Research ArticleEnergy-Efficient Control for an Unmanned Ground Vehicle in aWireless Sensor Network

José Alcaina,1 Ángel Cuenca ,1 Julián Salt ,1 Minghui Zheng,2

and Masayoshi Tomizuka 2

1Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, Spain2Mechanical Engineering Department, University of California, Berkeley, USA

Correspondence should be addressed to Julián Salt; julian@isa.upv.es

Received 20 December 2018; Accepted 13 August 2019; Published 7 October 2019

Academic Editor: Stelios M. Potirakis

Copyright © 2019 José Alcaina et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this paper, an energy-efficient control solution for an Unmanned Ground Vehicle (UGV) in a Wireless Sensor Network is proposed.This novel control approach integrates periodic event-triggered control, packet-based control, time-varying dual-rate Kalman filter-basedprediction techniques, and dual-rate control. The systematic combination of these control techniques allows the UGV to track the desiredpath preserving performance properties, despite (i) existing scarce data due to the reduced usage of the wireless sensor device, whichresults in less number of transmissions through the network and, hence, bandwidth and battery saving; (ii) appearance of somewireless communication problems such as time-varying delays, packet dropouts, and packet disorder; and (iii) coping with a realisticscenario where external disturbance and sensor noise can arise. The main benefits of the control solution are illustrated via simulation.

1. Introduction

AWireless Sensor Network (WSN) [1, 2] can be defined as agroup of sensors for monitoring and recording system condi-tions, which are wirelessly transferred to a central location. Inrecent years, the development of smart sensors has led WSNsto gain worldwide attention. Some trending applications onWSNs are target tracking [3, 4], health monitoring [5, 6],and environment exploration [7, 8]. Smart sensor nodes arelow-power devices equipped with one or more sensors, a dig-ital processor, memory, a power module, a wireless commu-nication module, and an actuator. Sensors of differing nature(mechanical, optical, magnetic, etc.) may be attached to thesensor node to measure system variables. Since memory ofthe sensor nodes is limited, the wireless communicationenables transferring of the measured data to a base station(e.g., a laptop), which is usually provided with powerful pro-cessing and storage capabilities. In this way, the base stationmay be able to compute complex control algorithms.

Differently from traditional networks, a WSN has its owndesign and resource constraints. Resource constraints include

short communication range, a limited amount of energy(which is supplied by battery), low bandwidth, and limitedprocessing and storage capabilities (being not capable of run-ning complex control algorithms). As sensor nodes operateon limited battery power, and data transmission is very expen-sive in terms of energy consumption [9], a central aspect inWSNs is the optimization of communication in order toreduce energy usage. In other words, one of the main aims inWSNs is to get efficient reliable wireless communications inorder to maximize network lifetime. This aspect has beenwidely treated in the literature therein from different pointsof view. In general, three main techniques are typically used[10]: duty cycling, data-driven approaches, and mobility. Dutycycling allows nodes to assume a low-power, idle state when-ever they are not transmitting or receiving (see, e.g., in [11,12]). Data-driven approaches are designed to reduce theamount of sampled and transmitted data (see, e.g., [13, 14]).Mobility is focused on minimizing the communication dis-tance and altering traffic flow (see, e.g., [15, 16]). In the presentpaper, a novel data-driven approach based on the systematiccombination of periodic event-triggered control, packet-

HindawiJournal of SensorsVolume 2019, Article ID 7085915, 16 pageshttps://doi.org/10.1155/2019/7085915

based control, time-varying dual-rate Kalman filter-based pre-diction techniques, and dual-rate control is proposed. As adata-driven approach, the control solution enables thereduction of the sensor node usage, which implies less packetdeliveries and, hence, battery and bandwidth saving. Thisreduction of the resource utilization can be reached whilepreserving performance propertieswhen tracking a desired tar-get. In addition, the control proposal is able to guarantee reli-able packet delivery by dealing with some wirelesscommunication problems such as network-induced delays,packet dropouts, and packet disorder. Finally, the controlapproach is also able to cope with realistic scenarios, whereexternal disturbance and sensor noise can arise.

In periodic event-triggered control (PETC) [17, 18], systemdata are transferred only when output variables satisfy certainevent conditions, which are periodically evaluated. Comparedto the traditional time-triggered control, PETC enables furtherreduction of resource utilization such as bandwidth and energyconsumption [19, 20]. As the controller (located at the base sta-tion) is provided with less system data, event-based state pre-diction techniques must be additionally included in order toestimate the nonavailable data and keep performance proper-ties. Both continuous-time (see, e.g., [17]) and discrete-time(see, e.g., [21]) frameworks are found in the literature on PETC.In this paper, the last case is adopted by integrating a time-varying dual-rate Kalman filter with a dual-rate controller.

Regarding event-based state prediction techniques, differentapproaches address this aspect in the literature, for instance, dis-tributed event-triggered filtering in [13, 14, 22], a model-basedpredictor in [18, 23], and time-varying Kalman filters in [24–26]. Following this line of research on time-varying Kalman fil-ters, in this paper, a time-varying dual-rate Kalman filter(TVDRKF) is used in order to provide nonavailable data andcompute an h-step ahead state prediction stage. The nature ofthis filter is (i) dual-rate, due to the consideration of a slow-rate state correction stage along with a fast-rate prediction stage,and (ii) time-varying, because the correction stage is carried outin a nonuniform fashion as a consequence of the event-triggeredsampling scheme. Unlike [26], the Kalman filter is now inte-grated in a WSN, where communication problems such asnetwork-induced delays and packet dropouts can appear.Hence, the TVDRKF is able to estimate the nonavailable datanot only due to the event-triggering sampling but also due tothe packet dropouts. In addition, the TVDRKF is also able tocompensate for the time-varying network-induced delays. Tocope with both problems, the integration of packet-based con-trol strategies in the control solution is needed.

Packet-based control [27, 28] is a technique whichenables decrease of the communication rate by simulta-neously sending a set of data in each transmission. In ourwork, this strategy is useful not only for resource-savingpurposes but also for complementing the TVDRKF, sincethe controller (located at the base station, including theTVDRKF) is allowed to send a set of h-step ahead controlsignal estimations in a packet through the network to theactuator (located at the sensor node). The computation ofthe control signal estimations is carried out from the set ofh-step ahead state predictions obtained by the TVDRKFand following a delay-free control algorithm. This is a

relevant aspect of this work, since, for implementation pur-poses, the round-trip time delay is not required to be mea-sured and compensated for, which makes the solutionapplicable to a wide range of WSNs where the time delay isdifficult to measure. In this way, at the actuator, when nopacket arrives, estimated control actions received in the pre-vious transmission are applied to the plant, without beinginfluenced by the time-varying network-induced delay.When the packet arrives after the delay, the estimated controlsignal is replaced with the actual one. The difference betweenactual and estimated control signals should be negligible,since (i) an accurate system model is assumed and (ii)although a realistic scenario is considered, where possibleexternal disturbance and measurement noise can arise, theseaspects are faced by the TVDRKF. To the best of the authors’knowledge, the working mode of the proposed control algo-rithm is novel in this kind of frameworks.

In dual-rate control [29–31], a slower sensing rate incomparison to a faster actuation can be assumed. Theevent-triggered conditions at the sensor node are periodicallyevaluated at the slow rate. Despite sensing in this way, the fastactuation enables achieving acceptable control properties. Inaddition, dual-rate control techniques provide twofold bene-fits: (i) to lessen the amount of transmissions through the net-work, which results in energy and bandwidth saving, and (ii)to elude packet disorder, selecting the sampling period to belarger than the largest round-trip time delay. As a statisticaldistribution for the network-induced delay is assumed to beknown [32], the largest delay can be easily found. In the pres-ent work, due to the broad knowledge of PID controllers inacademic and industrial environments, a dual-rate PID con-trol scheme is considered. The estimated disturbance signalobtained by the TVDRKF is used to finally tune the PID con-trol signal.

In order to show the potential of the ideas posed in thiswork, the control solution is employed in the context of apopular control application, that of Unmanned GroundVehicles (UGVs). In fact, the large number of UGV applica-tions such as target tracking, inspection, and mapping hasattracted the attention of the scientific community (see, e.g.,[33, 34]). In our work, a target tracking application in aWSN is developed, where the Pure Pursuit path trackingalgorithm [35, 36] is used in order to make the UGV followa predefined path approximately. The algorithm computesvelocity commands from velocity estimations provided bythe TVDRKF. The UGV chosen will be a differential robot.

In summary, the main contribution of the present work isthe development of a novel and complete approach forWSNs, where a TVDRKF, a dual-rate controller, and a PurePursuit path tracking algorithm are systematically broughttogether in a PETC scenario in order to considerably lessenresource usage (energy and bandwidth), and dealing withsome wireless communication problems and disturbanceand noise, while keeping satisfactory control properties.

Finally, the work is structured as follows. Section 2 pre-sents the energy-efficient control solution. Section 3 intro-duces the event-triggered conditions and control structuresused in the control solution. Section 4 presents some costindexes to analyze the trade-off between control performance

2 Journal of Sensors

and resource utilization. In Section 5, a realistic application ofthe control solution to UGVs is simulated and its effective-ness validated, via a simulation tool known as TrueTime[37], which is based on MATLAB/Simulink®. Section 6 sum-marizes the main conclusions of the paper.

2. Problem Scenario

The energy-efficient control solution taken into account inthis work is illustrated in Figure 1. The control system pre-sents two components: the sensor node, where the sensor,actuator, and plant are included, and the base station, wherethe control algorithm is implemented. In both components,some trigger mechanisms are used to decide when the datais going to travel through the network. The wireless networkconnects both sides and introduces some communicationproblems such as time-varying delays, packet dropouts, andpacket disorder. In the next subsections, these problems areformally described and the working mode of the controlstructure is presented.

2.1. Time-Varying Network-Induced Delays, Packet Dropouts,and Packet Disorder. As said in the previous section, dual-rate control is used in the proposed approach. Then, twodifferent periods are considered: T as the actuation periodand NT as the sensing period, with N ∈ℕ+ being the mul-tiplicity between the two periods of the dual-rate controlscheme [30]. Let us, respectively, denote ð:ÞTk and ð:ÞNT

kas a T-period and an NT-period signal or variable, wherek ∈ℕ are iterations at the corresponding period. For a

packet sampled at instant kNT , being effectively sent (i.e.,the trigger conditions hold) and not lost, the round-trip timedelay is defined as

τNTk = τNT

sc,k + τNTca,k + τNT

c,k , ð1Þ

with τNTsc,k being the sensor-to-controller network-induced

delay, τNTca,k the controller-to-actuator delay, and τNT

c,k a com-putation time delay. As a local clock is assumed to governthe different devices located at the sensor node, they can becompletely synchronized. As a consequence, in order to mea-sure the round-trip time delay, no additional time-stampingtechniques and synchronization are needed. The delay canbe measured by subtracting packet sending and receivingtimes. Note that, although a shared clock can be supposedin some WSN applications (as in this work), it might be hardto satisfy for other applications, for example, in distributedwireless sensor nodes, where an option may be to synchro-nize nodes [38].

To avoid packet disorder, in this work, it is strictlynecessary to know the maximum round-trip time delayτmax = max ðτNT

k Þ such that τmax <NT . This condition maybe relaxed by taking advantage of the Kalman filter-basedestimation techniques used in this work but additionallyrequiring the implementation of time-stamping techniquesto detect the disorder. From off-line experiences on theWSN, the statistical distribution of the round-trip time delaycan be obtained and, hence, τmax. Since, in the present work,UDP is used as the transport layer protocol, the delay

Dual-ratecontroller

Base station

Periodicevent-triggered

mechanism

Actuator+ZOH (at T)

Event-triggeredmechanism

UGV

NT

Tkv

Disturbancedynamics

Tkd

Tkw

TVDRKFˆ ˆ ˆ ˆ, ,

NT NT

k k+hwr,wl

xref , yref , 𝜃ref

wr,wl

Referencegenerator

ˆ ˆ ˆ ˆ, , , ,T T

r l r lk k+hN–1u u u u

Sensor node

SensorPure

Pursuit

,NT

r l kw w

ˆ ˆ( ) , ,NTk

NTk+h

wr,ref ,wl,ref

ˆ ˆ( )wr,ref ,wl,ref

Wirelessnetwork

Left Rightmotor motor

ˆ ˆ ˆ ˆ, , , ,T T

r lk k+hN–1dr dl d d

xref , yref , 𝜃ref

NT

kNT

k+h

, ,

( ) ( )

( )

( )

( ) ( )( ) ( )

( )

NT

sc,k𝜏

NT

sc,kd

NT

ca,k𝜏

NT

ca,kd

Figure 1: An energy-efficient control system for a WSN.

3Journal of Sensors

distribution may be approximated as a generalized exponen-tial distribution [39]. The consequent probability densityfunction can be expressed as follows:

P τNTk

� �=

1ϕe− τNT

k −ηð Þ/ϕ, if τNTk ≥ η,

0, if τNTk < η,

8><>: ð2Þ

with the variance of the delay being V ½τNTk � = ϕ2 and its

expected value being E½τNTk � = ϕ + η. The median of the delay

may be a viable choice for η, and ϕ can be deduced from ηand an experimental value of E½τNT

k �.As is well-known, if UDP is used as the transport layer

protocol, packet dropouts may appear. Since this phenome-non is basically random [32], it can be modeled as a Bernoullidistribution [40]. Let us, respectively, indicate the possiblesensor-to-controller and controller-to-actuator packet drop-outs by means of dNT

sc,k and dNTca,k. In the present work, both

cases are contemplated as a Bernoulli process, whose proba-bility of dropout is, respectively, given by psc and pca:

psc = Pr dNTsc,k = 0

h i∈ 0, 1½ Þ, ð3Þ

pca = Pr dNTca,k = 0

h i∈ 0, 1½ Þ: ð4Þ

2.2. Control Structure. Next, the two components (sensornode and base station) and the signals involved in theenergy-efficient control system are detailed.

As shown in Figure 1, the sensor node includes a UGV asthe plant to be controlled, which is composed of two motors(for the right and left wheels) and is subject to noise vTk anddisturbance dTk signals. The control action to be applied tothe right and left motors is ður , ulÞTk . The output to be sensedis the rotational velocity of both motors ðwr ,wlÞNT

k . This out-put is sent to the base station when the periodic event-triggered condition defined at the sensor device holds.

The base station includes the control algorithm, whichintegrates a time-varying dual-rate Kalman filter (TVDRKF),a Pure Pursuit path tracking algorithm (which receives thedesired path from the reference generator), and a dual-ratecontroller. In addition, an event-triggered condition isdefined in order to decide when the control signal is sent tothe actuator located at the sensor node. This condition isassessed only when a sampled output is received from thesensor. Thus, unlike the condition included at the sensor,the condition defined at the base station is not periodicallyevaluated.

Next, the proposed scenario is described (more detailscan be found in Section 3):

(i) When the periodic event-triggered condition is sat-isfied at the sensor, a new output ðwr ,wlÞNT

k is sentto the base station. If no dropout occurs in thesensor-to-controller link, dNT

sc,k = 1, the output isreceived at the base station after a delay τNT

sc,k . Then,

the control algorithm computes the number of NTperiods elapsed between the previous and currentoutputs that are received by the base station. Let usname this amount of NT periods as the multiplicitym of the TVDRKF, which relates the sensing rate1/NT to the receiving rate at the base station 1/�NT ,where �N =mN , with N being the multiplicity of thedual-rate sampled-data system. Since the data pat-tern received by the base station follows a nonuni-form scheme, the value m and, in consequence, �Nare time-varying

(ii) From �N , the gain Kð�NÞ of the TVDRKF can becalculated in order to perform the correction of theestimator, resulting in the estimate of the state,xTðk∣kÞ, where, in general, the notation xTði∣jÞ will be

used to define the estimate of the state xTi basedon the sensed process output up to time instant j,being j ≤ i

(iii) From xTðk∣kÞ, the estimated, corrected output

ðwr , wlÞNTk and a set of N-estimated values inside

the period NT for the disturbance signal that affects

each motor fðdr , dlÞTk , ðdr , dlÞ

Tk+1,⋯, ðdr , dlÞ

Tk+N−1g

can be obtained. The set of estimated values of thedisturbance will be later used by the dual-ratecontroller to finally tune the control action

(iv) From ðwr , wlÞNTk , and ðxref , yref , θref ÞNT

k , which is thepath reference, the Pure Pursuit path tracking algo-rithm calculates the rotational velocity command(dynamic reference) ðwr,ref , wl,ref ÞNT

k

(v) From ðwr , wlÞNTk and ðwr,ref , wl,ref ÞNT

k , the dual-ratecontroller is utilized to generate the set of N current,estimated control actions fður , ulÞTk , ður , ulÞTk+1,⋯,ður , ulÞTk+N−1g in order to achieve the desired controlperformance. The control signal is finally tuned bymeans of the set of N-estimated values of the distur-

bance fðdr , dlÞTk , ðdr , dlÞ

Tk+1,⋯, ðdr , dlÞ

Tk+N−1g in

order to compensate for the actual ones fdTk , dTk+1,⋯, dTk+N−1g (where a unique signal is consideredfor both motors)

(vi) From fður , ulÞTk , ður , ulÞTk+1,⋯, ður , ulÞTk+N−1g andthe model of the plant, the TVDRKF’s predictionstage can be carried out, giving xTðk+N∣kÞ. Then, the

next estimated output ðwr , wlÞNTk+1 and the next set of

estimated disturbances fðdr , dlÞTk+N , ðdr , dlÞ

Tk+N+1,

⋯, ðdr , dlÞTk+2N−1g can be calculated. From the esti-

mated output, and taking into account the nextpath reference ðxref , yref , θref ÞNT

k+1, the Pure Pursuitalgorithm gets the next dynamic referenceðwr,ref , wl,ref ÞNT

k+1. Finally, the dual-rate controller isable to compute the next set of N control actionsfður , ulÞTk+N , ður , ulÞTk+N+1,⋯, ður , ulÞTk+2N−1g from

4 Journal of Sensors

the estimated output, the dynamic reference, andthe set of estimated disturbances. By means of thish-step ahead prediction algorithm, a set of hNfuture, estimated values of the control signal fður , ulÞTk+N , ður , ulÞTk+N+1,⋯, ður , ulÞTk+hN−1g can becomputed

(vii) When the event-triggered condition at the basestation is satisfied, the current control signalfður , ulÞTk , ður , ulÞTk+1,⋯, ður , ulÞTk+N−1g and the hN future ones fður , ulÞTk+N , ður , ulÞTk+N+1,⋯,ður , ulÞTk+hN−1g are sent to the actuator in a packet.If no dropout occurs in the controller-to-actuatorlink, dNT

ca,k = 1, the whole set of control actions isreceived at the sensor node after a delay τNT

ca,k.Therefore, the actuator injects the current controlaction fður , ulÞTk , ður , ulÞTk+1,⋯, ður , ulÞTk+N−1g and

the future ones fður , ulÞTk+N , ður , ulÞTk+N+1,⋯,ður , ulÞTk+hN−1g while no new packet is receivedfor the hNT future periods. In each NT period,the actuation occurs at uniformly spaced instantskNT + lT , l = 0, 1,⋯,N − 1, under Zero OrderHold (ZOH) conditions (i.e., ður , ulÞTk is applied

at kNT , ður , ulÞTk+1 is injected at kNT + T , and

so on, up to ður , ulÞTk+N−1, which is actuated atkNT + ðN − 1ÞT). That results in a uniform actua-tion pattern f0, T ,⋯, ðN − 1ÞTg inside the sensorperiod NT . In conclusion, the working mode is touse estimated control actions when no new actualones are received by the sensor node and is toreplace the estimations with the actual actions whenthe packet is received. As external disturbance andmeasurement noise are faced by the TVDRKF, andan accurate system model is assumed, estimatedand actual values are usually very similar

3. Energy-Efficient Control Solution Design

Next, each component of the control system is defined indetail.

3.1. Plant Modeling. Considering state-space representa-tion, the model of the plant at sampling period T takesthis form:

xTp,k+1 = ApxTp,k + Bpu

Tk + Bpd

Tk ,

yTk = CpxTp,k + vTk ,

8<: ð5Þ

where, for the sake of simplicity, let us name

(i) yTk as the measurement, that is, the rotational velocityeither for the right motor wT

r,k or for the left motorwT

l,k

(ii) uTk as the control signal, regardless of the motor (uTr,kor uTl,k)

In addition, vTk is the measurement noise, dTk is the distur-bance signal, xTp,k is the process state (regardless of the motor),and Ap, Bp, and Cp are matrices with suitable dimensions.

Using Z-transform at period T , the input-output plantmodel for the control signal (input) and the measurement(output) is represented as a discrete-time transfer function:

Gp zð Þ = YT zð ÞUT zð Þ , ð6Þ

with z being the T-unit operator.Given a broadband noise ~wT

k , the disturbance dTk can be

generated through the following dynamics:

xTd,k+1 = AdxTd,k + Bd ~w

Tk ,

dTk = CdxTd,k,

(ð7Þ

where xTd,k is the disturbance state and Ad , Bd , and Cd arematrices with proper dimensions. Considering (5) and (7),the system can be augmented as follows:

xTp,k+1

xTd,k+1

" #=

Ap BpCd

0 Ad

" #xTp,k

xTd,k

" #+

Bp

0

" #uTk +

0

Bd

" #~wTk ,

yTk = Cp 0� � xTp,k

xTd,k

" #+ vTk ,

dTk = 0 Cd½ �xTp,k

xTd,k

" #:

8>>>>>>>>>>>>><>>>>>>>>>>>>>:

ð8Þ

Assuming the following notation:

A =Ap BpCd

0 Ad

" #,

B =Bp

0

" #,

B~w =0

Bd

" #,

C = Cp 0� �

,�C = 0 Cd½ �,

xTk =xTp,k

xTd,k

" #,

ð9Þ

5Journal of Sensors

the augmented system in (8) can be expressed as

xTk+1 = AxTk + BuTk + B~w ~wTk ,

yTk = CxTk + vTk ,

dTk = �CxTk ,

8>><>>: ð10Þ

that admits a lifted representation [41] such as

xTk+N = ANxTk + 〠N−1

c=0AN−1−cBuTk+c + 〠

N−1

c=0AN−1−cB~w ~w

Tk+c,

yTk = CxTk + vTk ,

8>><>>:

ð11Þ

which can be equivalently seen as a dual-rate sampled-datasystem, where the output at period NT , yNT

k , is obtained froma sequence of inputs at period T , fuTk , uTk+1,⋯, uTk+N−1g.3.2. Event-Triggered Conditions. Let us denote βNT

k ∈ f0, 1g asthe scheduling variable at the sensor. When βNT

k = 1, the sen-sor data yNT

k is transmitted, and when βNTk = 0, no transmis-

sion is carried out. The variable �yNTk is used to store the latest

sensor data in such a way that

�yNTk = βNT

k yNTk + 1 − βNT

k

� ��yNTk−1, for k ∈ℕ≥1, ð12Þ

where �yNT0 = yNT

0 . By means of a discrete-time version of theso-called mixed triggered mechanism [42] based on the pro-cess output yNT

k , the periodic event-triggered condition at thesensor can be implemented. In this way, the measurementyNTk is sent to the base station through the network (i.e.,βNTk = 1) when

�yNTk−1 − yNT

k

�� ��2 > σs yNTk

�� ��2 + δs, for k ∈ℕ≥1, ð13Þ

where �yNT0 = yNT

0 and σs and δs are positive constants.Note that usually, σs is chosen to take values close to zeroor even zero (in any case, smaller than one) [43].

When βk = 1, the control algorithm calculates the controlsignal fuTk , uTk+1,⋯, uTk+hN−1g. Let us denote γk ∈ f0, 1g as thescheduling variable for the control signal. When γk = 1, thesignal is transmitted, and when γk = 0, no transmission is car-

ried out. The variable �uTk is used to store the first value uTk ofthe last sent control signal in such a way that

�uTk = γkuTk + 1 − γkð Þ�uTk−1, for k ∈ℕ≥1, ð14Þ

where �uT0 = uT0 . By means of the following mixed trig-gered mechanism, the control signal is transmitted to thesensor node:

�uTk−1 − uTk��� ���2 > σc uTk

�� ��2 + δc, for k ∈ℕ≥1, ð15Þ

where �uT0 = uT0 and σc and δc are positive constants. As previ-ously commented with regard to the choice of σs, note thattypically σc is chosen to be less than one.

Observe that the feedback loop is only closed from sensornode to base station and back to sensor node, when theconditions (13) and (15) hold (and, hence, βk = γk = 1). Ifone of them is not satisfied (i.e., βk = 0 or γk = 0), thenthe control signal is not updated. Nevertheless, the futurecontrol actions fuTk+N ,⋯, uTk+hN−1g, which were previouslysent, can be used by the actuator in order to keep satisfactorycontrol properties.

3.3. Time-Varying Dual-Rate Kalman Filter. Considering ~wTk

and vTk as zero-mean white noises for the single-rate systemin (10), the best linear estimation for xTk in the sense of meansquare error is provided by the conventional Kalman filter[44]. When different rates are involved in the control system,a multirate Kalman filter containing corrections and predic-tions [45] is required. In our work, dual-rate control and peri-odic event-triggered control (PETC) are integrated in orderto save system resources (energy and bandwidth). As a conse-quence of using PETC, not all the measurements are sent tothe base station, which results in a time-varying dual-rateKalman filter (TVDRKF) [24–26]. From Extended StateObserver (ESO) [46] and multirate Kalman filter [45, 47]techniques, the proposed TVDRKF is able to estimate theplant measurement and disturbance, following a nonuni-form dual-rate scheme.

Taking into account (13), the outputs sampled at the slowrate 1/NT arrive at the base station at a slower rate 1/�NT in anonuniform fashion. The multiplicity m = �N/N of theTVDRKF was previously introduced in Section 2. It can benow enunciated from the previous output received by thebase station �yNT

k−1 (which was sampled in time, say, klsNT)and the current received output �yNT

k = yNTk . Hence,

m = k − kls: ð16Þ

Due to the nonuniform nature of the pattern, m andin consequence �N will be time-varying. From the currentreceived output, the TVDRKF can perform the correction(and filtering) stage and then the hN-step ahead statepredictions at the fast rate 1/T . In order to do it, thelifted representation in (11) can be taken, replacing N with�N =mN .

From the notation xTði∣jÞ introduced in Section 2, which is

used to denote the estimate of the state xTi based on the out-put previously sensed at instant j, the correction and

6 Journal of Sensors

prediction stages of the TVDRKF can be designed as follows(illustrated in Figure 2):

(i) Correction stage: when a new measurement yNTk c is

available at time kNT , it can be used to make correc-tion for the prediction xNT

ðk∣kÞ. Expressing this stage atperiod T results in

xTk∣kð Þ = xTk∣k−�Nð Þ + K �N� �

yTk − CxTk∣k−�Nð Þh i

, ð17Þ

where, from multirate Kalman filter design techniques, thetime-varying Kð�NÞ can be calculated:

K �N� �

=Mk+1Ct CMk+1C

t + V� �−1,

Mk+1 = A�NMk A

�N� �t

+We

− A�NMkC

t CMkCt + V

� �−1CMkCt A

�N� �t

,

ð18Þ

where ð·Þt denotes transpose function, V = CovðvÞ, and

We = Cov 〠�N−1

c=0A

�N−1−cB~w ~wk+c

!

= Cov weð Þ = E wewte

= 〠

�N−1

c=0A

�N−1−cB~w

!W 〠

�N−1

c=0A

�N−1−cB~w

!t

,

ð19Þ

where Ef·g denotes the expectation and W = Covð~wÞ.

(ii) Prediction stage: when no new measurement is avail-able between the previous sensed output yNT

k and thenext sensed output yNT

k+m (or, equivalently at period T ,between the previous sensed output yTk and the nextsensed output yTk+�N), the best estimates xTðk+ljkÞ, l = 1,⋯, hN , are obtained from the open-loop dynamic-based prediction:

xTk+l kjð Þ = AlxTk kjð Þ + 〠l−1

c=0Al−1−cBuTk+c, ð20Þ

where hmust be defined to fulfill hN ≥ �Nmax, with �Nmax beingthe maximum value of �N . This definition ensures the compu-tation of TVDRKF’s correction stage, since the requiredahead state xTðk+�NjkÞ will be available. Moreover, from (20),

the set of hN-estimated outputs and disturbances (regardlessof the motor) can be calculated:

yTk+lð Þ = CxTk+l kjð Þ,

dTk+lð Þ = CxTk+l kjð Þ:

ð21Þ

3.4. Pure Pursuit Path Tracking Algorithm. From the desiredkinematic reference ðxref , yref , θref ÞNT

k and the plant outputgenerated by the TVDRKF at period NT , yNT

k , which is com-posed of corrected estimations obtained when measurementsare received by the base station (i.e., when the condition (13)holds and, hence, βk = 1), the Unmanned Ground Vehicle(UGV) is able to infer its current position using a path track-ing algorithm. In this work, Pure Pursuit via odometry tech-nique is chosen. Basically, the Pure Pursuit algorithm tries todetermine the velocity and turning conditions at every timeinterval so that the UGV follows a prescribed trajectory[48]. Odometry is the simplest way for dead reckoning imple-mentation, which is a method used to compute the vehicle’scurrent position from a previous position, knowing

TVDRKF

NTkyCorrection/filtering

stage( | )ˆTk kx

Output and disturbancecalculation

Predictionstage

(k+1|k) (ˆ ˆ, ,T Tk+hN|)kx x

( | )ˆT

k+N kx

ˆ ˆ, ,T Tk k+hN–1u u

ˆ ˆ, ,T Tk k+hNy y ˆ ˆ, ,T T

k k+hNd d

Figure 2: Structure of the time-varying dual-rate Kalman filter.

7Journal of Sensors

additionally in advance the robot speed and path in a certainperiod of time. Odometry is usually based on motor rotationconsidering their encoder measurements.

The path tracking algorithm generates the dynamic refer-ence based on the rotational velocity for both wheels, i.e.,ðwr,ref , wl,ref ÞNT

k ≡ yNTref ,k, in order to properly reach the next

point of the desired trajectory. The UGV path trackingis composed of a set of h future dynamic referencesfyNT

ref ,k, yNTref ,k+1,⋯, yNT

ref ,k+hg. In order to establish these refer-ences, the trajectory that must be followed by the UGV isrequired to be known in advance. This task is developed bythe reference generator, which is in charge of providing thePure Pursuit algorithm with the sequence of h-step aheadkinematic references fðxref , yref , θref ÞNT

k , ðxref , yref , θref ÞNTk+1,

⋯, ðxref , yref , θref ÞNTk+hg.

3.4.1. Differential Kinematics. While direct kinematics spec-ifies the positions that the UGV is able to reach by givingthe wheel speed, differential kinematics establishes relationsbetween motion (velocity) in joint space and motion (linear/-angular velocity) in task space (e.g., Cartesian space). A two-wheel UGV rotates with respect to a point located in someplace of the axis, which is shared by the two wheels. Thispoint is known as Instantaneous Rotation Center (IRC), thatis, the point with zero velocity at a particular instant of timein a body undergoing planar movement. IRC varies accord-ing to wheel speed variations.

Each wheel follows a trajectory with the same rotationalvelocity ωR with respect to the IRC. This fact implies thatthe linear velocity of the wheels are

vr = ωR R +l2

� �, ð22Þ

vl = ωR R −l2

� �, ð23Þ

where vr and vl are, respectively, the linear velocity forthe right and left motors, l is the distance between thetwo wheels, and R is the distance between the IRC andthe middle point of the distance between the wheels.Therefore,

R =l2⋅vl + vrvr − vl

, ð24Þ

and the rotational velocity of the robot ωR is

ωR =vr − vl

l: ð25Þ

3.4.2. Path Tracking Algorithm. The Pure Pursuit algo-rithm is based on the computation of the curvature �γ that avehicle must adopt from its current position (x, y) to a targetposition (x + Δx, y + Δy). As depicted in Figure 3, for thispurpose, a circle of radius r that joints both points is defined.

The center of the circle is placed in x + Δx + d. In addition,the distance to the target point is L. Therefore, it is possibleto express

r = Δx + d,

L2 = Δxð Þ2 + Δyð Þ2,ð26Þ

being the curvature

�γ =Δxð Þ2 + Δyð Þ2

2Δx, ð27Þ

and the so-called Pure Pursuit control law:

�k =1�γ=2ΔxL2

: ð28Þ

As can be seen, the control law �k is proportional to thelateral shift and inversely proportional to the square of L.Assuming robot coordinates for the current position(xR, yR) and for the target, reference position (xR,ref , yR,ref ),and the angle θR as the current vehicle heading, the PurePursuit control law �k can be expressed as follows:

�k = 2yR,ref − yR� �

cos θRð Þ − xR,ref − xRð Þ sin θRð ÞxR,ref − xRð Þ2 + yR,ref − yR

� �2 : ð29Þ

Δy

Δx dx

rL

Targetpoint

y

Figure 3: Circumference between the current point and the targetpoint.

8 Journal of Sensors

For a desired linear velocity vref , the rotational velocityreference wref can be calculated as

ωref = vref�k: ð30Þ

The path tracking algorithm requires determining onepoint located at a minimum distance from the currentpoint, i.e., the so-called Look Ahead Distance (LAD), notconsidering the nearest points in the prescribed trajectory.This procedure avoids a severe correction, and hence, itleads to a soft movement.

Finally, these are the steps to be followed when the mainloop of the Pure Pursuit algorithm is implemented (depictedin more detail in Figure 4):

(1) UGV rotational and linear velocity calculationfrom system output estimations and correctionsprovided by the TVDRKF at period NT (i.e.,calculation of ωNT

R,k and vNTR,k , respectively, from

wNTr,k and wNT

l,k ,that is, yNTk ). This is obtained from

(22), where R + l/2 ≈ r, with r being the wheel radius,and (25):

(2) UGV position and orientation computation in thetime period NT :

xNTR,k = xNT

R,k−1 + vNTR,k NT cos θNT

R,k−1 + ωNTR,k NT

� �, ð32Þ

yNTR,k = yNT

R,k−1 + vNTR,k NT sin θNT

R,k−1 + ωNTR,k NT

� �, ð33Þ

θNTR,k = θNT

R,k−1 + ωNTR,k NT , ð34Þ

for k ∈ℕ≥1, where xNTR,0 , yNT

R,0 , and θNTR,0 are the initial position

and orientation.

(3) Generation of the future reference for the robot,ðxR,ref , yR,ref ÞNT

k: from the desired kinematic reference

and the Look Ahead Distance (LAD), the nearestpoint to the future path tracking that is located faraway from the LAD is calculated

(4) Control law computation: from ðxR,ref , yR,ref ÞNTk

and

ðxR, yR, θRÞNTk , the control law �k is computed at

period NT by using (29), and then, ωNTref is calculated

for each wheel by using (30) and from a desired vNTref

Finally, from these data, ðwr,ref , wl,ref ÞNTk ≡ yNT

ref ,k canbe calculated:

wr,refð ÞNTk =

vNTref + ωNT

ref br

,

wl,refð ÞNTk =

vNTref − ωNT

ref br

:

ð35Þ

PurePursuit

Rotational and linearvelocity calculation

Future referencegeneration

Position andorientation computation

ˆ ˆ, ,NT NT

k k hy y

, ,NT NTR,k R,k+hv v , ,NT NT

R,k R,k+hw w

Control lawcomputation

LAD

ˆ ˆ, ,NT NT

ref,k ref,k+hy y

xref,yref,𝜃ref

xref,yref,𝜃ref

NT

kNT

k+h

, ,( )

( )ˆ ˆ( ) , ,NT

k

NTk+h

xR,ref,yR,ref

ˆ ˆ( )xR,ref,yR,ref

xR,yR,𝜃RNT

kNT

k+h

, ,(

xR,yR,𝜃R(

)

)

Figure 4: Structure of the Pure Pursuit path tracking algorithm.

vNTr,k = wNT

r,k r,

vNTl,k = wNT

l,k r,

vNTR,k =

vNTr,k + vNT

l,k2

,

ωNTR,k =

vNTr,k − vNT

l,kl

:

ð31Þ

9Journal of Sensors

3.5. Dual-Rate Controller. In this work, in order to reach thedesired control performance, a dual-rate controller is used.From NT-period signals such as the dynamic referenceyNTref ,k generated by the Pure Pursuit path tracking algorithmand the estimated, corrected output yNT

k obtained by theTVDRKF, the dynamic dual-rate controller computes N con-trol actions at period T for each wheel, UT

k = fuTk , uTk+1,⋯,uTk+N−1g. This control signal is finally tuned by adding the dis-turbance estimations generated by the TVDRKF at period T ,

fdTk , dTk+1,⋯, dTk+N−1g. Following this operation mode for the

next h dynamic references and outputs, fyNTref ,k+1,⋯, yNT

ref ,k+hgand fyNT

k+1,⋯, yNTk+hg, respectively, and the next hN distur-

bances fdTk+N ,⋯, dTk+hN−1g, the set of future control actionsfuTk+N ,⋯, uTk+hN−1g can be obtained.

Different alternatives can be followed to design a dual-rate controller (see, e.g., in [29, 30]). In this case, themodel-based dual-rate controller design described in [29]is chosen, where the structure of the controller includes(see in Figure 5) the following:

(i) a slow-rate subcontroller GNT1 ðzNÞ = uNT

1,k /eNTk

(ii) a digital hold HNT ,TðzÞ = uT1,k/½uNT1,k �T

(iii) a fast-rate subcontroller GT2 ðzÞ =UT

k /uT1,k

where the input of GNT1 ðzNÞ is the error signal eNT

k = yNTref ,k −

yNTk , and note that the output of GNT

1 ðzNÞ (i.e., uNT1,k ) is

expanded ½uNT1,k �T before being injected to the digital hold

HNT ,TðzÞ. The expanded operation implies filling the slow-rate signal with zeros at the fast-rate instants (more detailscan be found in [29]). Then, the digital hold obtains its out-put uT1,k by means of

HNT ,T zð Þ = 1 − z−N

1 − z−1, ð36Þ

which in conclusion results in the subcontroller output uNT1,k

repeated N times. From the consideration of MðsÞ as thedesired closed-loop control performance of the original

continuous-time system design, the subcontrollers GNT1 ðzNÞ

and GT2 ðzÞ will be designed as follows:

GNT1 zN� �

=1

1 −M zNð Þ , ð37Þ

GT2 zð Þ = M zð Þ

Gp zð Þ , ð38Þ

where GpðzÞ was presented in (6) and comes from the discre-tization of the continuous-time plant model at period Tunder ZOH conditions and MðzÞ and MðzNÞ are the discre-tization of MðsÞ at periods T and NT , respectively, usingZOH techniques as well. This procedure leads to a behaviorthat perfectly matches MðsÞ in the sample points at periodNT , but sometimes (ifNT is too large), it can introduce a rip-ple between samples. The way to overcome this ripple is alsodescribed in [29], and it is based on modifying the fast-ratesubcontroller design in this way:

GT2 zð Þ = GR zð Þ

1 +GR zð ÞGp zð Þ , ð39Þ

with GRðzÞ being the discrete-time version at period T of theoriginal continuous-time controller design. By using (39), thedual-rate controller does not cancel the numerator of the pro-cess transfer function GpðzÞ, avoiding the ripple.

4. Cost Indexes for Control Performance andResource Usage

In this section, certain cost indexes closely related to controlperformance and resource usage will be presented. By meansof these indexes, the energy-efficient control proposal may becompared with the conventional time-triggered control strat-egy. Regarding control performance, similar to [49], thesethree cost indexes will be used:

(i) J1, which is based on the ℓ2-norm and with a goalto provide a measure about how accurately the pathis followed:

Dual-ratecontroller

ˆ ˆ, ,NT NTk k+hy y

ˆ ˆ, ,T Tku uˆ ˆ, ,NT NT

ref,ky y

+–

1 (zN)NTG ( )NT,TH z 2 ( )TG z +–

ˆ ˆ, ,T Tk k+hN–1

d d

Expandref,k+h k+hN–1

Figure 5: Structure of the dual-rate controller.

10 Journal of Sensors

J1 = 〠l

k=1min1≤k′≤l

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixNTR,k − xNT

ref ,k′

� �2+ yNT

R,k − yNTref ,k′

� �2r, ð40Þ

where l is the number of iterations required by the UGV toreach the final point of the path; ðxR, yRÞNT

k is the currentUGV position, which was defined in (32) and (33); andðxref , yref ÞNT

k′ is the nearest kinematic position reference to

the current UGV position

(ii) J2, which is based on the ℓ∞-norm and is defined toknow the maximum difference between the desiredpath and the current UGV position:

J2 = max1≤k≤l

min1≤k′≤l

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixNTR,k − xNT

ref ,k′

� �2+ yNT

R,k − yNTref ,k′

� �2r ),

(ð41Þ

(iii) J3, which measures the total amount of time (in sec-onds) elapsed to arrive at the final destination:

J3 = lNT: ð42Þ

To analyze the reduction of the resource usage in theenergy-efficient control solution compared to the traditionaltime-triggered control, the cost index J4 is defined by makinguse of the number of transmitted packets (NoT) in eachcase: NoTEEC for the energy-efficient control and NoTTTCfor the time-triggered control. In this way, J4 (in %) canbe expressed as

J4 =NoTEECNoTTTC

⋅ 100%: ð43Þ

5. Simulation Results via TrueTime

In this section, the main advantages of the energy-efficientcontrol solution compared to the time-triggered one will beshown. The study will be focused on the trade-off betweenresource usage and control properties. The section is splitinto two parts. Firstly, important data used for the simulationwill be presented (transfer function, delay distribution, con-trol parameters, and so on). Secondly, the cost indexes intro-duced in Section 4 will be evaluated by means of a TrueTimeapplication [37].

5.1. Application Data. Considering a similar model for bothwheel motors, the model is described by means of this trans-fer function:

Gp sð Þ = 0:12760:1235s + 1

, ð44Þ

where the output is in rad/s, and the input in V.From previous off-line experiences on this WSN frame-

work [49], different round-trip time delay distributions,

which can be modeled such as in (2), lead to considering amaximum time delay τmax slightly less than 200ms. Then,as commented in Section 2.1, the sensor period is chosen asNT = 0:2 s in order to ensure no packet disorder. As it willbe later detailed, in this case, choosing N = 2 allows theUGV to accurately track the path.

In this simulation, let us assume the packet dropout prob-ability as psc = 0:1 and pca = 0:3 in (3).

The discrete-time controller design comes from the dis-cretization at different periods of this continuous-time PIDcontroller, which is designed following classical procedures[50, 51] and this typical configuration:

u tð Þ = Kp e tð Þ + 1Ti

ðt0e τð Þdτ

� �, ð45Þ

where Kp = 6 and Ti = 0:12 in order to achieve some specifi-cations. The single-rate controllers are

GNTr zN� �

=6z + 4z − 1

, ð46Þ

GTr zð Þ = 6z − 1

z − 1, ð47Þ

The dual-rate controller is obtained by means of (37) and(39), bringing about

GNT1 zN� �

=z2 − 0:4734z + 0:05731z2 − 1:191z + 0:1914

, ð48Þ

GT2 zð Þ = 6:576z2 − 5:78z + 1:27

z2 − 0:9578z + 0:2394: ð49Þ

The disturbance, which is defined at period T as in (7), is

Ad =0:9993 0:09994

−0:0142 0:9985

" #, ð50Þ

Bd =3:769 ⋅ 10−5

0:7535 ⋅ 10−3

" #,

Cd = 0 1 ⋅ 105� �

:

ð51Þ

The time-varying dual-rate Kalman filter (TVDRKF) isdesigned considering the augmented state resulting fromthe consequent state-space realization (5) for (44) and fromthe disturbance (50).

The positive constants in (13) and (15) for the event-triggered conditions will be, respectively δs = 0:01 and σs = 0and δc = 0:5 and σc = 0.

Finally, the reference to be followed includes a sequenceof four right angles.

5.2. TrueTime Simulation and Cost Function Evaluation.Starting from a time-triggered single-rate control scenariowith neither noise nor disturbance and neither time-varyingdelays nor packet dropouts and using the controller at periodNT = 0:2 s in (46), some performance worsening is observed

11Journal of Sensors

when the UGV tries to track the path (depicted in Figure 6)compared to the single-rate version at period T = 0:1 s in(47) (shown in Figure 7). Let us consider the performancereached at period T as the nominal, desired one. Taking intoaccount the dual-rate controller in (48) and (49), the time-

triggered dual-rate control system is able to maintain a satis-factory control performance, very similar to the nominal one(as shown in Figure 8). But, including time-varying delaysand packet dropouts, the performance is clearly worsened,becoming unstable (see in Figure 9).

If the TVDRKF is incorporated into the time-triggereddual-rate control system, where packet-based control is alsointegrated, the performance is clearly improved (illustratedin Figure 10), being very similar to the nominal one, despiteadditionally including both measurement noise and externaldisturbance. Figure 11 shows that the disturbance estimationaccurately follows the actual disturbance.

Finally, event-triggered conditions are added to theWSN,and then, the system becomes a periodic event-triggered dual-rate control system. The performance obtained is similarto that reached by the time-triggered version of the system(see in Figure 12), but now a clear reduction of the number oftransmitted packets is achieved, which leads to reducingresource usage (bandwidth, energy).

To analyze the previous conclusions in more detail, thecost indexes presented in Section 4 are calculated for eachscenario. Table 1 shows these results, where each scenario isrepresented by the following letters:

(i) a: time-triggered single-rate control scenario atperiod NT

(ii) b: time-triggered single-rate control scenario atperiod T

(iii) c: time-triggered dual-rate control scenario

(iv) d: time-triggered dual-rate control scenario, addingTVDRKF, and packet-based control

X (m)

–200

0

200

400

600

800

1000

1200

Time-trig. single-rate NT = 0.2 s

ReferenceOutput

0 500 1000 1500 2000

Y (m

)

Figure 6: Time-triggered single-rate control at periodNT (no noise,no disturbance, no delays, and no dropouts).

ReferenceOutput

X (m)

–200

0

200

400

600

800

1000

1200

Y (m

)

Time-trig. single-rate T

0 500 1000 1500 2000

= 0.1 s (nominal performance)

Figure 7: Time-triggered single-rate control at period T (no noise,no disturbance, no delays, and no dropouts). Nominal performance.

ReferenceOutput

X (m)

–200

0

200

400

600

800

1000

1200

Y (m

)

Time-trig. dual-rate NT = 0.2 s, N = 2

0 500 1000 1500 2000

Figure 8: Time-triggered dual-rate control (no noise, nodisturbance, no delays, and no dropouts).

12 Journal of Sensors

(v) e: periodic event-triggered dual-rate control sce-nario, with TVDRKF, and packet-based control

As previously commented, the desired, nominal perfor-mance is presented by scenario b, and hence, J1, J2, and J3show the reference values to carry out the comparison. As

expected, scenario a shows the worst J1, since the desired tra-jectory is inaccurately followed by the UGV. Scenarios c andd show a similar J1 than scenario b (even 1% better). Scenarioe worsens this index J1 by around 13%. Regarding index J2, itis worsened by around 16% by every scenario compared tothe nominal performance. However, J3 presents the same

ReferenceOutput

X (m)

–1000

–500

0

500

Y (m

)

Time-trig. dual-rate NT = 0.2 s, N = 2 (delays, dropouts)

0 500 1000 1500 2000

Figure 9: Dual-rate time-triggered control (no noise and nodisturbance but with delays and dropouts).

ReferenceOutput

X (m)

–200

0

200

400

600

800

1000

1200

Y (m

)

Time-trig. dual-rate, TVDRKF, packet-based

0 500 1000 1500 2000

Figure 10: Time-triggered dual-rate control, with TVDRKF, andpacket-based control (noise, disturbance, delays, and dropouts).

t

–15

–10

–5

0

5

10Disturbance estimation by TVDRKF

ActualEstimated

0 20 40 60 80 100 120(s)

Figure 11: Disturbance estimation by TVDRKF.

ReferenceOutput

0 500 1000 1500 2000X (mm)

–200

0

200

400

600

800

1000

1200

Y (m

m)

Periodic event-trig., TVDRKF, packet-based

Figure 12: Periodic event-triggered dual-rate control, withTVDRKF, and packet-based control (noise, disturbance, delays,and dropouts).

13Journal of Sensors

value for cases c, d, and e, being 1% worse for scenario a.Finally, as expected, J4 presents the worst case in scenario b,being 50% reduced compared with scenarios a and cbecause of the network sampling being two times slowerand even a bit more than 50% of the reduction (around52%) in scenario d, due to the additional packet dropouts.Scenario e reaches the best value for index J4 with around75% of reduction.

As a summary, the proposed control approach is able tosignificantly reduce resource usage (around 75%) while keep-ing satisfactory control properties, which is only worsened byaround 15% on average, and despite the existence of wirelesscommunication problems such as time-varying delays andpacket dropouts.

6. Conclusions

The proposed energy-efficient control solution for a UGV ina WSN enables lessening the amount of transmissionsthrough the network, which results in bandwidth and batterysaving, despite keeping a satisfactory system performance.The solution integrates dual-rate control, periodic event-triggered control, packet-based control, and time-varyingdual-rate Kalman filter-based prediction techniques. Addi-tionally, the approach deals with wireless communicationproblems (such as time-varying delays, packet dropouts, andpacket disorder) and copes with a realistic scenario, wheremeasurement noise and external disturbance can occur.

Data Availability

The data can be provided under petition.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research work has been developed as a result of amobility stay funded by the Spain Visiting Fulbright ScholarProgramme of the Fulbright Commission and the SpanishMinistry of Education under “Programa Estatal de Promo-ción del Talento y su Empleabilidad en I+D+i, SubprogramaEstatal de Movilidad, del Plan Estatal de Investigación Cien-tífica y Técnica y de Innovación 2013-2016.” In addition, theresearch was funded in part by Grant RTI2018-096590B-I00from the Spanish Government and by the European Com-mission as part of Project H2020-SEC-2016-2017—topic:SEC-20-BES-2016—ID: 740736—“C2 Advanced Multi-

domain Environment and Live Observation Technologies”(CAMELOT). Part WP5 supported by Tekever ASDS,Thales Research and Technology, Viasat Antenna Systems,Universitat Politècnica de València, Fundação da Faculdadede Ciências da Universidade de Lisboa, Ministério da DefensaNacional-Marinha Portuguesa, Ministério da AdministraçãoInterna Guarda Nacional Republicana.

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Table 1: Cost indexes.

Index a b c d e

J1 1671.8 1043.4 1029.9 1030.0 1184.4

J2 44.55 38.76 44.33 44.33 44.97

J3 22.4 s 22.0 s 22.0 s 22.0 s 22.0 s

J4 50% 100% 50% 48.18% 26.13%

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