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\begin{document}
\title{Active Control Method of\\ Sensor Data Selection\\ for Autonomous Mobile Robot}
\date{}

\author{
\IEEEauthorblockN{%
Dmitry~G.~Korzun, Olga~I.~Bogoiavlenskaia
%
}
\IEEEauthorblockA{%
Petrozavodsk State University (PetrSU)\\ 
Petrozavodsk, Russia\\
\{dkorzun, olbgvl\}@cs.karelia.ru\\}
}
\maketitle

\begin{abstract}
An autonomous mobile robots have been discovering recently a wide range of applications in various areas of human activities, including industry, commerce, social life, environmental projects, health care, science, education, agriculture, housekeeping.  The amount of sensors carried by a robot normally is rather considerable.  In the sensor data stream the items are not equally important. We propose a method for data selection which is based on Additive Increase Multiplicative Decease Algorithm and could reduce the amount of data passed to the data fusion module.
\end{abstract}

\section{Background}
\label{sec: back}
An autonomous mobile robots have been discovering recently a wide range of applications in various areas of human activities, including industry, commerce, social life, environmental projects, health care, science, education, agriculture, housekeeping.  For several decades the efforts of the research community in the area is directed to the development of methods and technologies that could make such devices able to navigate in a completely or partly unknown environment without any or with a restricted supervision of a human distant operator, e.g.~\cite{Ru-Fra-Lo19, Ba-Cr-Go18}. 

Autonomous mobile robot as a system operates in the environment which is either completely unknown and  to be discovered or is partly described by a map and a path within the map the robot has to follow. Also the environment can change during the operation and those changes could be unpredictable. For the proper operation of the system the changes should be detected and a reaction should be designed. For these reasons an autonomous navigation is based upon sensors data which provide varied information about surrounding objects and inner information that could be useful for locomotion and navigation.

Nowadays there exists a wide variety of sensors that deliver diverse multitude of raw data. The sensors could be classified by the nature of the data they perceive, e.g., spatial, temporal, electromagnetic, mechanical and others, or by the nature of the sensor activity, e.g. inner (battery level, wheel angle) external (distance to the obstacle), active (sonar sensor), passive (camera). A range of classifications exists in the literature as well. Basically using sensor assumes that further processing of the sensors data could infer some information about the world around necessary for  a robot safe navigation and mission completion. There are two major problems to be solved:

\begin{enumerate}
\item The raw sensors data carry uncertainty due to the lack of precision, external factors intervention or noise of the signal (Gaussian of non Gaussian).
\item The amount of sensors carried by a robot normally is rather considerable. Hence the amount of the information they produce is rather considerable as well. In the data stream the items are not equally important. Some of them are critical for the device integrity, some are essential for it's proper operation and some are useless. In many cases the attributes enumerated above could not be attached to a particular sensor (if so, dismount it). Let's consider a battery level sensor. If the battery level is high there is no need to monitor it on the regular basis. But if the charge is low or it is high but decreases faster than expected these data should be examined by the inference modules.
\end{enumerate}

To deal with the first problem the methods of control theory are widely used. The sensor producers and the robot designers apply filters to smooth raw data. Different variations of the Kalman filter~\cite{Dron18} could be applied for the state estimation if there is a linear low that bounds observed variables, e.g. velocity and acceleration, or distance and velocity.  Another major method is Particle Filer~\cite{Ra-Jo-Ji16} which is sequential Monte-Carlo technique. Due to the computation complexity of these two methods simple techniques as moving arithmetical average, median, mode filters are widely used in practice as well. 

Smoothed data are further processed by sensor fusion algorithms~\cite{Nag-Udd-Singh14, Ra-Jo-Ji16}, which combine data from several sensors and relevant information from corresponding databases to produce more precise and specific inference about the surrounding environment. Meanwhile Kalman filter and Partical filter could be treated as fusion technique as well, e.g.~\cite{Erdem-Erscan15}.

Although the first problem enlisted above is researched extensively, the second problem is to be solved now by the choice of sensors set and their allocation. Meanwhile the battery charge and the computational facilities of an autonomous device are restricted and fusion useless data from the stream remains an important problem. We propose an approach to data selection which is based on Additive Increase Multiplicative Decease (AIMD) Algorithm and could reduce the amount of data passed to the data fusion module. The selection algorithms could be applied before, if possible, or after raw data smoothing stage and dynamically control the data flow passed to further processing.

\section{Data Selection Algorithms}
\label{sec: alg}

Let's consider a sensor as a mapping $S_m\mapsto S_n,$ where $S_m\subset\RR^m$ and $S_n\subset \RR^n.$ In most cases $|S_m|>|S_n|.$ This inequality forms one of the main sources of uncertainty for the raw sensor data since the actual mapping is many to one. The set $S_m$ represents the real world phenomenon. It could be continuous or discrete. Also it could be a conjunction of several continuous intervals or be any other subset of $\RR^m.$ The set $S_n$ is discrete in most cases due to the sensor output granularity. Smoothing raw data done internally by the sensor producer or by the robot computing facilities still keeps it discrete due to the discrete nature of the computing architecture but the latter transforms $S_n\mapsto \tilde S_n$ and $|S_n|\leq |\tilde S_n|.$

Let's consider $x, y\in S_n$ and introduce the norm $||x-y||\in \RR$ which defines the distance between two values measured by a sensor. The norm is additive and $||ax||=a||x||, \ a\in R,\  x\in S_n.$ Then let's denote a sequence $s^i=\{s_0^i, s_1^i, \dots\}, \ s^i_k\in \tilde S_n$ of data produced by $i$th sensor and a sequence $t^i=\{t_0^i, t_1^i, \dots\}$ of timestamps that label the corresponding elements of the sequence $s^i.$

The selection method maintains the geometrical average of $s^i$ sequence i.e.
\begin{equation}
||\hat s^i_k||=\kappa||\hat s^{i}_{k-1}||+(1-\kappa)||\hat s^i_k||,
\end{equation}
where $0<\kappa<1.$ This additional filter is applied if primiry filters don not suceed. Otherwise the primary filter output could bu used as $\hat s^i$ sequence. The filter is not applied for periodical or flctuating data. Then let's define a delay $\tau_n$ which is applied before the sensor data are passed to the  inference modules. The delay is dynamically adjusted depending on the properties of the data in the stream. It evaluates following AIMD algorithm as follows:

\begin{equation}\label{eq: aimd}
\tau_{n+1}= \left\lbrace
\begin{array}{ll}
\displaystyle\alpha\tau_n, &\mbox{if specified events has happened}\\[5pt]
\displaystyle \tau_n+\delta, &\mbox{otherwise}
\end{array}\right.
\end{equation}
Here $0<\alpha<1$ and $\delta>0.$ The specified events are one of the following
\begin{enumerate}
\item The value of $||\hat s^i_k-\hat s^{i}_{k-1}||>0$ for $k$ time in the row, where $k$ is a parameter.
\item The $||\hat s^i_k||=(1+\beta)||\hat s^{i}_{k-1}||,$ where $\beta>0.5$ is a parameter.
\item If KF or PF are used the event is: the error evaluated before a correction step does not change sign $k'$ times in a row.
\item A critical event is identified. The list of the critical events is formed in advance and normally they mean something which needs immediate reaction, e.g. sharp increase of acceleration.
 \end{enumerate}
At the end of $\tau_n$ interval the current value $\hat s^i_k$ is passed to the inference facility.

Thus if the sensor data are stable, uniform and correspond the current operation of the autonomous mobile robot they don't contain new insight about the environment and hence are not passed to the data fusion modules. If noticeable change happen then the data could be significant and are passed to the inference facility.

\section{Conclusion}
In this work the method of sensor data selection is proposed. It identifies data significant for autonomous mobile robot inference subsystem and reduces the amount of data processed. In the future the method could be extended by feedback exchange between selection algorithms and the sensor data fusion methods.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgment}
The work is implemented within the Government Program of Flagship University Development for Petrozavodsk State University (PetrSU) in 2017-2021.
%Можно еще поблагодарить рецензентов :))


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\begin{comment}
\bibitem{Dron18} W. V. Drongelen, ``Kalman filter,'' in Signal Processing for Neuroscien-
tists, 2nd ed. New York, NY, USA: Academic, 2018, ch. 19, pp. 361-374.

\bibitem{Ru-Fra-Lo19} F. Rubio, F. Valero, and C. Llopis-Albert, ``A review of mobile robots:
Concepts, methods, theoretical framework, and applications,'' Int. J. Adv.
Robotic Syst., vol. 16, no. 2, Apr. 2019, Art. no. 172988141983959.

\bibitem{Ba-Cr-Go18} R. Barber, J. Crespo, C. Gomez, A. C. Hernamdez, and M. Galli, Mobile
Robot Navigation in Indoor Environments: Geometric, Topological, and
Semantic Navigation. London, U.K.: IntechOpen, Nov. 2018, pp. 1-25.

\bibitem{Erdem-Ercan15} A. T. Erdem and A. O. Ercan, ``Fusing inertial sensor data in an extended
Kalman ffilter for 3D camera tracking,'' IEEE Trans. Image Process.,
vol. 24, no. 2, pp. 538-548, Feb. 2015.

\bibitem{Nag-Udd-Singh14}K. Nagla, M. Uddin, and D. Singh, ``Multisensor data fusion and integration
for mobile robots: A review,'' IAES Int. J. Robot. Autom. (IJRA),
vol. 3, no. 2, pp. 131-138, Jun. 2014.

\bibitem{Ra-Jo-Ji16}Y. Raaj, A. John, and T. Jin, ``3D object localization using forward looking
sonar (FLS) and optical camera via particle filter based calibration and
fusion,'' in Proc. OCEANS MTS/IEEE Monterey, Sep. 2016, pp. 1-10.

=============================
\bibitem{Phala-Kumar16} K. S. E. Phala, A. Kumar, and G. P. Hancke, ``Air quality monitoring
system based on ISO/IEC/IEEE 21451 standards,'' IEEE Sensors J.,
vol. 16, no. 12, pp. 5037-5045, Jun. 2016
\bibitem{Silva-Fisher15}B. Silva, R. M. Fisher, A. Kumar, and G. P. Hancke, ``Experimental link
quality characterization of wireless sensor networks for underground
monitoring,'' IEEE Trans Ind. Informat., vol. 11, no. 5, pp. 1099-1110,
Oct. 2015.
\end{comment}


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