Energy Modeling and Power Measurement for Mobile Robots

Article Energy Modeling and Power Measurement for Mobile Robots

Linfei Hou 1, Liang Zhang 1,* and Jongwon Kim 2

1 School of Mechanical, Electrical and Information Engineering, Shandong University (Weihai), Weihai 264209, China; [email protected] 2 Department of Electromechanical Convergence Engineering, Korea University of Technology and Education, Cheonan 31253, Korea; [email protected] * Correspondence: [email protected]; Tel.: +86-130-6118-7255

Received: 20 October 2018; Accepted: 21 December 2018; Published: 22 December 2018

Abstract: To improve the energy efficiency of a mobile robot, a novel energy modeling method for mobile robots is proposed in this paper. The robot can calculate and predict energy consumption through the energy model, which provides a guide to facilitate energy-efficient strategies. The energy consumption of the mobile robot is first modeled by considering three major factors: the sensor system, control system, and motion system. The relationship between the three systems is elaborated by formulas. Then, the model is utilized and experimentally tested in a four-wheeled Mecanum mobile robot. Furthermore, the power measurement methods are discussed. The energy consumption of the sensor system and control system was at the milliwatt level, and a Monsoon power monitor was used to accurately measure the electrical power of the systems. The experimental results showed that the proposed energy model can be used to predict the energy consumption of the robot movement processes in addition to being able to efficiently support the analysis of the energy consumption characteristics of mobile robots.

Keywords: robot energy modeling; energy measurements; energy consumption; mobile robot

1. Introduction Robotics is undergoing a major transformation in scope and dimension. From a largely dominant industrial focus, robotics is rapidly expanding into human environments and is vigorously engaged in new challenges [1,2]. In order to work better in complex situations, these robots are mobile and driven by batteries [3]. Mobile robots are widely used in modern manufacturing systems, while their use is also extending into human daily life [4]. Mobile robots are limited by heavy and expensive batteries, which makes energy efficiency a key constraint on robot performance. Thus, modeling and managing energy consumption is of vital importance to predict the lifetime and range of autonomous platforms. It is of great significance to study the energy consumption of mobile robots [5,6]. The energy problem of mobile robots has been paid more attention in order to meet requirements of reducing energy consumption. The energy consumption modeling of mobile robots [7] based on mathematical formulas can be more scientific to study the influence of operation states on energy consumption, which provides a guide to facilitate energy-efficient strategies [8]. Firstly, the robot itself can clearly understand the energy required for the robot’s motion and the specific energy consumption of each part; therefore, the energy consumption can be reduced according to different situations and the existing energy support can be estimated. Still, recent publications have adopted very different methods when it comes to the calculation of energy consumption. Many authors have attempted to achieve this through modifications in trajectory planning, control, or mechanical design [9–13].

Energies 2019, 12, 27; doi:10.3390/en12010027 www.mdpi.com/journal/energies EnergiesEnergies2019 2018, ,12 10,, 27 x FOR PEER REVIEW 2 ofof 1515

A novel method of energy consumption modeling is proposed in this paper. The method involvesA novel dividing method the of energy energy consumption modelingof the robot is proposed into three in parts: this paper. the sensor The method system, involves control dividingsystem, and the energymotion consumption system. The ofblock the robotdiagram into of three the parts:system the is sensorshown system, in Figure control 1. Figure system, 1a andrepresents motion the system. electrical The energy block diagram transmission of the and system Figure is shown1b represents in Figure the1 .signal Figure transmission1a represents during the electricalthe robot’s energy work. transmission and Figure1b represents the signal transmission during the robot’s work.

(a) (b)

FigureFigure 1. 1.Block Block diagram diagram of of the the system. system. ( (aa)) Electrical Electrical energy energy transmission; transmission; ( b(b)) Signal Signal transmission. transmission.

TheThe electrical electrical power power measurement measurement tools tools accurately accurately measure measure the the speciﬁc specific electrical electrical power power of of the the threethree parts parts and and then then give give a a complete complete mathematical mathematical formula formula to to summarize summarize the the energy energy consumption consumption of theof the robot robot in various in various situations. situations. ThisThis model model waswas utilized utilized andand experimentallyexperimentally testedtested inin aa four-wheeledfour‐wheeled MecanumMecanum mobilemobile robot.robot. TheseThese typestypes of robots robots can can move move sideways, sideways, turn turn on onthe the spot, spot, and andfollow follow complex complex trajectories trajectories [14]. These [14]. Theserobots robots are capable are capable of easily of easily performing performing tasks tasks in environments in environments with with static static and anddynamic dynamic obstacles obstacles and andnarrow narrow aisles aisles [15]. [The15]. electrical The electrical power power of the sensor of the sensorsystem systemand control and system control was system at the was milliwatt at the milliwattlevel, and level, a Monsoon and a Monsoon power monitor power monitor was used was to used accurately to accurately measure measure the electrical the electrical power power of the of thesystems. systems. The The electrical electrical power power of ofthe the motion motion system system was was at at the the watt watt level, level, and aa RigolRigol DP1308ADP1308A programmableprogrammable direct direct current current (DC) (DC) power power supply supply (RIGOL (RIGOL Technology Technology Co., Co., Ltd., Ltd., Beijing, Beijing, China) China) was was usedused to to measure measure the the motion motion system. system.

2. Related Works 2. Related Works WithWith thethe aimaim ofof energy energy consumption consumption minimizationminimization inin robots,robots, manymany publishedpublished worksworks havehave describeddescribed effective effective methods methods to to achieve achieve this this goal. goal. AnAn energy energy modeling modeling method method by by measuring measuring the the total total power power for for an an industry industry robot robot was was proposed proposed byby Xu Xu et et al. al. [ [8].8]. ThisThis methodmethod avoidsavoids thethe problemproblem ofof directlydirectly measuringmeasuring relevant relevant parameters parameters inside inside the the robot.robot. The The main main content content of of this this method method is is joint joint torque torque modeling, modeling, and and the the parameter parameter estimation estimation is is one one ofof the the most most important important steps steps in in the the process process of of the the torque torque modeling. modeling. VerstratenVerstraten et et al. al. [ 9[9]] studied studied how how well well different different modeling modeling approaches approaches commonly commonly foundfound inin thethe literatureliterature cancan predict the the energy energy consumption consumption of of a ageared geared DC DC motor motor performing performing a dynamic a dynamic task. task. The Theresults results from from their their work work serve serve to toaid aid designers designers in in deciding deciding which which elements elements to to include include in their model,model, whetherwhether their their purpose purpose is is to to compare compare designs designs or or to to obtain obtain an an actual actual estimate estimate of of the the consumed consumed power. power. InIn References References [16 [16,17],,17], energy energy optimization optimization was was investigated investigated by hardwareby hardware replacements. replacements. Using Using low powerlow power hardware hardware can reduce can reduce the overall the overall electrical electrical energy energy consumption consumption of the of robot. the robot. BukataBukata etet al. al. [ 18[18]] studied studied the the energy energy optimization optimization of of industrial industrial robotic robotic cells, cells, which which is is essential essential forfor sustainablesustainable productionproduction inin thethe longlong term. term. AA holisticholistic approachapproach thatthat considersconsiders aa roboticrobotic cellcell asas aa wholewhole robot robot was was proposed proposed in orderin order to minimize to minimize energy energy consumption. consumption. The mathematical The mathematical model, model, which considerswhich considers various robotvarious speeds, robot positions, speeds, positions, power-saving power modes,‐saving and modes, alternative and ordersalternative of operations, orders of canoperations, be transformed can be into transformed a mixed-integer into a linear mixed programming‐integer linear formulation programming that is,formulation however, suitable that is, onlyhowever, for small suitable instances. only for To small optimize instances. complex To robotic optimize cells, complex a hybrid robotic heuristic cells, accelerated a hybrid heuristic method usingaccelerated multicore method processors using multicore and the Gurobi processors simplex and the method Gurobi for simplex piecewise method linear for convex piecewise functions linear wasconvex implemented. functions was implemented.

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A European Commission-funded research project developed a novel generation method for energy-efficient direct current (DC)-supplied robots to overcome current industrial robots’ energetic limitations and to leverage the exchange, storage, and recovery of energy at the factory level. The novel DC-supplied robots developed with the AREUS project (www.areus-project.eu) may enable DC industrial smart grids with full regenerative bidirectional DC power flow and the seamless integration of renewable energy sources [19]. Many research works have achieved the goal of saving energy through trajectory optimization [20–22]. Xie. et al. studied the online minimum-energy trajectory planning of both nonholonomic and holonomic drives on a straight-line path. Their energy cost function is the sum energy drawn from the onboard batteries and includes energy dissipation by the motor armature, the energy over-coming frictions, and the kinetic energy of the robot. A closed-form solution of the minimum-energy rotational velocity trajectory was found using Pontryagin’s minimum principle, and the minimum-energy translational velocity trajectory was found using a new researching algorithm. Their results showed that following the same straight-line path via different velocity profiles consumed different amounts of energy. However, their studies were restricted to straight-line paths and stationary states in the beginning and at the end, and hence became less practical for autonomous navigation [21]. Bartlett et al. proposed a probabilistic, data-driven approach to estimating the energy consumption of a mobile robot on a set of trajectories, whether they have been traversed or not. In particular, the robot was treated as a black box, thereby removing the reliance on often unavailable system characteristics. They measured the consumption directly on the routes traversed and utilized features derived from publicly available maps to extrapolate to energy consumption on real-world routes [22]. A self-supervised approach was presented which considers terrain geometry and soil types. In particular, this paper analyzed soil types which affect energy usage models, then proposed a prediction scheme based on terrain type recognition and simple consumption modeling [23]. Many articles have discussed the energy consumption of a robot’s mechanical structure [24–26]. The total energy consumption of the robot consists of the energy consumption of the mechanism and the subsidiary electrical power loss. Caponetto et al. [27] used a neural network to develop a nonlinear dynamical model of a fuel cell stack that can be exploited as a component of complex control systems to manage the energy flows between the fuel cell stack, battery pack, auxiliary systems, and electric engine.

3. Practical Energy Modeling Method In order to optimize the energy consumption model, researchers focused on single-component as well as system-level energy optimization through dynamic power management. The energy consumption model of the mobile robot is divided to three parts: the sensor system, control system, and motion system.

3.1. Energy Consumption of the Sensor System Firstly, the energy consumption of the sensor part is almost stable. Thus, the energy consumption of the sensor part is multiplied by the electrical power and time.

Esensor = Psensor × ∆t (1)

Psensor is the electrical power of the sensor system and Esensor is the electrical energy consumption. Secondly, the energy consumption of sensors is related to the speed of the robot. Because the sensor’s transmission speed is fast, it can quickly model the surrounding environment. The speed of a mobile robot changes from low to high. If the robot is moving slowly, instead of working all the time, the sensor can wait for the robot to move for a while and then re-model the surrounding environment. Similarly, when the robot is in a standby state, there is no need to model its surroundings, so the sensor is dormant. When the robot reaches its maximum speed, the speed is very fast, and the surrounding Energies 2019, 12, 27 4 of 15 environment changes very quickly, thus the sensor needs to work continuously. Thus, the overall energy consumption of the sensor is proportional to the speed.

1 Z Esensor = (υ ∗ Psensor) dt (2) Vmax

Vmax is the maximum speed of the mobile robot. Obviously, this method can reduce the energy consumption of sensors compared with the scenario in which the sensors are working all the time.

3.2. Energy Consumption of the Control System The energy consumption of the control system depends on the power of the control circuit boards [21], which is related to the running state of the robot. The energy modeling of the control system is mainly divided into the following three parts: the energy consumption in the standby state, the energy consumption when the robot just starts to move, and the energy consumption when the robot runs smoothly.  Estandby = Pstandby ∗ ∆t   = R ∗ + 2 + Econtrol = Estartup φ ∆υ t /10 Pstandby dt (3)  R 2  Estable = Pstandby + t dt

Pstandby represents the power of the control part in the standby state. It is determined that the control system only accepts the signal of the sensor during standby, so the power is a constant. φ is the starting factor of the robot; this factor determines the energy demand for the controller during the start of the robot. ∆υ is the rate of change of the current moment and t is the time when the robot starts moving.

3.3. Energy Consumption of the Motion System Concerning the motion system, the energy consumption can be divided into four parts: the traction energy consumption, increase of kinetic energy, friction energy dissipation, and energy dissipated in thermal form. The motion of a robot is divided into three stages: standby, startup, and stable operation. The power is constant in the standby stage. In the startup stage, there is an instantaneous pulse, which is needed to send the start signal to the electric motors. When a robot moves, it enters the stable operation stage. Z Emotion = Pmotion dt = Ek + E f + Ee + Em (4)

Emotion is the energy consumed to attain and sustain robotic motion, while the motion power Pmotion is motion-dependent [14]. Ek is the kinetic energy of the robot, M is the mass of the mobile robot, and υ is the speed of the current moment of the robot.

Ek = M ∗ υ2/2 (5)

E f is the friction dissipation during the movement of the robot; µ is the friction coefﬁcient between the wheel and the ground. Z E f = (µ ∗ M ∗ υ)dt (6)

Ee is the energy dissipation as heat in the armatures of motors; e and λ are the time-heat constants; σ is the speed-heat constant of the robot. Z Ee = e ∗ t2 + σ ∗ υ + λ ∗ t dt (7) Energies 2019, 12, 27 5 of 15

Em is the mechanical dissipation caused by overcoming the friction torque in the actuators. ζ is the drag coefficient of the robot itself; the coefficient is only related to the robot itself. ψ is the vibration velocity coefficient of the robot.

Z M Em = M ∗ eζt ∗ cos ψ ∗ t + v + + M dt (8) Energies 2018, 10, x FOR PEER REVIEW 2 5 of 15 Consequently, the energy behavior of the motion system can be expressed by Equation (9): 휁푡 푀  퐸푚 = ∫[푀∗ 푒 ∗ 푐표푠 (휓 ∗푡 + 푣 + ( )) + 푀] 푑푡  (8) 0 0 0 0 2 0       Consequently, theµ energy0  behavior 0 of 0the motion system can be0 expressed by Equation (9): B =  ,D =  ,H =    0 σ0 0 0λ0 e   0 0  0휇 0 0 000 0 eˆζt cos(0ψt + v + M/2) + 1  B=[  ] , D=[ ] , H=[ ]  (9) M ∗ υ2/2 0 휎 휆 휖 0 Ek " # " #!  0 0 0 0 t0 푒^휁푡 푐표푠 (휓푡 +Mv푣 + 푀/2) + 1 E f   + R ∗ + ∗ + ∗ =     D 2 M H B dt  . (9)  0 푀∗ 휐2/2 t v 퐸푘  Ee  0 0 푡 푀푣 퐸푓 Em [ ]+∫ (D ∗ [ ] + M ∗ H + B ∗ [ ]) 푑푡 =[ ]. 0 푡2 푣 퐸푒 The speciﬁc parameter values0 of Equations (5)–(8) are listed in Table1.퐸푚 The value of each parameter was obtained through the estimation method. The energy model was simulated through MATLAB The specific parameter values of Equations (5)–(8) are listed in Table 1. The value of each software. The graphics in Figure2, Figure3, and Figure4 represent the simulation results of the model. parameter was obtained through the estimation method. The energy model was simulated through MATLAB software. The graphics in Figures 2, 3, and 4 represent the simulation results of the model. Table 1. Value of each parameter.

TableVariable 1. Value of each Value parameter.

Variableφ 0.7 Value 흓 M 6.5 0.7 µ 0.5 푴 6.5 e 0.01 흁 0.5 σ 0.001 흐 λ 0.1 0.01 흈 ζ −0.5 0.001 흀 ψ 5 0.1 휻 −0.5 흍 5 The speed change of the robot is shown as a function of time in Figure2a and the maximum is The speed change of the robot is shown as a function of time in Figure 2a and the maximum is 1 1 m per second. Bringing the speed value v into Equation (5), the kinetic energy of the robot can be m per second. Bringing the speed value v into Equation (5), the kinetic energy of the robot can be calculated as shown in Figure2b. Bringing the speed value v into Equation (6), the friction dissipation calculated as shown in Figure 2b. Bringing the speed value v into Equation (6), the friction dissipation is shown as in Figure2c. is shown as in Figure 2c.

(a) (b) (c)

Figure 2.2. Speed, 퐸Ek푘, and E퐸푓 f changechange versusversus time.time. (a)) SpeedSpeed changechange versus time; ((b)) KineticKinetic energy changes;changes; ((cc)) FrictionFriction dissipation. dissipation.

Figure3a shows the energy dissipation as heat. Figure3b shows the variation of the mechanical Figure 3a shows the energy dissipation as heat. Figure 3b shows the variation of the mechanical energy consumption over time. energy consumption over time.

Energies 2018, 10, x FOR PEER REVIEW 6 of 15 Energies 2019, 12, 27 6 of 15 Energies 2018, 10, x FOR PEER REVIEW 6 of 15

(a) (b)

Figure 3. Thermal dissipation(a) and mechanical dissipation. (a) Thermal( bdissipation;) (b) Mechanical dissipation. FigureFigure 3. ThermalThermal dissipation dissipation and mechanical and mechanical dissipation dissipation.. (a) Thermal dissipation; (a) Thermal (b) dissipation; Mechanical (bdissipation.) Mechanical dissipation. In the end, we can obtain the total power of the motion system from Equation (4) as shown in FigureInIn the 4,the and end, end, the we we power can can obtain obtainis convergent. the the total total power power of of the the motion motion system system from from Equation Equation (4) (4) as as shown shown in in FigureFigure 4 ,4, and and the the power power is is convergent. convergent.

FigureFigure 4. 4.Total Total power power of of the the motion motion system. system. Figure 4. Total power of the motion system. 3.4.3.4. The The Connection Connection between between the the Three Three Systems Systems 3.4. TheThe C energy onnectionenergy consumption consumption between the model T hree model ofSystems mobile of mobile robots robot consistss consists of three of parts: three the parts: sensor the system,sensor controlsystem, system,control and system motion, and system. motion Concerning system. the Concerning energy consumption, the energy there consumption, are mutual constraints there are between mutual the threeThe systems.energy consumption Firstly, when model a robot of is inmobile a standby robot state,s consists the energy of three consumption parts: the sensor of the controlsystem, controlconstraints system between, and the motion three systemsystems. .Concerning Firstly, when the a energy robot isconsumption, in a standby there state, are the mutualenergy part, the moving part, and the sensor part is very low. Thus, the total energy consumption can be constraintsconsumption between of the control the three part, systems the moving. First lypart, when, and athe robot sensor is partin a isstandby very low. state, Thus the, the energy total considered as the sum of the idle energy (Eidle) and the motional energy (Emotion). consumptionenergy consumption of the control can be consideredpart, the moving as the sumpart, ofand the the idle sensor energy part (퐸푖푑푙푒 is )very and thelow. motional Thus, the energy total 퐸푚표푡푖표푛 energy( consumption). can be considered as the sum of the idle energy (퐸푖푑푙푒) and the motional energy Etotal = Eidle + Emotion (10) (퐸푚표푡푖표푛). 퐸푡표푡푎푙 = 퐸푖푑푙푒 + 퐸푚표푡푖표푛 (10) where Eidle represents the energy consumed during the standby state when the robot has not moved, where 퐸푖푑푙푒 represents the energy consumed퐸푡표푡푎푙 during = 퐸푖푑푙푒 +the 퐸푚표푡푖표푛 standby state when the robot has not moved,(10) and Emotion represents the energy consumed by the robot during movement [14]. Moreover, there is almostwandhere Emotion no퐸푖푑푙푒 data represents represents transmission the the energy energy between consumed consumed the three byduring systems. the robot the standby during state movement when the [14] robot. Moreover, has not moved,there is almost no data transmission between the three systems. and WhenEmotion arepresents robot starts the to energy move, theconsumed control systemby the ofrobot the robotduring starts movement sending [14] and. receivingMoreover, data there and is ita takeslmostWhen timeno data a to robot accelerate transmission starts from to move,between zero tothe maximumthe control three system systems. speed. of At the ﬁrst robot the robotstarts doessendin notg moveand receiving very fast, data so theand sensors iWhent takes doa timerobot not to need starts accelerate to to be move, working from the zero allcontrol theto maximum time. system The of higherspeed. the robot theAt speed,first starts the thesendin robot higherg does and electrical notreceiving mov powere datavery requiredandfast, isot takes the by sensors the time sensor to do accelerate not system. need from Onceto be zero theworking robotto maximum all starts the totime. speed. move, The At thehigher first control the speed,robot system does the of thehigher not robot mov electricale must very keepfast,power working,so requiredthe sensors as thisby dothe system not sensor need is responsiblesys to tembe working. Once for the accepting all robot the time. starts the The sensor to highermove signals, thethe ascontrolspeed, well asthesystem motion higher of feedbacktheelectrical robot signals,powermust keep required calculating working by data,the, as sensor this and system sending system is. outresponsibleOnce control the robot signals.for astartsccept Thus, toing move the the sensor,power the control signal required systems as bywell theof as the control motion robot systemmustfeedback keep will signal working increase.s, calculat, Asas this theing speedsystem data, ofand is the responsible send roboting increases, out for control accept the signaling frequency thes. sensorThus of, the datasignal power received,s as requiredwell processed, as motion by the andfeedbackcontrol transmitted system signal s bywill, calculat robots increase.ing will data increase,As , the and speed send and ingmore of theout power robotcontrol will increases signal be requireds., Thusthe frequency, bythe the power systems. of required data When received, by the the robotcontrolprocessed reaches system, and its transmittedwill maximum increase. speed, by As robots sensorthe speedwill and increase of motion the, robotand systems more increases workpower, with thewill frequency thebe required highest of power. bydata the received,systems. processedWhen the, and robot transmitted reaches its by ma robotsximum will speed increase, sensor, and andmore motion power systemswill be required work with by the the systems highest. Whenpower. the robot reaches its maximum speed, sensor and motion systems work with the highest power.

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Energies 2018, 10, x FOR PEER REVIEW 7 of 15 3.5. Energy Consumption of the Whole System 3.5. Energy Consumption of the Whole System Because mobile robots are driven by lithium batteries, following the basic relationship between Because mobile robots are driven by lithium batteries, following the basic relationship between power and energy, we can calculate the electrical energy consumption (E ) from the source power power and energy, we can calculate the electrical energy consumption (𝐸𝑒𝑙𝑒𝑐elec ) from the source power (Psource) by the integration of time [9]. (𝑃𝑠𝑜𝑢𝑟𝑐𝑒) by the integration of time [9]. Z 𝐸Eelec𝑒𝑙𝑒𝑐 =𝑃P𝑠𝑜𝑢𝑟𝑐𝑒source(t𝑡)dt 𝑑𝑡 (11)(11)

4. Electrical Energy Consumption Evaluation and Result Analysis 4. Electrical Energy Consumption Evaluation and Result Analysis The model was utilized and experimentally tested in a four-wheel-drive Mecanum mobile robot, as shownThe model in Figure was5 .utilized and experimentally tested in a four‐wheel‐drive Mecanum mobile robot, as shown in Figure 5.

Figure 5. FourFour-wheel-drive‐wheel‐drive Mecanum mobile robot and power measurement.

A Monsoon solution solution AAA10F AAA10F power power monitor monitor (Monsoon (Monsoon Solutions Solutions Inc., Inc., Bellevue, Bellevue, WA, WA, USA) USA) was wasused used to measure to measure the theelectrical electrical power power of ofthe the sensor sensor and and controller. controller. A A Rigol Rigol DP1308A (RIGOL Technology Co., Co., Ltd., Ltd., Beijing, Beijing, China) China) was was used used to to measure measure the the electrical electrical power power of of the the motion motion system system as wellas well as as the the total total power power consumption. consumption. The The power power of of the the system system can can also also be be monitored monitored byby measuringmeasuring the real-timereal‐time voltage andand currentcurrent ofof thethe battery.battery. The experimentalexperimental environment was aa commoncommon laboratorylaboratory environment.environment. The chassis of the McNam’s wheeled car moved across the ceramic tile floor ﬂoor of the laboratory. laboratory. The experimental method was asas follows:follows: a mobile phone app was used to remotely move the robot forward 4 m; then, the energy consumption ofof thisthis processprocess waswas calculated.calculated. 4.1. Power Measurement of the Sensor System 4.1. Power Measurement of the Sensor System Measuring the power of the sensor using a power monitor, as shown in Figure6b, the power Measuring the power of the sensor using a power monitor, as shown in Figure 6b, the power consumption of the sensor was between 600 and 700 mW. It exhibited a stable curve with almost no consumption of the sensor was between 600 and 700 mW. It exhibited a stable curve with almost no ﬂuctuation. This result which is shown in Figure7 conforms to the sensor power model. fluctuation. This result which is shown in Figure 7 conforms to the sensor power model.

Result display

Laser radar sensor

Power monitor

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Result display

Laser radar sensor Energies 2018, 10, x FOR PEER REVIEW 8 of 15 Power monitor (a) (b)

Figure 6. Power measurement of the sensor. (a) Sensor power measurement; (b) Power result display. (a) (b)

FigureFigure 6. 6.Power Power measurement measurement of of the the sensor. sensor. ( a(a)) Sensor Sensor power power measurement; measurement; (b (b) Power) Power result result display. display.

(a) (b)

Figure 7. a b Figure 7. Sensor system power. ( (a)) Sensor Sensor power power sampled sampled every every 0.02 0.02 s; s; ( (b)) Sensor power sampled every 0.04 s. (a) (b)

Figure 7. Sensor system power. (a) Sensor power sampled every 0.02 s; (b) Sensor power sampled Comparing the power from different sampling frequencies, it was found that when the the sampling sampling every 0.04 s. frequencyfrequency was reduced, the power of the sensor also decreased. As shown in TableTable2 ,2, the the lower lower the the robot robot speed, speed, the the lower lower the the power power of the of the sensor sensor system, system, and and the Comparing the power from different sampling frequencies, it was found that when the sampling theerror error between between the the measured measured value value and and the modeledthe modeled value value was was within within 7%. 7%. frequency was reduced, the power of the sensor also decreased. As shown in Table 2.2,Sensor the lower power the comparison robot speed, between the lower model the and power measurement. of the sensor system, and Table 2. Sensor power comparison between model and measurement. the error between the measured value and the modeled value was within 7%. TimeTime (s) (s) Speed Speed (m/s) (m/s) Model Model Total Total Powe Powerr (mW) (mW) Measurement Measurement Powe Powerr (mW) Error Error Percent Percent (%) 0 00 Table 0 2. Sensor0 power comparison 0 between0 model 0and measurement.0 0 0.05 0.1 64 68 6.25 0.05 0.1 64 68 6.25 Time0.10 (s) Speed 0.2(m/s) Model Total 128 Power (mW) Measurement 132 Power (mW) Error Percent 3.12 (%) 0.100.15 0.2 0.3128 192132 1873.12 2.60 0.150 0.20 0.30 0.41920 2561870 2452.600 4.29 0.200.050.25 0.40.1 0.525664 32024568 3154.296.25 1.56 0.250.100.30 0.50.2 0.6320128 384315132 3981.563.12 3.64 0.150.35 0.3 0.7192 448187 4322.60 3.57 0.300.40 0.6 0.8384 512398 5253.64 6.04 0.20 0.4 256 245 4.29 0.350.45 0.7 0.9448 576432 5803.57 0.694 0.400.250.50 0.80.5 1.0512320 640525315 6156.041.56 3.91 0.450.30 0.90.6 576384 580398 0.6943.64 0.35 0.7 448 432 3.57 4.2.0.50 Power Measurement1.0 of the640 Control System 615 3.91 0.40 0.8 512 525 6.04 0.45 0.9 576 580 0.694 4.2. PowerSelecting Measurement the low power of the controlControl chipSystem and interface circuit can reduce the total power of the control system.0.50 The mobile1.0 robot used640 an STM32F103 chip as615 the main control chip, as shown3.91 in Figure8. Selecting the low power control chip and interface circuit can reduce the total power of the control4.2. Power system. Measurement The mobile of the robot Control used System an STM32F103 chip as the main control chip, as shown in Figure 8.

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Figure 8. Block diagram of the control system. Figure 8. Block diagram of the control system. Figure9 displays the powerFigure measurement 8. Block diagram of of the the controller control system. board and the result. Not only hardwareFigure 9 but displays also software the power makes measurement a signiﬁcant of contributionthe controller to board the overall and the power result. consumed Not only by hardwaresmall-sizeFigure but embedded also9 displays software systems the makes power [ 28a significant]. measurement In order contribution to accurately of the controller to study the overall the board power power and situation consumed the result. of by the Not small control only‐ size embedded systems [28]. In order to accurately study the power situation of the control system at hardwaresystem at but each also stage, software it needed makes to a besignificant ensured contribution that there was to the sufﬁcient overall power time to consumed sample the by power.small‐ each stage, it needed to be ensured that there was sufficient time to sample the power. Therefore, in Therefore,size embedded in the systems setting stage,[28]. In we order set the to accelerationaccurately study of the the robot power to a situation relatively of small the control value. Figure system 10 ata the setting stage, we set the acceleration of the robot to a relatively small value. Figure 10a shows the eachshows stage, the powerit needed of theto be control ensured system that there during was startup. sufficient Figure time 10 tob sample shows thethe powerpower. of Therefore, the control in power of the control system during startup. Figure 10b shows the power of the control system after thesystem setting after stage, the we robot set runsthe acceleration smoothly. of It the was robot found to a through relatively the small comparison value. Figure that 10a the shows faster the the robot runs smoothly. It was found through the comparison that the faster the acceleration, the poweracceleration, of the control the higher system the during frequency startup. of the Figure pulse 10b signal shows emitted the power by the of controlthe control part. system Thus, after the higher the frequency of the pulse signal emitted by the control part. Thus, the pulse signal can be pulsethe robot signal runs can smoothly. be regarded It was as thefound acceleration through the signal comparison sent by the that control the faster part the to theacceleration, moving part. the regarded as the acceleration signal sent by the control part to the moving part. After stabilization, the Afterhigher stabilization, the frequency the of controlthe pulse part signal keeps emitted the original by the powercontrol almostpart. Thus, unchanged, the pulse but signal there can is nobe control part keeps the original power almost unchanged, but there is no pulse signal. pulseregarded signal. as the acceleration signal sent by the control part to the moving part. After stabilization, the control part keeps the original power almost unchanged, but there is no pulse signal.

Result display Result display

Controller boards Power monitor Controller boards Power monitor

(a) (b) (a) (b) Figure 9. Power measurement of the controller boards. (a) Control boards power measurement; (b)Figure Power 9. result.PowerPower measurement measurement of of the the controller controller boards. boards. (a) (Controla) Control boards boards power power measurement; measurement; (b)) PowerPower result. result.

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(a) (b) (a) (b) FigureFigure 10. 10. PowerPower of of the the control control system. system. (a (a) )Start Start process process power; power; ( (bb)) Smooth Smooth running running power. power. Figure 10. Power of the control system. (a) Start process power; (b) Smooth running power. 4.3.4.3. Power Power Measurement Measurement of of the the Motion Motion System System 4.3. Power Measurement of the Motion System AccurateAccurate measurement andand analysisanalysis of of energy energy consumption consumption are are essential essential for for the the evaluation evaluation of theof thehardware- hardware andAccurate‐ and software-related software measurement‐related energy and energy analysis consumption consumption of energy of consumption a processingof a processing are system essential system [28 ,for29 [28,29].]. the The evaluation model The model of of the the hardware‐ and software‐related energy consumption of a processing system [28,29]. The model ofcontrol the control system system can affect can affect the energy the energy consumption consumption of the of whole the whole system system [30]. [30]. Therefore, Therefore, the robotthe robot was set to runof the by acontrol speciﬁc system program, can affect the the ﬂowchart energy consumption of which is of shown the whole in Figure system 11 [30].. Therefore, the robot was set towas run set by to runa specific by a specific program, program, the flowchart the flowchart of which of which is isshown shown in in Figure Figure 11.

Figure 11. Flowchart of the robot’s motion. Figure 11. Flowchart of the robot’s motion.

Figure 11. Flowchart of the robot’s motion.

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In order to ensure the accuracy of the experimental measurement, we set the maximum speed Energies 2019, 12, 27 11 of 15 of the robot at 1 m/s through the program. When the speed of the robot reached 1 m/s, the robot stopped accelerating. The robot was closed‐loop controlled. Photoelectric encoders on the motors measuredIn order the to speed ensure of thethe accuracymotor and of provided the experimental feedback measurement, data in real time we to set the the control maximum system speed of the ofrobot. the robot When at the 1 m/s control through system the detected program. that When the thespeed speed of the of the robot robot had reached reached 1 m/s,the set the value, robot it stoppedstopped accelerating. accelerating and The maintained robot was closed-loop that speed. Otherwise, controlled. it Photoelectric continued to encoders accelerate. on the motors measuredTable the 3 shows speed ofthe the comparison motor and between provided the feedback real data data we inmeasured real time and to the the control data we system obtained of theusing robot. the When proposed the control model. systemThe difference detected between that the the speed modeled of the robotdata and had the reached actual the measured set value, data it stoppedwas small, accelerating reaching andno more maintained than 3%. that speed. Otherwise, it continued to accelerate. Table3 shows the comparison between the real data we measured and the data we obtained using the proposed model.Table The 3. difference Motion power between comparison the modeled between model data and and themeasurement. actual measured data was small, reaching no moreRobot than 3%.Modeling Total Power Measurement Time (s) Error Percent (%) Speed (m/s) (W) Power (W) 0 Table0 3. Motion power comparison0 between model0 and measurement. 0 0.2 0.8 15 14.3 4.89 Time (s) Robot Speed (m/s) Modeling Total Power (W) Measurement Power (W) Error Percent (%) 0.4 0.97 19.8 20 1.00 00.6 0.99 0 17 0 18 05.55 0 0.2 0.8 15 14.3 4.89 0.40.8 0.971 13.2 19.8 13.7 203.78 1.00 0.61.0 0.991 10.2 17 10.3 180.97 5.55 0.81.2 1 12.2 13.2 12.3 13.70.81 3.78 1.01.4 1 15.3 10.2 15.7 10.32.54 0.97 1.21.6 1 17.3 12.2 17.7 12.32.25 0.81 1.4 1 15.3 15.7 2.54 1.8 1 16.8 17 1.17 1.6 1 17.3 17.7 2.25 1.82.0 1 14.5 16.8 14.7 172.68 1.17 2.02.2 1 12.6 14.5 12.9 14.71.36 2.68 2.22.4 1 13.3 12.6 13.1 12.91.50 1.36 2.42.6 1 14.8 13.3 14.6 13.11.36 1.50 2.6 1 14.8 14.6 1.36 2.8 1 15.2 15.3 0.653 2.8 1 15.2 15.3 0.653

FigureFigure 12 12 shows shows the the power power of of the the motion motion system system obtained obtained by by the the model. model. The The power power changed changed rapidlyrapidly at at the the beginning, beginning, then then the powerthe power converged converged to a smaller to a smaller interval, interval, and remained and remained almost constant almost inconstant the end. in the end. power(w)

Figure 12. Power of the motion system obtained by the model. Figure 12. Power of the motion system obtained by the model. In Table4, the maximum deviation means the degree of deviation from the maximum motion In Table 4, the maximum deviation means the degree of deviation from the maximum motion power and the stable deviation means the degree of deviation from the stable motion power when the power and the stable deviation means the degree of deviation from the stable motion power when robot runs smoothly. The robot’s motion electrical power tends to stabilize over time. the robot runs smoothly. The robotʹs motion electrical power tends to stabilize over time.

Table 4. Motion electrical power.

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Gap Between Extremes Current Current Motion Time (s) Table 4. Motion electricalMaximum power. Deviation Stable Deviation Speed (m/s) Power (W) (%) (%) Current Speed Current Motion Gap Between Extremes Time (s)0 0 0 100 100 0.2 (m/s)0.8 Power (W)15 Maximum Deviation24.6 (%) Stable Deviation0.67 (%) 00.4 00.97 019.8 1000.5 32.8 100 0.20.6 0.80.99 1517 24.614.5 14 0.67 0.40.8 0.971 19.813.2 0.533.6 11.4 32.8 0.61.0 0.991 1710.2 14.548.7 31.5 14 0.81.2 11 13.212.2 33.638.7 18.1 11.4 1.01.4 11 10.215.3 48.723.1 2.68 31.5 1.21.6 11 12.217.3 38.713.1 16.1 18.1 1.4 1 15.3 23.1 2.68 1.8 1 16.8 15.5 12.7 1.6 1 17.3 13.1 16.1 2.0 1 14.5 27.1 2.68 1.8 1 16.8 15.5 12.7 2.02.2 11 14.512.6 27.136.7 15.4 2.68 2.22.4 11 12.613.3 36.733.1 10.7 15.4 2.42.6 11 13.314.8 33.125.6 0.067 10.7 2.62.8 11 14.815.2 25.623.6 2.01 0.067 2.8 1 15.2 23.6 2.01

4.4.4.4. Robot’s Robot’s Total Total Power Power Comparison Comparison between between the the Model Model and and Measurements Measurements TableTable5 shows5 shows the the results results of of the the ﬁve five experiments. experiments. DP1308A DP1308A was was employed employed to to record record the the power power consumptionconsumption as as the the robot robot was was run run through through the the power power meter, meter, which which was was then then imported imported into into MATLAB MATLAB forfor analysis. analysis. Ghost Ghost power power represents represents the the power power of of the the robot robot when when it it was was not not moving. moving.

Table 5. Total power of experiment results. Table 5. Total power of experiment results.

ExperimentExperiment MaximumMaximum Power Powe (W)r (W) Average Operating PowerPower (W) Ghost Ghost Powe Powerr (W) (W) 1 24.55 24.5518.98 18.980.23 0.23 2 24.95 24.9518.75 18.750.25 0.25 3 24.58 24.5818.55 18.550.20 0.20 4 24.79 24.7918.45 18.450.23 0.23 5 24.98 24.9818.75 18.750.26 0.26 6 24.65 18.52 0.23 6 24.65 18.52 0.23

As seen from Figure 13, the power calculated by the model and the actual measured power error As seen from Figure 13, the power calculated by the model and the actual measured power error were both within an acceptable range. were both within an acceptable range. Total power 25

10 total power consumption by energy model

5 total power consumption by measurement

0 0 0.5 1 1.5 2 2.5 3 3.5 Time(s)

FigureFigure 13. 13.Comparison Comparison between between energy energy model model and and measurement. measurement.

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Figure 14a shows the change in the percentage of electrical power of the three parts of the robot from theFigure startup 14a showsto 1 m/s the of changerobot movement. in the percentage Figure 14b of electrical shows the power electrical of the power three percentage parts of the of robot the robot'sfrom the three startup parts to during 1 m/s the of robotsmooth movement.-running state Figure of 14 thbe showsrobot. The the electricalproportion power of the percentage motion system of the torobot’s the total three power parts far during exceeds the that smooth-running of the sensor state system of the and robot. control The system. proportion of the motion system to the total power far exceeds that of the sensor system and control system.

(a) (b)

FigureFigure 1 14.4. PercentagePercentage of power of power.. (a) P (owera) Power percentage percentage of the of three the system three systems;s; (b) Smooth (b) Smooth running running power percentagepower percentage..

5.5. Conclusion Conclusionss and and Future Future Work Work TheThe energy energy modeling modeling method method for for mobile mobile robot robotss presented presented in in this this paper paper can can be be used used to to calculate calculate andand predict predict energy energy consumption, consumption, provid providinging a a guide guide to to facilitate facilitate energy energy-efficient-efficient strategies strategies as as well well as as aavoidingvoiding action action obstacle obstacless due due to to lack lack of of energy energy.. The The operation operation of of robots robots can can be be divided divided into into three three states:states: standby, standby, start startup,up, and and running. running. Compared Compared with with the the other other modeling modeling methods, methods, this this model model does does notnot consider consider the the path path of of the the robot. robot. The The electrical electrical power power calculation calculation method method is related is related to the to thespeed speed of theof therobot robot and andthe characteristics the characteristics of the of robot the robot itself. itself. By dividing By dividing the energy the energy consumption consumption of the robot of the intorobot three into parts, three the parts, model the can model be simplified can be simplified.. Therefore, Therefore, very complicated very complicated parameters parameters in the process in the ofprocess motion of are motion not needed, are not and needed, the calculation and the calculation of electrical of power electrical becomes power very becomes simple. very It is simple.convenient It is forconvenient us to put for this us model to put into this our model program into our so programthat the robot so that has the the robot ability has of the self ability-perception. of self-perception. Through ourThrough model, our we model, established we established the relationship the relationship and connection and connection among t amonghe three the parts, three which parts, can which make can themake model the modelof the robot of the more robot complete. more complete. ExperimentsExperiments showedshowed thatthat the the power power model model created created in this in paper this paperis feasible is feasible and effective. and effective. However, Howeverthe experiments, the experiments were carried were out carried on horizontal out on horizontal roads only. roads The only. operation The operation of robot involves of robot involve stopping,s stopaccelerating,ping, accelerating, slowingdown, slowing turning, down, movement turning, movement uphill and uphill downhill, and anddownhill so on,, alland of so which on, all is not of whichentirely is coverednot entirely by thecovered proposed by the energy proposed model. energy Thus, model. further Thus, research further should research aim toshould complete aim theto completeenergy model the energy according model to according all robot actions, to all robot using actions, a better using and morea better comprehensive and more comprehensive experimental experimentalfield. Moreover, field. the Moreover battery, energy the battery model energy is very model important is very and important should and be included should be in included a complete in aenergy complete model energy for mobilemodel for robots. mobile robots.

AuthorAuthor Contrib Contributions:utions: Conceptualization,Conceptualization, L L.Z..Z. and and J. J.K.;K.; Methodology, Methodology, L L.Z.;.Z.; Software, Software, L L.H.;.H.; Validation, Validation, L L.H.,.H., LL.Z.;.Z.; Formal Formal Analysis, Analysis, L L.H.;.H.; Investigation, Investigation, L.Z. L.Z.;; Resources, Resources, L.H L.H.;.; Data Data Curation, Curation, L.H L.H.;.; Writing Writing-Original-Original Draft Draft Preparation,Preparation, L.H L.H.;.; Writing Writing-Review-Review & & Editing, Editing, J.K J.K.;.; Visualization, Visualization, J.K J.K.;.; Supervision, Supervision, L.Z. L.Z.;; Project Project Administration, Administration, L.Z.; Funding Acquisition, L.Z. L.Z.; Funding Acquisition, L.Z. Funding: This research received no external funding. Funding: This research received no external funding Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. References References 1. Burghardt, A.; Kurc, K.; Szybicki, D.; Muszyńska,M.; Szcz˛ech,T. Monitoring the parameters of the 1. Burghardt,robot-operated A.; Kurc, quality K.; controlSzybicki, process. D.; Muszyńska,Adv. Sci. Technol. M.; Szczęch, Res. J. T.2017 Monitoring, 11, 232–236. the parameters [CrossRef] of the robot- operated quality control process. Adv. Sci. Technol. Res. J. 2017, 11, 232–236, doi:10.12913/22998624/68466.

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