development of a mobile robot test platform and methods ......development of a mobile robot test...

Development of a Mobile Robot Test Platform and Methods forValidation of Prognostics-Enabled Decision Making Algorithms

Edward Balaban1, Sriram Narasimhan2, Matthew J. Daigle1, Indranil Roychoudhury3,Adam Sweet1, Christopher Bond4, Jose R. Celaya3, and George Gorospe6

1 NASA Ames Research Center, Moffett Field, CA, 94035, USAedward.balaban, matthew.j.daigle, [email protected]

2 University of California, Santa Cruz, NASA Ames Research Center, Moffett Field, CA, 94035, [email protected]

3 SGT Inc., NASA Ames Research Center, Moffett Field, CA, 94035, [email protected], [email protected]

4 NASA Kennedy Space Center, FL, 32899, [email protected]

5 USRA, NASA Ames Research Center, Moffett Field, CA, [email protected]

ABSTRACT

As fault diagnosis and prognosis systems in aerospace appli-cations become more capable, the ability to utilize informa-tion supplied by them becomes increasingly important. Whilecertain types of vehicle health data can be effectively pro-cessed and acted upon by crew or support personnel, others,due to their complexity or time constraints, require either au-tomated or semi-automated reasoning. Prognostics-enabledDecision Making (PDM) is an emerging research area thataims to integrate prognostic health information and knowl-edge about the future operating conditions into the process ofselecting subsequent actions for the system. The newly devel-oped PDM algorithms require suitable software and hardwareplatforms for testing under realistic fault scenarios. The pa-per describes the development of such a platform, based onthe K11 planetary rover prototype. A variety of injectablefault modes are being investigated for electrical, mechanical,and power subsystems of the testbed, along with methods fordata collection and processing. In addition to the hardwareplatform, a software simulator with matching capabilities hasbeen developed. The simulator allows for prototyping andinitial validation of the algorithms prior to their deploymenton the K11. The simulator is also available to the PDM al-gorithms to assist with the reasoning process. A reference setof diagnostic, prognostic, and decision making algorithms isalso described, followed by an overview of the current testscenarios and the results of their execution on the simulator.

Edward Balaban et.al. This is an open-access article distributed under theterms of the Creative Commons Attribution 3.0 United States License, whichpermits unrestricted use, distribution, and reproduction in any medium, pro-vided the original author and source are credited.

1. INTRODUCTION

New designs of aerospace vehicles have been gradually gain-ing system health diagnostic and, in some cases, even prog-nostic capabilities (Reveley, Kurtoglu, Leone, Briggs, &Withrow, 2010), with the next logical step in autonomy mat-uration being decision-making based on such health informa-tion. A vehicle capable of evaluating its own health state andmaking (or assisting with making) decisions extending its re-maining useful life or improving safety margins, may be ableto go further and accomplish more objectives than a vehiclefully dependent on human actions. In addition to helping withmission execution, prognostics-enabled decision making sys-tems may also prove valuable for vehicle maintenance, supplychain logistics, and fleet management.

While the research and development efforts for PDM systemsare, for the most part, in their early stages, a need alreadyexists for suitable platforms and techniqiues for their test-ing. At NASA Ames Research Center, test platforms fromprior research efforts, such as (Poll et al., 2007) for electricalpower systems or (Smith et al., 2009; Balaban et al., 2010)for electro-mechanical actuators, were created primarily withthe diagnostic and prognostic elements of system health man-agement in mind. In order to support our work in PDM a newplatform was therefore needed. Such a platform is expectedto support the following five high-level tasks: (i) develop-ment of system- and component-level PDM algorithms; (ii)development of realistic fault injection and accelerated agingtechniques for algorithm testing; (iii) maturation and stan-dardization of interfaces between reasoning algorithms; (iv)performance comparison of PDM algorithms from different

International Journal of Prognostics and Health Management, ISSN2153-2648, 2013 0061

INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT

sources; and (v) generation of publicly available datasets forenabling further PDM research.

While an aerial test vehicle, such as an unmanned fixed-wing airplane or a helicopter, would allow testing of PDMtechnologies on complex scenarios and with motion in three-dimensional space, operating it is often expensive. A singleflight hour often requires many days of preparation. Safetyrequirements for an aerial vehicle, whether manned or un-manned, are also usually quite stringent. In contrast, a groundvehicle can operate at low speeds in a controlled environment,making experiments easier, faster, and safer to set up. The ex-periments can still involve motion, complex subsystems inter-actions, and elaborate mission plans, however the possibilityof a dangerous situation occurring is reduced significantly.For technologies in their early phases of development in par-ticular, a ground vehicle platform could provide a suitable testenvironment for the majority of development goals at a frac-tion of the cost of an aerial vehicle (and usually with a cleartransition path to the latter).

This paper updates and expands our previous description ofthe effort to develop such a platform and the associated PDMvalidation techniques (Balaban, Narasimhan, et al., 2011).The new features of the K11 testbed (a planetary rover pro-totype) include a redesigned sensor suite and a more capablebattery management system. The K11 software simulator hasalso been updated with more accurate physics models. A newsoftware architecture has been deployed on the testbed, sup-porting rapid integration of reasoning algorithms. The paperalso provides an updated description of the reasoning algo-rithms currently under development and presents the formu-lation and results from the latest set of validation scenarios.

This paper is organized as follows. Section 2, describes re-lated efforts. Section 3 presents the hardware and systemsoftware of the K11, while Section 4 describes the simulatorand the experimental validation of the physics models. Sec-tion 7 presents the reasoning algorithms (diagnostic, prog-nostic, and decision making) currently being developed onthe K11. The fault management experiments executed onthe K11 simulator and their results are the subject of Section8. Finally, Section 9 provides a summary of the accomplish-ments and outlines directions for future work.

2. RELATED WORK

Brown, Georgoulas, and Bole (2009) report on a prognostics-enhanced fault-tolerant controller that trades off performancefor remaining useful life. The controller is based on model-predictive control principles, with control boundaries for agiven remaining useful life estimate (corresponding to a par-ticular input) used as soft cost constraints. The work isextended with error analysis and estimation of uncertaintybounds for long-term Remaining Useful Life (RUL) predic-tions in (Brown & Vachtsevanos, 2011). In (Bole, Tang,

Goebel, & Vachtsevanos, 2011) the authors also study the op-timal load allocation problem given prognostic data on faultmagnitude growth. Value at Risk, coming from the field offinance, is used as the key performance metric. The casestudy used for the experiments is an unmanned ground ve-hicle (UGV), where winding insulation on the drive motors isdegrading due to thermal stress.

The work done by Tang, Edwards, Orchard, and others onAutomated Contingency Management (ACM) includes ele-ments of prognostics-enhanced control, but also extends tomission replanning based on prognostic information (Tang etal., 2007; Edwards, Orchard, Tang, Goebel, & Vachtsevanos,2010; Tang, Hettler, Zhang, & Decastro, 2011). Diagnosticand prognostic algorithms for various types of componentsare developed and integrated into a prototype UGV decision-making framework. RUL estimates are used either as a con-straint or an additional element in the cost function in theUGV path planning algorithm. A Field D*-style search al-gorithm is used for receding horizon planning. Methods forestimating and managing uncertainty are also developed.

3. TESTBED

The K11 (shown in Figure 1) is a four-wheeled rover, origi-nally designed as a platform for testing power-efficient roverdesigns in Antarctic conditions (Lachat, Krebs, Thueer, &Siegwart, 2006). Since being repurposed for PDM research,the rover has been substantially updated, with its power distri-bution system, sensor suite, data acquisition module, and sys-tem software redesigned from the ground up. The followingsubsections provide more details on the K11 hardware, soft-ware, and fault injection methods (both those methods thathave already been implemented and those that are planned tobe added in the near future).

3.1. Hardware

The rover is roughly 1.4 m long by 1.1 m wide by 0.63 m tall.Its chassis is a lightweight H-structure with a joint around thefront roll axis to ensure that the wheels stay in contact withthe ground on uneven terrain. Each wheel is driven by anindependent 250 W graphite-brush motor, connected througha bearing and gearhead system, with control performed by asingle-axis digital motion controller. The rover is powered bytwenty four 2.2 Ah lithium-ion single cell batteries (18650form factor), organized in two parallel strings of twelve bat-teries in series. An onboard laptop computer runs the con-trol and data acquisition software, as well as the reasoningalgorithms. A second laptop computer currently serves as aground control station.

The battery management system (BMS) provides batterycharging and load balancing capabilities. The BMS alsosends voltage and temperature measurements for each of theindividual cells to the onboard computer via a Controller Area

2


Network (CAN) bus interface. The data acquisition (DAQ)module collects current and motor temperature measurementsand sends them to the onboard computer. The motor con-trollers send back motion data such as encoder position val-ues, commanded speed, and actual speed. Finally, a GoogleNexus S smartphone is utilized as an additional sensor suite.It contains a GPS receiver, a gyroscope, an accelerometer, aphoto and video camera, a magnetic compass, as well as dataprocessing and storage resources. The phone also has a built-in wireless capability for communicating with other on-boardcomponents (and directly with the ground station). Table 1presents the measurements available on the K11.

Figure 1. The K11 rover

3.2. Software

The K11 testbed software provides navigation, inter-modulecommunication (middleware), and telemetry functions. Thesmartphone hosts a data acquisition module that collects datafrom the phone’s sensors and sends it over a User DatagramProtocol (UDP) socket to the onboard computer. The centraldata acquisition software, running on the computer, receivesthe data, merges it with the data received from the DAQ sys-tem and the motor controllers, and records it in a unified datafile. A unified data stream is also transmitted to the groundcontrol station. The central data acquisition software on theK11 is based on LabView from National Instruments. Theuser interface on the ground station is also created in Lab-View, and, among other functions, allows the operator to takemanual control.

Integration between the rover testbed (or its simulator) andthe reasoning algorithms is accomplished through a pub-lish/subscribe architecture. The architecture is implementedthrough the Internet Communication Engine, ICE (Henning,2004). Standardized interface definition files are used to de-scribe messages exchanged among the software and hardware

modules. The message types include command inputs, sen-sor data, vehicle state information, fault diagnosis candidates,as well as unordered and ordered waypoint lists. A centralserver coordinates message exchanges among any number ofdevices on the same network. In order to be integrated intothe architecture, a new reasoning module needs to only imple-ment a minimal interface code necessary to register with theICE server and to publish/subscribe to the appropriate mes-sages. For example, a diagnostic module would subscribe torover commands and sensor data and publish diagnostic mes-sages. Thus the architecture allows for easy accommodationof modules implemented in different programming languagesand running on dissimilar platforms.

Table 1. Measurements available on the K11

Measurement Type Comments UnitsGPS Longitude and latitude degGyroscope Roll, pitch, yaw rates rad/secAccelerometer 3-axis acceleration m/sec2

Magnetometer 3-axis magnetic field µTMotor temperature On each motor (to be im-

plemented)deg C

Battery temperature On each individual bat-tery cell

deg C

Battery voltage On each individual bat-tery cell

V

Position encoder On each individual motor countsTotal current A current sensor on the

power bus from the bat-tery to the motor con-trollers

A

Individual motorcurrent

Custom sensors on thelines from the power busto the motors

A

3.3. Fault Injection and Accelerated Aging Techniques

A number of fault modes have been selected for implementa-tion on the K11 testbed, summarized in Table 2. The criteriafor their selection include relevance to a variety of aerospacevehicle types, feasibility of implementation, and the progres-sion time from fault to failure. If the progression time is toobrief, then a meaningful prediction of remaining useful life(and, consequently, actions based on it) may not be possi-ble. On the other hand, if the fault-to-failure progression timeis measured in years, then executing experiments for thosefault modes is impractical. While faults in these two cate-gories are outside of the scope of this research, that certainlydoes not mean that they cannot (or should not) be handledby a health management system. Abrupt failures, unless re-sulting in a complete loss of control over the vehicle, canstill be detected and identified by a diagnoser, then analyzedand acted upon by a decision-making system. Long duration

3


fault modes (e.g. airframe component fatigue) can be mod-eled with detailed simulations of future loads and operatingconditions. Ideally, long-term degradation would be trackedfrom the time the vehicle (or a specific component) is new,in order to allow for a better estimation of the current healthstate.

Several modes described in Table 2 were selected for the ex-periments in the initial phase of the project. The methodsfor modeling progression of these faults are described in Sec-tion 4. The techniques (current and planned) for injecting thefaults on the hardware testbed are described next.

Table 2. Potential fault types

Fault Mode Injection Method SubsystemBattery capacitydegradation

Accelerated aging Power

Battery charge deple-tion

Discharging Power

Parasitic electric load Programmable Powerdistribution

Motor driver faults Electronic com-ponents replace-ment with agedunits

Powerdistribution

Motor controller fail-ure

Software Electro-mechanical

Increased motor fric-tion

Mechanical brake Electro-mechanical

Sensor (bias, drift,scaling, or failure)

Software Sensors

Out of the modes listed in Table 2, battery charge depletionis expected to have the shortest time of progression to fail-ure (a few hours of continuous use at the most). The faultswith the longest time-to-failure values are expected to bethe electronic component faults, possibly taking on the orderof months to fail (assuming the current fault seeding tech-niques). The other fault modes fall somewhere in betweenthese two cases.

3.3.1. Remaining Battery Charge Tracking

While not being, in the strict sense, a fault, tracking the re-maining battery charge will be one of the main tasks for theprognostic system. End-of-charge is an end-of-life criterion,so the remaining charge estimate will be an important fac-tor for the PDM software. Most battery-powered vehiclesincorporate some form of state-of-charge (SOC) monitoring.Usually SOC monitoring is based on Coulomb counting, i.e.integrating the current drawn over time, divided by the ratedcapacity of the battery. We will use a somewhat more ro-bust, model-based approach, described in Section 7.2 (seealso (Saha & Goebel, 2009; Saha, Quach, & Goebel, 2012)).

3.3.2. Battery Capacity Degradation

As the rover batteries go through charge/discharge cycles,their capacity to hold charge diminishes. The degradationrate will depend on several factors, such as imposed loads,environmental conditions, and charge procedures. For exam-ple, lithium-ion chemistry batteries undergo higher rates ofcapacity fade with higher current draw and operational tem-peratures. Even at rest, this type of battery has chemical pro-cesses occurring that have long-term effects - for instance,latent self-discharge and transient recovery during relaxation(Huggins, 2008). The depth-of-discharge and even the stor-age temperature have major influences on the overall life ofthe battery as well. The batteries will age naturally in thecourse of rover operations, and one method of injecting thisfault is to use older, degraded batteries on the rover. The bat-tery aging test stand (Saha & Goebel, 2009) at NASA Ameswill be used to age rover battery cells to a desired point intheir life cycle.

3.3.3. Parasitic Load

A parasitic electrical load will be injected on the main powerdistribution line via a remotely controlled rheostat. The rheo-stat can be set for resistance from 0 to 100 Ohms and is capa-ble of dissipating up to 600 Watts of power. The rheostat willsimulate a situation where, for example, an accessory motor iscontinuously engaged due to a failed limit microswitch. Thiscould also represent losses in efficiency in the power distri-bution system, due to, for example, degradation of switchingelements.

3.3.4. Motor Controller Failure

Several types of motor controller faults will be emulated bychanging its settings. The simplest is to disable a controllercompletely, simulating a failure in the system which leavesthe wheel unpowered but able to rotate. Another fault canbe injected by setting the commanded speed to 0, leaving thewheel to drag (to the limit of the controller’s ability). Othertypes of faults, including the effects of various software er-rors, will also be investigated and implemented.

3.3.5. Increased Motor Friction

An increased friction fault (caused by a jam in the sup-port bearing or the gearbox, for example) can result in de-creased efficiency, increased current consumption, overheat-ing of motor windings, deterioration of their insulation, andeventual failure of the motor due to a short in the windings.To ensure realism, a performance region for the motor will bechosen where a healthy motor would have no problems keep-ing up with either speed or load requirements. With frictionincreased, however, the amount of current needed to satisfythe same speed and load demands will be higher, leading tooverheating. Unless speed and/or load are reduced or duty cy-

4


cle (the proportion of time the motor is on versus duration ofcool-down intervals) is adjusted, the heat build-up will even-tually destroy the insulation of the windings and lead to motorfailure. This fault mode was first implemented in the simula-tor and its model validated using experimental data collectedon smaller-sized motors that were run to failure under similarconditions (Balaban, Saxena, Narasimhan, Roychoudhury, &Goebel, 2011). More details on the model validation areprovided in Section 4.1. A hardware fault injection using amechanical brake on one of the rover motors is to be imple-mented next. The motor will not be run to complete failureinitially; instead the model parameters and prognostic algo-rithms will be validated in experiments stopping just shortof creating permanent damage. Eventually, experiments thatwill take motors all the way to failure will be performed.

3.3.6. Sensor Faults

Sensor faults of particular interest are those that exhibit off-nominal behavior for some time before the failure threshold isreached, such as bias and drift faults. In order to simulate biasand drift faults, constant and increasing offsets will be addedto the true measured sensor value, respectively. In additionto bias and drift, other sensor fault modes useful for testingthe diagnostic components are ’stuck’ (where the sensor valueremains unchanged regardless of the system state) and scaling(signal amplification fault).

Sensor faults will be injected by substituting the sensor’svalue with a different one before sending the data to the rea-soning algorithms (Poll et al., 2007; Balaban, Saxena, Bansal,Goebel, & Curran, 2009; Balaban, Saxena, et al., 2011). If thecharacteristics of a fault can be determined with an acceptabledegree of certainty, the decision-making system can attemptto compensate for it by adjusting the output value accordingly(in the case of a drift, bias, or scaling fault) or removing thesensor from the set of active measurements (in the case of a‘stuck’ fault).

4. TESTBED SIMULATOR

As previously mentioned, a simulator has been developed toaid in the design of PDM algorithms and use in the decision-making process. It captures both nominal and faulty behavior,with a controlled ability to inject faults. In this way, it servesas a virtual testbed through which algorithms can be initiallytested and validated. In this section, we describe the underly-ing physics model used in the simulator.

4.1. Rover Modeling

The rover consists of a symmetric rigid frame with fourindependently-driven wheels. Generalized rover coordinatesare shown in Figure 2, where the rover pose is given by(x, y, θ). The rover length is denoted by l, the width by b,and the distance from the rover center to each wheel by d.

Figure 2. Generalized rover coordinates

4.1.1. Rover Body

Wheels are denoted with F , B, L, and R subscripts, standingfor front, left, back, and right, respectively, so a wheel w islabeled from the set {FL,FR,BL,BR}. The forces actingon the rover body are summarized in Figure 3. The slip forceon wheel w, Fsw, is described by

Fsw = µs(vw − v), (1)

where µs is a friction coefficient, vw is the translational wheelvelocity, and v is the translation velocity of the rover body.When there is a difference between vw and v, slip is presentand the resulting force acts to push the wheel parallel to theground. When the rover is turning, there are friction forcesacting on the wheels opposing the sliding caused by the rota-tional velocity. The rotational friction force Fgrw is describedby

Fgrw = µgrdω, (2)

where µgr is a friction coefficient, and ω is the rotational ve-locity of the rover.

Figure 3. Rover forces

The translational and rotational rover velocities can be ex-pressed based on these forces1. The translational velocity v

1Note that velocity in the lateral direction is negligible (Mandow et al., 2007).

5


of the rover can be obtained from

v =1

m(FsFL + FsFR + FsBL + FsBR

+ (FgrFL − FgrFR + FgrBL − FgrBR) cos γ),

where m is the rover mass, γ = arctan lb , and the cos γ term

projects the Fgrw forces onto the translational direction. Therotational velocity ω can be obtained from

ω =1

J(d(FsFR + FsBR − FsFL − FsBL) cos γ

− d(FgrFL − FgrFR − FgrBL − FgrBR)),

where J is the rover rotational inertia and the moments aretaken in the counter-clockwise direction.

The rotational velocities of the wheels are determined by thetorques produced by the ground forces, as well as the motortorque, τmw = kτ iw, where iw is the motor current and kτis an energy transformation gain; and an axle friction torquethat opposes the wheel rotation, τfw = sign(τfw0

) +µfwωw,where τfw0

is the static friction torque and µfw is a fric-tion coefficient. In addition, while rolling, due to the de-formation of the wheel on the rolling surface, an upward-pointing rolling resistance force is produced ahead of thewheel center, creating a torque that opposes the rotation.The torque depends on speed and can be approximated byτrrw = sign(ωw)τrrw0

+ krrωw (Genta, 1997), where τrrw0

is a static friction torque and krr is an empirical parameter.The wheel speeds are thus governed by

ωFL =1

Jm(τmFL − τfFL − τsFL − τrrFL + τgrFL) ,

(3)

ωFR =1

Jm(τmFR − τfFR − τsFR − τrrFR − τgrFR) ,

(4)

ωBL =1

Jm(τmBL − τfBL − τsBL − τrrBL + τgrBL) ,

(5)

ωBR =1

Jm(τmBR − τfBR − τsFR − τrrBR − τgrBR) ,

(6)

where Jm denotes the wheel/motor inertia; τsw = rwFswis the torque due to slippage, where rw is the wheel radius;τgtw = rwFgtw is the torque due to the translational roverfriction force; and τgrw = rwFgrw cos γ is the torque due tothe rotational rover friction force.

The rover pose is then described by

x = v cos θ, (7)y = v sin θ, (8)

θ = ω. (9)

4.1.2. Motors

The wheels are driven by direct-current (DC) motors withproportional-integral-derivative (PID) control that sets thevoltages V applied to the motors as a pulse-width modulated(PWM) signal. Here, we ignore the PWM dynamics and as-sume an averaged model. For wheel w, the motor currents iware governed by

diwdt

=1

L(Vw − iwRw − kωωw). (10)

Here, L is the motor inductance, R is the motor resistance,and kω is an energy transformation term. The voltages ap-plied to the motors are determined by the controllers, wherefor wheel w, Vw = P · (uw −ωw) + I · eiw +D · edw, whereP is a proportional gain, uw is the commanded wheel speed,I is an integral gain, eiw is the integral error term, D is aderivative gain, and edw is the derivative error term.

The motor controllers take in total battery voltage VB andstep it down to apply to the motors to control the speed. Thecurrents drawn from the batteries by each motor controller,ibw for wheel w, respect a power balance with some loss dueto motor controller power efficiency. For wheel w, these cur-rents are therefore determined as

ibw =ηwVwiwVB

, (11)

where ηw is the motor controller power efficiency.

The motor windings are designed to withstand temperaturesup to a certain point, after which, the insulation breaks down,the windings short, and the motor fails. It is therefore impor-tant to model the temperature behavior of the motor. The mo-tor thermocouple is located on the motor surface. The surfaceloses heat to the environment and is heated indirectly by thewindings, which, in turn, are heated up by the current passingthrough them. The temperature of the windings for the motorof wheel w is given by

Tdw =1

Cdw

(i2wR− hdw(Tdw − Tmw)

), (12)

where Cdw is the thermal capacitance of the windings, hdw isa heat transfer coefficient, and Tsw is the motor surface tem-perature (Balaban, Narasimhan, et al., 2011). It is assumedthat heat is lost only to the motor surface, and that windingresistance R is approximately constant for the temperaturerange considered. The surface temperature of the motor forwheel w is given by

6


Tsw =1

Csw(hdw(Tdw − Tsw)− haw(Tsw − Ta)), (13)

where Csw is the thermal capacitance of the motor surface,haw is a heat transfer coefficient, and Ta is the ambient tem-perature. Heat is transferred from the windings to the surfaceand lost to the environment.

The motor temperature model was validated for DC motorsusing experimental data collected on the Flyable Electro-Mechanical Actuator (FLEA) testbed (Balaban et al., 2010).The unknown parameters Cdw, Csw, hdw, haw, and R wereidentified to match data acquired from a scenario where themotor was overloaded and, as a result, heated up consider-ably. The motor current and surface temperatures were mea-sured. A comparison of predicted vs. measured temperatureis shown in Figure 4.

0 500 1000

30

40

50

60

70

Time (s)

Tem

pera

ture

(o C)

MeasuredPredicted

Figure 4. Comparison of measured and model-predicted mo-tor surface temperature for a DC motor

4.1.3. Batteries

The input voltage to the motors is provided by the rover bat-teries. The battery model is based on an electrical circuitequivalent shown in Figure 5, and extends the model pre-sented in (Daigle, Saxena, & Goebel, 2012) that is similar tomodels presented in (Chen & Rincon-Mora, 2006; Ceraolo,2000). The large capacitance Cb holds the charge qb of thebattery. The RCP -CCP pair captures the major nonlinearvoltage drop due to concentration polarization, Rs-Cs paircaptures the so-called I-R drop, and Rp models the parasiticresistance that accounts for self-discharge. This simple bat-tery model is enough to capture the major dynamics of thebattery, but ignores temperature effects and other minor bat-tery processes.

The state-of-charge, SOC, is computed as

SOC = 1− qmax − qbCmax

, (14)

where qb is the current charge in the battery (related to Cb),qmax is the maximum possible charge, andCmax is the maxi-mum possible capacity. The concentration polarization resis-tance is a nonlinear function of SOC:

RCP = RCP0 +RCP1 exp (RCP2(1− SOC)), (15)

where RCP0, RCP1, and RCP2 are empirical parameters.The resistance, and, hence, the voltage drop, increases ex-ponentially as SOC decreases (Saha et al., 2012).

Figure 5. Battery equivalent circuit

Voltage drops across the individual circuit elements are givenby

Vb =qbCb, (16)

VCP =qCPCCP

, (17)

Vs =qsCs, (18)

Vp = Vb − VCP − Vs, (19)

where qCP is the charge associated with the capacitanceCCP , and qs is the charge associated with Cs. The voltageVb is also the open-circuit voltage of the battery, which isa nonlinear function of SOC (Chen & Rincon-Mora, 2006).This is captured by expressing Cb as a third-order polynomialfunction of SOC. The terminal voltage of the battery is

V = Vb − VCP − Vs. (20)

Currents associated with the individual circuit elements aregiven by

ip =VpRp

, (21)

ib = ip + i, (22)

iCP = ib −VCPRCP

, (23)

is = ib −VsRs

, (24)

where i = ibFL + ibFR + ibBL + ibBR is the battery currentat the terminals.

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The charges are then governed by

qb = −ib, (25)qCP = iCP , (26)qs = is. (27)

The battery temperatures are modeled with a simple thermalmodel described as follows. For battery k, the temperature isdescribed by

Tbk =1

Cbtk

(Rbtki

2b + hbtk(Ta − Tbk)

), (28)

where Cbtk is a thermal capacitance, Rbtk is a thermal resis-tance, ib is the total battery current, and hbtk is a heat transfercoefficient.

Two parallel sets of batteries power the rover. Each set con-sists of 12 cells connected in series to provide a nominal of48 V. When fully charged, each cell provides up to 4.2 V.The current i is split between the two sets, so each individualbattery is drained by a current of i/2 when balanced.

The battery model was validated with data from the batterytestbed at NASA Ames Research Center (Saha & Goebel,2009). A comparison of real and measured voltage for a con-stant discharge is shown in Figure 6, where it is clear that themodel predicts a nominal discharge curve very accurately.

4.1.4. Sensors

Sensors measure the voltages and temperatures of the batter-ies (Vbi and Tbi), the motor currents (ibw), the total current(i), the motor temperatures (Tmw), the wheel positions, andthe wheel speeds (ωw).

The phone provides additional GPS, accelerometer, gyro-scope, and magnetometer sensors. The nominal output of theGPS sensor is modeled as

λ = λ0 + arctan

(y

rE

), (29)

φ = φ0 + arctan

(x

rE

), (30)

h = h0, (31)

where λ0 is the initial latitude, φ0 is the initial longitude,and rE is the radius of the Earth. Here, we assume that therover does not undergo elevation changes within the measure-ment interval (∆h = 0) and that the curvature of the Earth isapproximately flat within the rover’s operating range. Thephone also provides accelerometer, gyroscope, and magne-tometer measurements. The accelerometer readings in the x,y, and z directions are computed as

ax = v cos(θ) + wl

2cos

(θ +

π

2

), (32)

ay = v sin(θ) + wl

2sin

(θ +

π

2

), (33)

az = 9.81. (34)

For the gyroscope, we assume that the only rotation is alongthe z-axis, so

gx = 0, (35)gy = 0, (36)gz = ω. (37)

For the magnetometer, since we assume only rotation aboutthe z-axis, we have

mx = M sin(θ + θd) · cos θi, (38)my = M cos(θ + θd) · cos θi, (39)mz = M · sin θi, (40)

where M is the maximum output of the magnetometer in anyone axis for the area of operation, θd is the declination anglefrom true north (the angle between magnetic and true northat the rover location), and θi is the inclination angle fromhorizontal.

0 500 1000 1500 2000 2500 3000 3500

3

3.5

4

Time (s)

Vol

tage

(V

)

MeasuredPredicted

Figure 6. Comparison of measured and model-predicted bat-tery voltage for a single battery cell

4.2. Fault Modeling

Most faults are captured in the model as changes in parametervalues. For example, increased motor friction is representedthrough changes in the friction coefficients (µfw), and inter-nal resistance increases in the batteries associated with agingare represented through changes in Rs and RCP . A parasiticload on the batteries is captured as an additional current, ipl,that is drawn from the batteries. Sensor faults are capturedwith bias, drift, and gain terms. Ranges for typical fault mag-nitude values have been identified through a literature searchand discussions with manufacturers (Balaban et al., 2009).Faults in common sensors, such as current, voltage, tempera-ture, and position, are modeled.

8


4.3. End of Life Constraints

We are interested in predicting when any of the rover batterycells are at their voltage threshold, beyond which the cellswill be damaged. The constraints are given as

ci : Vi > V −, i ∈ {1, 2, 3, 4}, (41)

where the voltage threshold is given by V − = 3.0 V.

We are also interested in when the motor temperature gets toohigh. The motors windings are designed to withstand temper-atures up to a certain point, after which, the insulation breaksdown, the windings short, and the motor fails (see subsection3.3). The constraints are given as

c5 : TdFL < T+d , (42)

c6 : TdFR < T+d , (43)

c7 : TdBL < T+d , (44)

c8 : TdBR < T+d , (45)

where the temperature limit is given by T+d = 70◦ C.

The rover cannot be operated when one or more of these con-straints are violated.

5. INTEGRATED ARCHITECTURE

A typical rover mission consists of visiting and performingdesired science functions at a set of predetermined waypointsW = {(xi, yi), ri}Ni=1, where ri is the reward associated withlocation (xi, yi). An autonomous PDM system for the roverdetermines the order to visit the waypoints and the speed vito travel between them, so as to maximize the reward whileminimizing the power used and health deterioration. Whendiagnostic and prognostic information is available, the deci-sion making system may alter the waypoint list (reduce and/orreorder) to minimize the impact of the faults and slow theirprogression over time. Figure 7 presents the integrated deci-sion making architecture, which consists of four main compo-nents, namely (i) locomotion controller (LC), (ii) diagnostics(DX), (iii) prognostics (PX), and (iv) decision making (DM).

The LC is responsible for guiding the rover to the currentwaypoint, wi = {{xi, yi}, ri}, by commanding individualwheel velocities to be vt at time, t. The rover is a skid-steeredvehicle, meaning that the wheels cannot be steered and therover is rotated by commanding the wheel speeds on the leftand right sides to different values. The low-level controllermust be robust to drive system faults, therefore, it receivesthe current diagnosis Ft from the DX algorithm.

The DX module takes in the inputs ut and sensor data zt,and reasons about faults in the system. The DX runs contin-uously, trying to detect when a fault (or faults) occur, isolatethe actual fault(s) from a set of possible candidates, and iden-tify fault magnitudes. In case of a fault, as a diagnosis Ft

becomes available, it is passed on to the LC for mitigation,as well as to the prognoser, which uses the information as astarting point for predicting fault progression.

If an off-nominal condition is detected, the PX module beginsto continuously estimate the health state of the affected com-ponents (and the rover overall) and generates predictions ofthe remaining useful life, RULt. RUL is the time until thesystem violates functional or performance constraints. TheRUL prediction is conditional on the future usage of the ve-hicle, determined by the waypoint list.

The DM module is responsible for planning under nominaland faulty conditions. At the mission start, the DM gets aset W of desired waypoints. The DM also has a terrain mapM that describes the geographical layout of the terrain onwhich the waypoints are located. The DM then, based onthe predicted power usage and RUL predictions, determinesan ordered (and possibly reduced) list of waypoints. A num-ber of different protocols may be implemented for invokingthe module. For example, after the first solution is produced,the DM may be called again if PX predictions start divergingsubstantially from the initial ones. Alternatively, DM may becalled after each waypoint is reached.

We anticipate that the architecture described in this sectioncan be applied with only minimal changes to an aerial testvehicle, such as the Edge 540 unmanned aerial vehicle de-scribed in (Hogge, Quach, Vazquez, & Hill, 2011). Motioncontrol components would, of course, need to be adapted tooperate with six degrees of freedom instead of three. Execu-tion of the reasoning algorithms would need to be optimizedto accommodate the faster position change rates and to ac-count for the fact that an aerial vehicle, unlike a rover, doesnot have the option of pausing motion while a fault is beinganalyzed or a new course of action is being formulated.

6. LOCOMOTION CONTROL

The task of the locomotion controller is to direct the rover toa given waypoint wi = {(xi, yi), ri} by sending appropri-ate wheel speed commands to the individual motors based onthe estimated pose (x, y, θ). We define two different controlstrategies: one which does not take into account diagnosticinformation and one that does.

6.1. Proportional Control

The waypoint wi and desired cruise speed uv are given asinputs to the proportional controller. It implements a pro-portional control based on the error between the current esti-mated heading θ and the desired heading θ∗, eθ. The averagewheel speed is set to uv and the desired speeds of the left andright sides are set to turn toward the waypoint based on eθ:

9


Diagnoser Prognoser DecisionMaker

LocomotionControl

Rover/Simulator

Inputs Outputs

Waypoint

Waypoint List

Remaining LifeTerrain Map

Waypoint Set

DiagnosedFault Set

Figure 7. Autonomy Architecture

uL = uv − Pθeθ, (46)uR = uv + Pθeθ, (47)

where Pθ is the proportional gain. The individual wheelspeeds are then set to

uFL = uL, (48)uFR = uR, (49)uBL = uL, (50)uBR = uR. (51)

6.2. Differential Speed

In the proportional control, the wheel speeds on one side ofthe rover are always set to the same value. However, if amotor friction fault is present on one side of the rover, thenit is more efficient overall to increase the desired velocity ofthe good wheel and decrease the velocity of the faulty wheelon that side. The optimal amount of change depends on themagnitude of the friction fault.

This controller uses the proportional control as the basis andmodifies its outputs based on the value of the friction coeffi-cient. First it computes nominal wheel speeds for the left andright sides (equations 46-47). Then, it modifies the speedscommanded to the front and back wheels on each side ac-cording to the estimated friction coefficient.

uFL = uL2

1 +1+µfFL

1+µfBL

, (52)

uFR = uR2

1 +1+µfFR

1+µfBR

, (53)

uBL = uL2

1 +1+µfBL

1+µfFL

, (54)

uBR = uR2

1 +1+µfBR

1+µfFR

. (55)

Note, from equations 52 and 54, that

uFL + uBL2

= uL. (56)

Similarly, from equations 53 and 55

uFR + uBR2

= uR. (57)

On a given side of the rover, if the friction on the front wheelis larger than friction on the back wheel, the speed of thefront wheel is decreased and the speed of the back wheel isincreased. If the back wheel has more friction than the frontwheel, its speed is decreased while the speed on the frontwheel is increased. The overall speed on that side of the roverremains the same, but the total current drawn is less than ifboth wheels were set to the same speed.

7. REASONING ALGORITHMS

The primary purpose for building the K11 is to enablehardware-in-the-loop testing of reasoning algorithms (diag-nostic, prognostic, and decision-making). The current set ofalgorithms, in addition to demonstrating certain novel PDMideas, serves to validate the integrated reasoning architectureand the concept of operations for the testbed. Some of thealgorithms have been used in previous research efforts (e.g.Qualitative Event-based Diagnosis (QED), Hybrid Diagnos-tic Engine (HyDE), and some of the prognostic methods),while others are being developed concurrently with the K11.The details of the algorithms are provided in the rest of thissection.

7.1. Diagnosis

Diagnosis involves detection, isolation, and identification offaults. A fault is a change in the system that causes its be-havior to deviate from nominal. Detection involves deter-mining when a fault occurs based on some observable symp-toms. Isolation involves determining the true fault out of aset of, possibly, several fault candidates, and identification isthe process of determining the extent of the damage to thesystem. Numerous diagnosis approaches exist in the litera-ture. We apply two model-based diagnosis approaches to the

10


rover testbed: the QED algorithm and the HyDE, both devel-oped at NASA Ames Research Center on the basis of earlierwork at Vanderbilt University (the algorithms are overviewedin the following subsections). The motivation for two distinctalgorithms to be used in the same role is to demonstrate theability of the testbed to easily accommodate reasoning algo-rithms from different sources, as long as they adhere to thesame interfaces. Several diagnostic algorithms could even,potentially, run in parallel, with their output aggregated by ahigher level reasoner.

7.1.1. QED

QED, described in (Daigle & Roychoudhury, 2010), utilizesa qualitative diagnosis methodology that isolates faults basedon the transients they cause in system behavior, manifestingas deviations in residual values (Mosterman & Biswas, 1999).Transients produced by faults are abstracted using qualita-tive + (increase), - (decrease), and 0 (no change) values toform fault signatures. Fault signatures represent these mea-surement deviations from nominal behavior as the immediate(discontinuous) change in magnitude and the first nonzeroderivative change. These symbols are computed from theresiduals using symbol generation. In addition to signatures,QED captures the temporal order of measurement deviations,termed relative measurement orderings. The fault signaturesand measurement orderings can be computed manually or au-tomatically from a system model. They are compared withobserved signatures and orderings in order to isolate faults.The combination of signatures and orderings establishes anevent-based fault isolation framework.

QED uses the model of the rover described in Section 4.Given this model, fault signatures and measurement orderingsare derived. Algebraic functions computing fault magnitudesare also derived and used for fault identification.

7.1.2. HyDE

HyDE is a consistency-based diagnosis engine that uses hy-brid (discrete/continuous) models and reasoning (Narasimhan& Browston, 2007). The models are also allowed to incor-porate stochastic behavior. Users first build models of con-stituent components of the system and then compose the sys-tem model by defining the connections between the compo-nents. Component models include a set of discrete modes(nominal or off-nominal) the components could be in and thebehavior of the component in each mode. A transition from anominal mode to a fault mode indicates an occurrence of thecorresponding fault. At any point in time, HyDE maintains aset of candidates that offer alternative versions of the systemstate that are consistent with the sensor observations seen sofar (the size of the candidate set can be limited). When ad-ditional observations become available, the candidate set ispruned of inconsistent candidates and augmented with new

consistent candidates. Several parameters are available to ad-just the performance of the engine, including heuristics to de-termine the candidate ranking or the type of system simula-tion used.

Similarly to QED, the HyDE model for the rover was de-veloped directly from the simulation models, with the com-ponents and equations in one-to-one correspondence. Faultmodes were defined for all of the sensors, as well as for themotors (increased friction fault) and batteries (parasitic loadfault).

7.2. Prognosis

Prognosis is concerned with predicting the end of (useful) life(EOL) and RUL of a component, subsystem, or system. EOLis defined as the earliest time point at which the system nolonger meets specified functional or performance constraints,and RUL is the time remaining until that point. These con-straints do not necessarily have to correspond to completefailure, e.g., for the rover we are interested in when a bat-tery reaches end-of-discharge. In order to predict EOL/RUL,we require an estimate of the current system state (includingknown fault conditions), some estimate of the future usage ofthe system, and some model that can predict the evolution ofthe system state up to EOL. This model may be determinedthrough physical modeling of the system (Daigle, Saha, &Goebel, 2012) or through data-driven methods (Schwabacher,2005).

For the rover, prognostics algorithms can be used for severalcomponents. For the batteries, we must predict when a bat-tery will be fully discharged, because the rover cannot be op-erated beyond that point. This has obvious implications fordecision-making. As the batteries are used over several rovermissions, they will naturally age and the capacity rating willdrop, therefore we must also predict when the battery capac-ity falls below the required minimum. For the drive motors,we need to predict when an overheating may occur, since itcan lead to permanent motor damage.

7.2.1. Model-based Prognosis

The model-based prognosis paradigm (Orchard, 2007;Daigle, Saha, & Goebel, 2012) consists of two steps: (i) stateestimation, which computes a joint state-parameter estimateof the system, and (ii) prediction, which simulates the modelforward from a given health state out to the EOL threshold,based on hypothesized future inputs to the system. State esti-mation can be performed with Kalman filters (Celaya, Kulka-rni, Biswas, & K., 2012), unscented Kalman filters (Daigle,Saha, & Goebel, 2012), particle filters (Orchard, 2007; Saha& Goebel, 2009; Daigle & Goebel, 2011), or similar algo-rithms. Prediction is typically performed by sampling fromthe state estimate and simulating each sample to EOL, tak-ing into account process noise and future input uncertainty

11


(Daigle, Saxena, & Goebel, 2012).

The prediction step requires knowledge of the future usage ofthe system. For the rover, this involves the expected futuretrajectory and environmental inputs, such as the terrain andthe ambient temperature. The physics models developed forthe simulator can be utilized in both the estimation and pre-diction phases. Damage progression processes that are diffi-cult to model may require the use of data-driven prognosticsmethods.

As an example of the model-based prognosis approach, con-sider prognostics of the rover batteries. In this particular case,we predict when the battery voltage will decrease to 3 V (fo-cusing on one particular battery). The total current drawnfrom the batteries is shown in Figure 8a (recall that each indi-vidual battery sees only half that current). The measured andestimated voltages are shown in Figure 8b. The battery doesnot start at full charge (which would be approximately 4.2 V)and so reaches EOL around 1800 s. The estimated batterySOC is shown in Figure 8c, and, according to the model, thebattery starts at only 22% SOC. The corresponding predictionresults, assuming future inputs known exactly, are shown inFigure 8d. As can be seen, the predictions are very accuratefrom early on in the process, which means that, since the fu-ture inputs are known, the model is accurate in the open loop.

7.2.2. Data-driven Prognosis

In data-driven prognostics the degradation model for a faultmode is learned from training data. While potentially requir-ing less domain knowledge a priori than model-based tech-niques, reliance on availability of such data can be a limitingfactor in some types of practical applications. Methods suchas Neural Networks, Relevance Vector Machines, and Gaus-sian Process Regression (GPR) have been utilized for data-driven prognostics (Schwabacher, 2005).

In this work a machine-learning algorithm based on GPR isused to predict when the interior of a drive motor would reachthe temperature at which insulation of the windings is likelyto melt, thus disabling the motor. This fault mode is likelyto occur if the motor, in addition to its nominal load, has tocompensate for increased mechanical friction. An increase infriction can occur due, for example, to a failed bearing or adamaged gear inside the gearbox (please refer back to sub-section 3.3 for more details). The thermal build-up model, asdescribed in the Section 4, will be used for comparison.

The GPR-based algorithm was previously tested in prognos-tic experiments involving motor faults in electro-mechanicalactuators (Balaban, Saxena, et al., 2011). An increased fric-tion fault was injected and the relevant sensor data collectedas the actuator continued to be used in a degraded state (var-ious position and load profiles were utilized in the experi-ments). Several motors were run to complete failure, with

GPR demonstrating a high accuracy in predicting their re-maining useful life.

GPR does not need explicit fault growth models and canbe made computationally less expensive by sampling tech-niques. Further, it provides variance bounds around thepredicted trajectory to represent the associated confidence(Rasmussen & Williams, 2006). Domain knowledge avail-able from the process is encoded by the covariance functionthat defines the relationship between data points in a time se-ries. In our present implementation, a Neural Network typecovariance function is used.

7.3. Decision Making

The overall objective of this work is to develop PDM algo-rithms that enhance a vehicle’s capability to achieve its high-level goals - be it under a localized fault condition, degradedoperation of a subsystem, or an anticipated catastrophic fail-ure. There has been an increasing volume of research con-ducted over the last several years in prognostic methodolo-gies for various types of components or systems. The ef-fort described in this section aims to bring more attention tothe management aspect of prognostic health management, i.e.what could be done after a fault is detected and a prognosticprediction for it is produced.

While the components involved and the particulars of eachoff-nominal situation may be different, there are, however,common elements in all of them. There is always an objec-tive (or a set of objectives) to be met and a series of actions tobe selected by the decision making process in order the meetthose objectives. In many circumstances a satisfactory solu-tion (one that satisfies constraints defined for the system) is allthat is required; in this work, however, we chose to define thedecision-making process as an optimization problem, wherea Pareto Optimal Set of solutions (Fudenberg & Tirole, 1991)is produced given the objectives, prognostic system estimates,system constraints, and the projected future operating condi-tions. The Pareto formulation is used to accommodate multi-ple potential objectives.

Some of our initial work in PDM was described in (Balaban,Narasimhan, et al., 2011). A more recent publication(Balaban & Alonso, 2012) provides a PDM problem formu-lation from a multi-objective optimization point of view anddescribes the overall approach being pursued. The currentwork focuses on the following aspects of PDM: (i) decom-position of the overall decision-making problem into smallersubproblems; (ii) subproblem modeling methods; (iii) sub-problem decision-making algorithms; and (iv) methods foradjusting problem formulations (such as constraints or objec-tives) in real-time, if necessitated by prognostic predictionsin off-nominal situations.

Two K11-related case studies are used in research in these

12


0 200 400 600 800 1000 1200 1400 16000

1

2

3

4

5

6

Time (s)

Cur

rent

(A

)

(a) Measured battery current

0 200 400 600 800 1000 1200 1400 16003

3.2

3.4

3.6

3.8

4

4.2

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tage

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0 200 400 600 800 1000 1200 1400 16000

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SOC

(%

)

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0 200 400 600 800 1000 1200 1400 16000

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RU

L (

S)

[(1 − α)RUL∗, (1 + α)RUL∗]RUL∗

RUL

(d) Predicted battery remaining useful life

Figure 8. Battery prognosis results

four areas. One involves relaxation of the maximum oper-ating temperature constraints on the batteries and motors inorder to achieve a desired destination in the presence of anincreased friction fault. The other is built around the way-points optimization scenario mentioned in the earlier parts ofthe paper and described in detail in Section 8.

For the constraint relaxation case study, both a method toperform system decomposition from the game-theoretic per-spective and an approach to adjust select system constraints(if that is needed to satisfy high-priority performance goals)are explored. Decomposition is performed based on thesubsystem-level abstraction, where the subsystems cooper-ate in exploring the (potentially) very large option space bytaking turns in searching for a suitable solution. The currentformulation of the decomposition algorithm tests the conceptfor two rover subsystems (power and propulsion), with exten-sion to larger numbers of subsystems planned for subsequentversions.

The waypoints optimization case study forms the basis ofthe experiments covered in this paper. It motivated the workof exploring decision-making models suitable for PDM andalgorithms capable of using the models to generate an op-timal action policy in the presence of system degradation,

multiple objectives, uncertainty, and constraints. The gen-eral modeling approach currently used for waypoints opti-mization is Partially Observable Markov Decision Process,POMDP (Cassandra, Kaelbling, & Littman, 1995). Severalalgorithms have been applied to generate solutions. DynamicProgramming, backtracking search, and Particle Filter areamong them. In the set of experiments presented in the nextsection a stochastic algorithm patterned on the ProbabilityCollectives (PC) approach (Wolpert, 2006) is used. The al-gorithm belongs to the class of blackbox optimization meth-ods. Such methods, generally, have the goal of finding a valuex ∈ X that minimizes an associated value F (x). X is an op-timization space and F (x) could be an objective or a utilityfunction. The following process is repeated iteratively: (1) anx is chosen from X; (2) statistical information about F (x) isupdated; (3) the next value of x is chosen using the (x, F (x))pairs found up to that point. For waypoint optimization, par-tial paths form the optimization space X and objective func-tions are created for scientific payoff, energy use, and vehiclehealth. Further details on the approach and the algorithm im-plemented are provided in (Balaban & Alonso, 2012).

13


8. EXPERIMENTS AND RESULTS

This section provides examples of integrated prognostics-enabled decision making on a set of fault scenarios executedon the K11 simulator. The case study presented is that of therover starting its mission at a waypoint w0 and attempting tovisit, at an average speed of 0.5 m/s, a set of other 10 way-points, accomplishing a scientific objective at each. As men-tioned previously, every waypoint is associated with a rewardvalue and the primary objective is to maximize the cumula-tive reward. In absence of system faults the rover has enoughenergy stored in its batteries to visit all of the waypoints. Inaddition to this nominal scenario, however, three fault sce-narios are considered: a parasitic load in the power distribu-tion system, increased motor friction (Figure 9), and a batteryvoltage sensor fault. In the fault scenarios, the diagnostic sys-tem is expected to detect and identify the fault mode duringthe w0 → w1 transition. The decision-making system is thenexpected to modify the waypoint traversal plan, taking intoaccount prognostic estimates of future energy consumptionand fault magnitude progression. An a posteriori estimate ofchange in these two quantities during thew0 → w1 transition,given the fault diagnosis, is made as well.

8.1. Battery Parasitic Load Fault

As a first scenario, we consider an abrupt parasitic load faultthat draws an additional amount of current from the batteries.A parasitic current of 0.1 A is injected starting at 50 s. As aresult, the net current increases and the battery voltages de-crease in response to the increased current. No other effectsappear, but the batteries will drain faster and therefore pathanalysis will have to be performed to determine if all of thewaypoints can still be visited with this increased load. SeeFigure 10 for a diagram that illustrates the timing of variousevents in this scenario.

QED detects the fault at 50.4 s with an increase in i, the cur-rent drawn from the batteries. The candidate set reduces to:motor failures, motor friction faults, the parasitic load fault,and a bias or drift in the current sensor. At 51.2 s, the changeis determined to be abrupt, eliminating the friction faults andthe drift fault. At 76.15 s, a decrease in the voltage of battery4 is detected. This eliminates the current sensor fault, sinceit would not affect another sensor, and eliminates the motorfailure faults, as these would cause a change in individual mo-tor currents before a change in voltage (i.e., there is a relativemeasurement ordering for these faults expressing this con-straint), thus uniquely isolating the parasitic load fault. Theparasitic current is computed as the difference between thebattery current and the sum of the motor currents, averagedfrom the time of detection to the present time. At 51.2 s,the value of the parasitic current is estimated at 0.127 A. By100 s, the estimate is at 0.103 A.

HyDE detects the fault at 50.05 and isolates the fault to either

a parasitic load or one of the motors being in an unknownmode.2 In addition, HyDE was tested on a double fault sce-nario where there is a battery parasitic load and the batterycurrent sensor is faulty. HyDE is able to use other sensorsto determine this condition. The overall result is the same aswith the parasitic load fault, since sensor faults do not affectthe decision-making.

0 20 40 60 80 100

10

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Time (s)

Vol

tage

(V

)

V1

MeasuredPredicted

0 20 40 60 80 1000

1

2

Time (s)

Cur

rent

(A

)

i

0 20 40 60 80 1000

0.51

1.5

Time (s)

Cur

rent

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)iBL

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20.5

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pera

ture

(o C)

TBL

0 20 40 60 80 1000

0.2

0.4

Time (s)

Vel

ocity

(m

/s)

vBL

Figure 9. Sensor readings for motor friction fault

Prognosis begins once the fault is identified. Here, we de-termine when the batteries will reach end-of-discharge withthe current mission plan. The prognosis algorithm reportsthat the batteries will reach this point in 3.83 h (as opposedto 4.54 h without the fault). Continuing at an average speedof 0.5 m/s, the rover can cover about 6.9 km with the fault(8.2 without the fault). Since the rover must cover at least6.9 km to visit all of the waypoints, mission optimization isrequired. The DM module estimates that there will not be

2In the unknown mode, the behavior of the motor is undefined and henceit could be drawing more current. However, unknown faults are catch-allmodes that should be considered only when no other explanations are avail-able.

14


Time (s)50 55 60 65 70 75 80

Fault Injected at 50 s

- Fault Detected at 50.4 s

- Decrease in i observed

Decrease in i determined to be abrupt at 51.2 s

- Decrease in battery 4 voltage observed at 76.15 s

- Correct fault (parasitic load fault) isolated

- Identify parasitic load fault at 100s

- Initiate prognosis

- DM module replans mission

100 105 110

Time (s)50 55 60 65 70 75 80


Correct fault (parasitic load fault) isolated at 50.05 s

- Identify parasitic load fault at 100s



100 105 110

QED

HyDE

Figure 10. Timing diagram for the battery parasitic load fault scenario

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g0g1

g2g3

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Figure 11. Decision making results (with r1 = 40, r2 = 50, r3 = 30, r4 = 20, r5 = 60, r6 = 40, r7 = 100, r8 = 50, r9 = 30,and r10 = 60)

enough energy to visit all of the waypoints and eliminateswaypoints 9 and 4 from the plan, reconfiguring the path to beqs = {1, 6, 3, 5, 2, 8, 10, 7}. See Figure 11 for the decision-making results under different scenarios.

8.2. Motor Friction Fault

As a second scenario, we consider a motor friction fault inthe back-left motor (Figure 9). The friction coefficient valueis increased by a factor of 10 at 50 s. As a result, the motorcurrent increases because its PID controller is still trying tomaintain the wheel speed at the same level. This correspondsto an increase in the total current drawn from the batteries andan accelerated rate of discharge (and, thus, decreased RUL).The motor temperature also rises due to the increased currentdraw, and this can lead to an EOL condition of the motor dueto the overheating. As a result, decision making will have tooptimize RUL with respect to battery life and motor health.

QED detects the fault at 50.15 s with an increase in vBL, the

velocity of the back-left wheel 9. The candidate set reduces toa failure of the back-left motor, increased friction in the back-left motor, and a bias or drift in the vBL sensor. At 50.25 s, anincrease in both i and iBL are detected, eliminating the motorfailure fault (which would have decreased the current) andthe faults in the vBL sensor (since they cannot affect any othersensors), leaving the motor friction fault as the sole candidate.The friction value is computed using the steady-state wheelspeed equation, averaged from the time of detection to thepresent time. At 50.25 the friction value is estimated at 1.47times its nominal value. By 100 s, the estimate is at 10.1 timesits nominal value. HyDE is also able to diagnose this faultat 50.2. However, HyDE does not support fault magnitudeestimation (identification). See Figure 12 for a diagram thatillustrates the timing of various events in this scenario.

Prognosis begins once the fault is identified. Here, multi-ple possible future input trajectories may be assumed thatwill help with decision making. The increase in currentdue to the fault will cause the batteries to discharge earlier

15


Time (s)50 55 60 65 70 75 80



- Decrease in vBL observed

- Decrease in i and iBL detected at 50.25 s

- Correct fault (motor friction fault) isolated

- Identify motor friction fault at 100 s



100 105 110

Time (s)50 55 60 65 70 75 80


Correct fault (motor friction fault) isolated at 50.2 s

- Identify motor friction fault at 100 s



100 105 110

QED

HyDE

Figure 12. Timing diagram for the motor friction fault

Time (s)50 55 60 65 70 75 80



- Increase in voltage sensor of battery 1 observed

- Voltage change in battery 1 determined to be abrupt at 50.9 s

- Correct fault (voltage sensor of battery 1 fault) isolated

100 105 110

Time (s)50 55 60 65 70 75 80


100 105 110

Correct fault (voltage sensor of battery 1fault) isolated at 50.1 s

QED

HyDE

Figure 13. Timing diagram for the voltage sensor fault

than expected, and the increase in motor temperature maybring the motor to its EOL due to overheating. Accordingto the prognosis algorithm, the overheating event occurs in1423 s if the rover continues to travel at the same speed andat 4084 s at 80% speed (0.4 m/s). At 60% speed (0.3 m/s), thesteady-state value of the temperature is below motor temper-ature limit, so the rover can travel indefinitely without over-heating the motor, and EOL is determined solely by batteryend-of-discharge, which ends up being 6313 s. However, ifthe friction-robust controller is used, then the overall currentdraw decreases and motor overheating can be prevented. Fur-thermore, less overall current is drawn from the batteries forthe same forward speed of the rover, resulting in improvedRULs of 4283 s at normal speed (0.5 m/s), 6004 s at 0.4 m/s,and 8897 s at 0.3 m/s.

If the non-robust LC is used, the decision-making mod-ule considers traverses with different speeds (0.3, 0.4, and0.5 m/s) in order to arrive at the optimal payoff. Travelingat 0.5 m/s does not allow the rover to visit any of the otherwaypoints due to high energy draw. Traveling at 0.4 m/sgets the rover to waypoints 3 and 6, with R(qs)=11. Reduc-ing the speed further to 0.3 m/s allows the rover to get toa higher-reward (but more difficult to get to) waypoint 7 in-stead (R(qs)=14). Consequently, the rover speed is reducedto 0.3 m/s. Introducing the friction-robust LC allows to keepthe motor temperature within safe limits at any of the speedsconsidered and, due to the reduced power draw, makes it pos-sible to accomplish longer traverses: qs = {1, 2, 5} at 0.5 m/s(R(qs)=15); qs = {1, 6, 3, 5} at 0.4 m/s (R(qs)=17); andqs = {1, 3, 5, 2} at 0.3 m/s (R(qs)=18). Since travel time

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is not one of the optimization constraints, the lower speed of0.3 m/s is therefore selected (Figure 11).

8.3. Voltage Sensor Fault

As a third scenario, we consider a bias fault in the voltagesensor of battery cell 1. The bias has a value of 0.5 V and isinjected at 50 s. QED detects the fault at 50.3 s, and, sinceno other faults can produce an increase in voltage, only biasand drift faults in the voltage sensor are valid candidates. At50.9 s, the change is determined to be abrupt, isolating thebias fault as the only candidate. The bias value is estimatedto be 0.51 V. HyDE is able to detect a voltage sensor fault onBattery 1 at 50.1. However the HyDE model does not try tofurther isolate the fault as a bias or drift. The timing of theevents is shown in Figure 13.

Because the fault was determined to be in a sensor (and onethat is not part of a control loop), the rover was deemed tobe capable of operating without reconfiguration or missionchanges required. Therefore, neither the prognoser nor thedecision-making module were invoked.

In all of the above scenarios the PC-based decision-makingalgorithm produced the same results as a (much slower) ex-haustive search algorithm. The latter was used as a determin-istic way to verify the general correctness of the former. Themaximum number of the remaining waypoints was limitedto 10 as beyond that running the exhaustive search algorithmbecame impractical (with execution times of 300 seconds orlonger). Execution times for the PC-based algorithm largelydepended on the hyperparameter values used (see Balabanand Alonso (2012)) for a more in-depth discussion on thesubject), however the algorithm appeared to be suitable forreal-time use even on scenarios involving 25 waypoints (themaximum number attempted). While the results produced byPC and other approximate algorithms will degrade in accu-racy and repeatability as the number of waypoints grows, thesize of the search space in problems of this type may stillleave them as the best option.

9. CONCLUSIONS

The work described in this paper is aimed at providing aninexpensive, safe platform for development, evaluation, andcomparison of prognostics-enabled decision-making algo-rithms. Technologies resulting from this research are plannedto be transferred for further maturation on unmanned aerialvehicles and other complex systems. At present, the K11testbed already constitutes a promising platform for PDM re-search. A list of fault modes of interest has been identifiedand a number of them have been implemented in softwareand/or hardware. A software simulator has been developedthat incorporates models of both nominal and off-nominal be-havior, with the models validated using experimental data.The software architecture for the testbed has been defined in

such a way as to allow quick replacement of autonomy el-ements depending on the testing objectives and customers.The sensor suite and the data acquisition system support awide range of reasoning algorithms. The first set of such algo-rithms, for performing diagnostics, prognostics, and decision-making, is being deployed and tested. At this point it has beentested in simulation on scenarios involving battery parasiticload, increased motor friction, and voltage sensor faults.

Plans for the near future include addition of further hardware-injectable fault modes, field experiments of greater complex-ity, simulator model refinement, and extension of PDM meth-ods to handle more complex problems, including constraintsrelaxation when the situation requires that. Data collected onthe testbed is planned for distribution to other researchers inthe field.

10. ACKNOWLEDGMENTS

The authors would like to gratefully acknowledge the con-tributions of researchers and student interns at NASA AmesResearch Center: Bhaskar Saha, Sankalita Saha, Kai Goebel,Brian Bole, Terry Fong, Liam Pedersen, Vinh To, Susan Lee,Hans Utz, Lorenso Fluckiger, Maria Bulaat, Vytas SunSpi-ral, Jeremy Frank, Michael Dalal, Zachary Ballard, SterlingClarke, Tabitha Smith, Kevin Rooney, and Sebastian Hening.Many ideas in this work have been borne out of discussionswith colleagues at Impact Technologies (Liang Tang, EricHettler, Bin Zhang, and Jonathan DeCastro). The fundingfor this research is provided by NASA ARMD System-wideSafety & Assurance Technology (SSAT) project.

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BIOGRAPHIES

Edward Balaban is a research engineer in the Diagnosticsand Prognostics group at NASA Ames Research Center. Hereceived the Bachelor degree in Computer Science from TheGeorge Washington University in 1996 and the Master degreein Electrical Engineering from Cornell University in 1997.His main areas of interest are diagnostics, prognostics, andprognostics-enabled decision making. During his years atAmes he has participated in the research and development ofsystem health management elements for the X-34 experimen-tal reusable launch vehicle, the International Space Station,robotic astronaut assistants, autonomous planetary drills, andother aerospace applications. He is a member of the PHMSociety, the IEEE, and the AIAA.

Sriram Narasimhan is a Project Scientist with Universityof California, Santa Cruz working as a contractor at NASAAmes Research Center in the Discovery and Systems Healtharea. He received his M.S and Ph.D. in Electrical Engineer-ing and Computer Science from Vanderbilt University. Healso has a M.S in Economics from Birla Institute of Technol-ogy and Science. His research interests are in model-baseddiagnosis with a focus on hybrid and stochastic systems. Heis the technical lead for the Hybrid Diagnosis Engine (HyDE)project.

Matthew J. Daigle received the B.S. degree in Computer Sci-ence and Computer and Systems Engineering from Rensse-laer Polytechnic Institute, Troy, NY, in 2004, and the M.S.and Ph.D. degrees in Computer Science from Vanderbilt Uni-versity, Nashville, TN, in 2006 and 2008, respectively. FromSeptember 2004 to May 2008, he was a Graduate ResearchAssistant with the Institute for Software Integrated Systemsand Department of Electrical Engineering and Computer Sci-ence, Vanderbilt University, Nashville, TN. From June 2008

to December 2011, he was an Associate Scientist with theUniversity of California, Santa Cruz, at NASA Ames Re-search Center. Since January 2012, he has been with NASAAmes Research Center as a Research Computer Scientist.His current research interests include physics-based model-ing, model-based diagnosis and prognosis, simulation, andhybrid systems.

Indranil Roychoudhury received the B.E. (Hons.) degreein Electrical and Electronics Engineering from Birla Instituteof Technology and Science, Pilani, Rajasthan, India in 2004,and the M.S. and Ph.D. degrees in Computer Science fromVanderbilt University, Nashville, Tennessee, USA, in 2006and 2009, respectively. Since August 2009, he has been withSGT, Inc., at NASA Ames Research Center. Dr. Roychoud-hury is a member of the Prognostics and Health ManagementSociety and the IEEE. His research interests include hybridsystems modeling, model-based diagnostics and prognostics,distributed diagnostics and prognostics, and Bayesian diag-nostics of complex physical systems.

Adam Sweet is a research engineer in the Diagnostics andPrognostics group at NASA Ames Research Center. Hegraduated with an MS in Mechanical Engineering from UCBerkeley in 1999, and has worked at Ames ever since. Hisproject experience encompasses robotics, hybrid system sim-ulation, model-based diagnosis, and flight software develop-ment for nanosatellites.

Christopher Bond is an electrical engineer with the Controland Data Systems group at NASA Kennedy Space Center.He received the B.S.E.E (summa cum laude) from the Geor-gia Institute of Technology in 1995. He has been involvedwith various projects throughout his career at NASA, includ-ing design modifications to and testing of the Space Shut-tle ground landing systems, instrumentation for weather sys-tems, as well as his current role as senior network engineerfor the new Spaceport Command and Control system beingbuilt at Kennedy Space Center.

Jose R. Celaya is a research scientist with SGT Inc. atthe Prognostics Center of Excellence, NASA Ames ResearchCenter. He received a Ph.D. degree in Decision Sciences andEngineering Systems in 2008, a M. E. degree in OperationsResearch and Statistics in 2008, a M. S. degree in ElectricalEngineering in 2003, all from Rensselaer Polytechnic Insti-tute, Troy New York; and a B. S. in Cybernetics Engineeringin 2001 from CETYS University, Mexico.

George Gorospe received the B.E. degree in Mechanical En-gineering from the University of New Mexico, Albuquerque,New Mexico, USA, in 2012. Since October 2012, he has beenwith the Universities Space Research Association, at NASAAmes Research Center. His current research interests includemission design, systems engineering, and autonomous mobilerobot control.

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