>i</sup>*

**17**

*<sup>k</sup>*; *μ<sup>i</sup> k* � �.

predefined and known to it (i.e., *xi*

average rate of encounters can be modelled as follows [13]:

ln *<sup>λ</sup> a* � � exp

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

4*D*

� �<sup>2</sup> <sup>q</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *<sup>D</sup>τ*<sup>∕</sup> <sup>1</sup> <sup>þ</sup> *<sup>U</sup>*2*<sup>τ</sup>*

The probability that a sensor at location **r***<sup>i</sup>*

*<sup>k</sup>* <sup>¼</sup> *<sup>t</sup>*<sup>0</sup> � *<sup>R</sup> <sup>η</sup>*0*;* **<sup>r</sup>***<sup>i</sup>*

function of a concentration measurement *zi*

where *D*, *τ* and *U* are known environmental parameters,

*<sup>k</sup>* � *Y*<sup>0</sup>

*Decentralised Scalable Search for a Hazardous Source in Turbulent Conditions*

P *z*; *μ<sup>i</sup> k* � � <sup>¼</sup> *<sup>μ</sup><sup>i</sup>*

*k*

pose vector of the *i*th robot platform at time *tk* be denoted *θ<sup>i</sup>*

� �<sup>⊺</sup> has already been introduced and *ϕ<sup>i</sup>*

*xc <sup>k</sup>* <sup>¼</sup> <sup>1</sup> *<sup>N</sup>* <sup>∑</sup> *N i*¼1 *xi k, y<sup>c</sup>*

For each platform *i* ¼ 1*,* …*, N*, the offset Δ*xi;* Δ*yi*

Motion of the *i*th platform during interval *T<sup>i</sup>*

*<sup>t</sup>*�*<sup>δ</sup>;* **<sup>u</sup>***<sup>i</sup> k*

<sup>1</sup> Robot locations are assumed to be non-coincidental with the source location **r**0.

*t* ; *β θ<sup>i</sup>*

*<sup>t</sup>*�*<sup>δ</sup>;* **<sup>u</sup>***<sup>i</sup> k* � � is: *<sup>k</sup>* <sup>¼</sup> *xi*

a series of encounters with the particles released from the emitting source. The

*<sup>X</sup>*<sup>0</sup> � *xi k* � �*U* 2*D* � �

*i*th sensor platform, *K*<sup>0</sup> is the modified Bessel function of the second kind of order

particles (where *z* is a non-negative integer) during a time interval *t*<sup>0</sup> is Poisson

<sup>r</sup> � � depends on environmental parameters only.

*k* � �*<sup>z</sup> <sup>z</sup>*! *<sup>e</sup>* �*μ<sup>i</sup>*

The motion model of a coordinated group of robots is described next. Let the

of searching vehicles moves in a formation. The centroid of the formation at time *tk*

*<sup>k</sup>* <sup>¼</sup> *xc*

The assumption is that sensing is suppressed during the travel time.

*<sup>k</sup>* <sup>¼</sup> <sup>1</sup> *<sup>N</sup>* <sup>∑</sup> *N i*¼1 *yi*

*<sup>k</sup>* <sup>¼</sup> *<sup>y</sup><sup>c</sup>*

� �*;* **Q** � �. The process noise covariance matrix **Q** cap-

*<sup>k</sup>* <sup>þ</sup> <sup>Δ</sup>*xi*, *<sup>y</sup><sup>i</sup>*

The measurements of concentration are taken at time instants *tk*, *k* ¼ 1*,* 2*,* ⋯. Between two consecutive sensing instants, each platform is moving. Let the duration of this interval (referred to as the *travel time*) for the *i*th platform be *T<sup>i</sup>*

*<sup>k</sup>*. Given that the motion control vector **u***<sup>i</sup>*

applied to the *i*th platform, its dynamics during a short integration time interval

*<sup>k</sup>* can be modelled by a Markov process whose transitional density is

tures the uncertainty in motion due to the unforeseen disturbances. The vehicle

*<sup>k</sup>; y<sup>i</sup> k* � �<sup>⊺</sup>

� *K*<sup>0</sup>

� � in (2) is the mean number of particles expected to

*<sup>k</sup>* during interval *t*0. Eq. (2) expressed the likelihood

*<sup>k</sup>* collected by *i*th sensor, i.e.,

*di <sup>k</sup>* **r**0*;* **r***<sup>i</sup> k* � � *λ* !

is the distance between the source and the

*<sup>k</sup>* is hit by *z*∈Z<sup>þ</sup>∪f g0 dispersed

*<sup>k</sup> :* (2)

*<sup>k</sup>* <sup>¼</sup> **<sup>r</sup>***<sup>i</sup> k* � �<sup>⊺</sup> *; ϕ<sup>i</sup> k* � �<sup>⊺</sup>

� � from the centroid *x<sup>c</sup>*

*<sup>k</sup>* þ Δ*yi* ).

*<sup>k</sup>* is the vehicle heading. The group

*<sup>k</sup>:* (3)

*<sup>k</sup>* is controlled by linear velocity *V<sup>i</sup>*

*<sup>k</sup>* <sup>¼</sup> *<sup>V</sup><sup>i</sup>*

*<sup>k</sup>;* Ω*<sup>i</sup> <sup>k</sup>; T<sup>i</sup> k* � �<sup>⊺</sup> is

. This sensor will experience

(1)

, where

*<sup>k</sup>; y<sup>c</sup> k* � � is

*<sup>k</sup>* ≥0.

*k*

This chapter summarizes our recent results in development of an autonomous infotaxic coordinated search strategy for a group of robots, searching for an emitting hazardous source in open terrain under turbulent conditions. The assumption is that the search platforms can move and sense. Two types of sensor measurements are collected sequentially: (a) the concentration of the hazardous substance; (b) the platform location within the search domain. Due to the turbulent transport of the emitted substance, the concentration measurements are typically sporadic and fluctuating. The searching platforms form a moving sensor network, thus enabling the exchange of data and a cooperative behaviour. The multi-robot infotaxis have already been studied in [16, 17, 20, 24]. However, all mentioned references assumed *all-to-all* (i.e., fully connected) communication network with *centralised fusion and control* of the searching group.

We develop an approach where the group of searching robots operate in a fully decentralised coordinated manner. Decentralised operation means that each searching robot performs the computations (i.e., source estimation and path planning) locally and independently of other platforms. Having a common task, however the robotic platforms must perform in a coordinated manner. This coordination is achieved by exchanging the data with immediate neighbours only, in a manner which does not require the global knowledge of the communication network topology. For this reason, the proposed approach is scalable in the sense that the complexities for sensing, communication, and computing per sensor platform are independent of the sensor network size. In addition, because all sensor platforms are treated equally (no leader-follower hierarchy), this approach is robust to the failure of any of the searching agents. The only requirement for avoiding the break-up of the searching formation is that the communication graph of the sensor network remains *connected* at all times. Source-parameter estimation is carried out sequentially, and on each platform independently, using a Rao-Blackwellised particle filter. Platform path planning, in the spirit of *infotaxis*, is based on entropyreduction and is also carried out independently on every platform.
