ORangE: Operational Range Estimation for Mobile Robot Exploration on a Single Discharge Cycle
OORangE: Operational Range Estimation for MobileRobot Exploration on a Single Discharge Cycle
Kshitij Tiwari ∗ , Xuesu Xiao † , Ville Kyrki ∗ , and Nak Young Chong ‡∗ School of Electrical Engineering, Aalto University, Finland, 02150Email: { kshitij.tiwari, ville.kyrki } @aalto.fi † Dept. of Comp. Sci. & Eng., Texas A&M University, College Station, TX 77843Email: [email protected] ‡ School of Info. Sci., JAIST, Japan, 923-1211Email: [email protected]
Abstract —This paper presents an approach for estimatingthe operational range for mobile robot exploration on a singlebattery discharge. Deploying robots in the wild usually requiresuninterrupted energy sources to maintain the robot’s mobilitythroughout the entire mission. However, due to unknown natureof the environments, recharging is usually not an option, dueto the lack of pre-installed recharging stations or other missionconstraints. In these cases, the ability to model the on-boardenergy consumption and estimate the operational range is crucialto prevent running out of battery in the wild. To this end, thiswork describes our recent findings that quantitatively breakdown the robot’s on-board energy consumption and predictthe operational range to guarantee safe mission completion ona single battery discharge cycle. Two range estimators withdifferent levels of generality and model fidelity are presented,whose performances were validated on physical robot platformsin both indoor and outdoor environments. Model performancemetrics are also presented as benchmarks.
I. I
NTRODUCTION
Autonomous robots are becoming ubiquitous in all walks-of-life: agriculture [2], logistics [3], household [5], defense[7], search-and-rescue [17], to name but a few. Majority ofthe robots used in such applications, are powered by energysources like the Li-Po battery. Depending on the end-use, it isoften not possible to recharge the batteries in the form of solarenergy or electric charging stations distributed over the entireworkspace. While there is on-going research which focusesprimarily on the optimal recharging strategies [9, 14], the aimof this work is to highlight a more pressing concern:
How to ensure the robots return to base whilst avoid-ing complete immobilization amidst the mission?
Consider a scenario where a robot is being used to deliverpackages as shown in Fig. 1a. This application is gainingtraction amongst college communities in America and isbeing harnessed by start-ups like Kiwibot, who use robots formodernizing food delivery. A more common sight for a tech-savy household would be to have a vacuum cleaning robotlike the one shown in Fig. 1b to automate mundane tasks,like cleaning the floors. Whilst these robots are modernizingthe way of life, the mission will fail when the robot runsout of battery. This would mean either a delivery robot maynever reach its destination or return to base, or a vacuumcleaning robot may only be able to partially clean the floor. If a robot is completely immobilized amidst its task, it requiresextra manpower to retrieve the stranded robot, adding moreworkload for the human supervisors.The aim of this work then is to formalize this failurein terms of the operational range estimation for a singledischarge cycle. Unforeseen hardware failures aside, this worksummarizes our recent findings in the domain of operationalrange estimation , which allows for offline or online missionplanning with homing constraints. To this end, a simplified operational range estimation (ORangE) framework is firstpresented which is then extended to be applicable for a varietyof robot platforms. (a) Delivery robot called Kiwibot. (b)
Vacuum cleaning robot.
Fig. 1:
Some recent use-cases of autonomous robots.
In what follows, two schools of mission characterization aredescribed: the endurance and energy estimation approach isdiscussed, followed by our novel operational range estimationapproach. Empirical results are also presented in support ofour model to validate the model fidelity. This work is a briefoverview of our findings that were recently published in [11]and [12].II. E
NDURANCE & E
NERGY E STIMATION
A body of research focuses on the endurance and energyestimation approaches to characterize the mission require-ments. On the one hand, endurance estimation is primarilyconcerned with vehicles which constantly consume kineticenergy even for hovering in place, such as fixed-winged orrotary-winged drones as shown in [13] and [6], respectively.On the other hand, energy estimation has primarily been shownfor unmanned ground vehicles, which do not require energy to a r X i v : . [ c s . R O ] J un aintain a stationary workspace configuration, like the Pack-Bot [1]. Thus, both estimators have contrasting approacheswhen it comes to modeling the stationary kinematic energyconsumption. Also, in either case, only the kinetic energydispensed in Cartesian space is considered, whilst ignoring theenergy used for other robotic functions aside from locomotion.In case of endurance estimation, existing works mainlyfocuses on hovering energy consumption for rotor-crafts andsoaring for fixed wings in wind tunnel. However, simplyhovering and soaring does not represent the full maneuveringcapacity of either kind of vehicle. Therefore, the endurancecould be largely over-estimated. Similarly, in case of energyestimation, researchers focus on simplified and pre-meditatedtrajectories as described in [8].III. O PERATIONAL R ANGE E STIMATION (OR
ANG
E)Compared to the body of research described above, we posethe mission characterization as a problem where the robots’resources must dictate how the mission progresses. For this, wepresent two of our proposed approaches that allow operationalrange estimation (ORangE) for a variety of robot platforms.
A. Simplified Range Estimation Framework
For robots venturing into unknown environments for explo-ration purposes, it would be ideal that all the energy carriedon-board in the form of battery is utilized in locomotion, suchas maneuvering and propulsion from the motion actuators(Fig. 2a). In such a case, the exploration can span longerdistances and wider coverage of the unknown region. However,energy carried on-board has to be dispensed for a varietyof purposes, including sensing, computation, communications,friction, heating, etc. [11, 16] (Fig. 2b). Due to their contra-dicting effects on achieving better operational range, energyconsumed by such consumers is in fact termed as losses whichare described next.
1) Losses
Energy losses could occur due to a variety of reasons. Someare inevitable due to physical and chemical properties. Othersare introduced deliberately by the designer for the mission.Due to the fact that all these sources impede the robot fromventuring further, we generalize them into the following fourgroups: • Battery charge storage loss ( η ) : refers to the batteryself-discharge characteristics. Even without any load at-tached, the battery tends to suffer self-discharge therebyreducing the net amount of energy available for a mission. • Drive motor losses ( η ) : owing to internal friction alongwith actuation losses. • Mechanical losses ( η ) : refers to power train losses likefriction in transmission, damping from lubricants, etc. • Ancillary losses ( η ) : accounts for heat losses incurredby sensors, motor drivers, micro-controllers, etc. So, the overall system efficiency can be summarized as Ω ∆ =Π i =1 ¬ η i . In order to obtain these losses quantitatively for aparticular robot, wheels-up tests were performed to eliminate the useful work done by the robot to overcome resistancefrom the environment during locomotion. The isolated energyconsumption is only contributed by those internal losses [11].Next, a simplified range estimation model for indoor explo-ration is presented. (a) Idealistic model. (b)
Realistic model.
Fig. 2:
In Fig. 2a, we show an idealistic battery disseminationmodel, where all the energy stored in the battery is used as itis for performing maneuvers. In Fig 2b, we present a realisticmodel where we account for battery losses ( η ) , maneuveringlosses ( η , η ) and ancillary losses ( η ) .2) Range Estimation Model For a robot weighing m R g and traversing on an elevatedsurface with an elevation of θ , the normal force ( N ) supportingthe robot and the traction force propelling it are: N = m R g cos θ .T raction = C rr N + cv + m R g sin θ . (1)In Eq. (1), C rr N represents friction, cv is the aerialdraf force, and m R g sin θ is the weight component impedingthe motion. Therefore, the energy needed for displacing therobot by an amount d on a graded plane (referred to as the Maneuvering
Energy (ME)) can be given by:
M E = T raction × d , = ( C rr N + cv + m R g sin θ ) d , = ( C rr m R g cos θ + cv + m R g sin θ ) d . (2)Eq. (2) is the mechanical energy necessary to displace therobot. However, the realistic energy losses are not consideredyet. Fig. 2b shows the other consumers of energy from thebattery which are referred to as the ancillary consumers.With regards to the battery charge storage loss ( η ), an ex-ponential decay function is suggested to represent the reducedbattery capacity due to aging ( t ) and recharging cycles ( C ) as: ˆ E = E O exp − ( k C + k t ) (3)where k , k are constant coefficients and E O represents therated energy.The total available energy from the battery is composed ofancillary energy (AE) and traversal energy (TE): E = AE + T E , = Ancillary P ower × time + ME r Ω Man , = P Anc × dvD + ( C rr m R g cos θ + cv + m R g sin θ ) d r Ω Man , = d × (cid:26) P anc vD + ( C rr m R g cos θ + cv + m R g sin θ ) r Ω Man (cid:27) . (4) where D is duty cycle which is the proportion of net missiontime that the robot was actually mobile and vD represents theaverage velocity throughout the mission. While D accountsfor the fact that the robot may occasionally need to stopand process the data acquired, r Ω Man = ¬ Π i =2 η i representsthe constant maneuvering efficiency of the robot ( r ) . Thesimplified linear model of ancillary power is given by: P Anc = { s + s f s } (cid:124) (cid:123)(cid:122) (cid:125) P Sense (5)which defines the linear increase in power consumption asa function of the operational frequency f s for sensors likecamera, laser range finders, sonars, etc., as defined in [11].The maximum range d max is achievable at an operationalvelocity ( v opt ) , that is the maximal target velocity attainablefor safe operation as determined by the human supervisor.Thus, d max = ˆ EP Anc v opt D + ( C rr m R g cos θ + cv + m R g sin θ ) r Ω Man (6)
B. Generalized Range Estimation Framework
The previous section described the simplified ORangE ap-proach which was primarily focused on unmanned groundrobots operating in indoor environments with known elevation ( θ ) . However, in most missions, especially those conductedoutdoors, this may not always be readily available. Addi-tionally, missions might involve aerial or marine robots asidefrom only ground robots. This section presents our generalizedORangE approach, which is suited for a variety of robotplatforms and allows for both offline and online estimation ofthe operational range. For this, the revised energy dissipationmodel will be described first.
1) Energy Dissipation Model
As for the propulsive energy , any robot ( r ) carrying out amission ( m ) in an environment of choice experiences kindsof forces:1) Constant resistive force F ( r, m ) , as a function of robot ( r ) and the mission ( m ) : e.g., the force acting on a robot when it is traversing in a straight line under the influenceof a constant magnetic field.2) Environment dependent force F ( x, r, m ) , which is de-pendent on the current position x : e.g., changing grav-itational potential along with changing frictional forcebecause of change in coefficient of friction.3) Time dependent resistive force F ( t, r, m ) , which is afunction of current time t : e.g., unforeseeable distur-bances (strong wind gusts etc. ).4) Instantaneous operational velocity dependent resistiveforce F ( v, r, m ) , which varies with instantaneous ve-locity v : e.g., aerodynamics and gyro effect.Thus, the (revised) net traversal energy (TE) is given interms of mechanical energy (ME) based on the longitudinaldynamics model and the net mechanical efficiency ( r Ω Man ) as: T E = M E r Ω Man = (cid:82) P ath F Net dx r Ω Man = (cid:82) P ath { F ( r, m ) + F ( x, r, m ) + F ( t, r, m ) + F ( v, r, m ) } dx r Ω Man (7)Then, the duration ( t ) can be expressed as a function ofposition ( x ) , velocity ( v ) , mission ( m ) and duty cycle ( D ) as: t = g ( x, v, D, m ) (8)Substituting Eq. (8) into Eq. (7) gives : T E = { F ( r, m ) + F ( v, r, m ) } d r Ω Man + d (cid:82) P ath { F ( x, r, m ) + F ( x, v, D, r, m ) } dxd r Ω Man (9)As an enhancement over the ancillary power consumptionmodel shown in in Eq. (5), the generalized ancillary powermodel of Eq. (10) additionally considers the on-board compu-tation cost and the communication overhead incurred due todata transmission as explained in [12]. P Anc = { s + s f s } (cid:124) (cid:123)(cid:122) (cid:125) P Sense + { P Comp + P Comm } (cid:124) (cid:123)(cid:122) (cid:125) P c (10)
2) Range Estimation Model
So, similar to Eq. (4), the operational range for any robot ( r ) can be can now be generalized as: d = ˜ EP Anc vD + { F ( r, m ) + F ( v, r, m ) } r Ω Man + (cid:82) P ath { F ( x, r, m ) + F ( xvD , r, m ) } dxd r Ω Man (11)rom Eq. (11), it is evident that in order to estimatethe operational range, we need to approximate the term (cid:82)
Path { F ( x,r,m )+ F ( xvD ,r,m ) } dxd r Ω Man and the operational range esti-mate would be as good as the approximation. Depending onwhether this integral is approximated with real-time missiondata or approximated in one-shot by the human supervisor apriori , we get online or offline estimators, respectively, thedetails of which can be found in [12].IV. E XPERIMENTS
This section provides the empirical results of the simplifiedand generic range estimators to validate their respective modelfidelity.
First, the robot platforms used for validation arepresented followed by results from the indoor trials and finally,the outdoor experiments with two different platforms. Whilstthe indoor environments are considerably safe operationalsettings for robots, outdoor environments present challengingoperational conditions owing to unforeseen environmentaldisturbances like wind gusts or sudden rain showers. Thus,the proposed approaches were tested in myriad of conditions.
A. Robot Platforms
The results presented herewith were obtained using the robotplatforms shown in Fig. 3. (a)
Rusti V . . (b) Rusti V . . (c) AR Drone . . Fig. 3:
Various custom and commercial robot platforms forempirical validation of range estimators.B. Indoor Validation of Simplified ORangE with UGV
Using the Rusti V . (shown in Fig. 3, left) for indoornavigation scenario, the following two kinds of experimentswere performed: Firstly, the robot was made to execute a box-type trajectory on a flat floor until a fully charged batterywas completely drained.
Secondly, the robot was made toexecute an oscillating trajectory on a mildly graded plane. Theresults obtained are shown in Fig. 4 [11]. As is evident, themodel simplifications and noisy sensors rendered the modelto achieve an accuracy ranging from ∼ . C. Outdoor Validation of Generalized ORangE
For the validation of the generalized ORangE approach,several outdoor trails were performed with custom designedRusti V . and commercial AR Drone platforms as shown inFig. 3. Some of the results are illustrated below.
1) Unmanned Ground Robot
In order to validate the generalized ORangE for unmannedground robots, several experiments were performed on grass, (a)
Flat plane. (b)
Graded plane.
Fig. 4:
Range estimation error for flat plane and graded slopeexperiments using Rusti V . operating at various duty cycles. asphalt, and tiled surfaces using the Rusti V . . The resultshence obtained are show in Fig. 5. b1-v1 b1-v2 b2-v1 b2-v20102030405060 (a) Grass trials. b1-v1 b1-v2 b2-v1 b2-v20102030405060 (b)
Asphalt trials. b1-v1 b1-v2 b2-v1 b2-v20102030405060 (c)
Tile trials.
Fig. 5:
Range estimation error for Rusti while traversingon grass, asphalt and tiles, respectively. Here b , b refer tothe mAh and mAh batteries and v , v refers to . , . m/sec velocities, respectively.2) Unmanned Aerial Vehicle Additionally, several outdoor trials were performed usingthe AR Drone in occasionally windy conditions. The resultsobtained using both the offline and the online variants ofgeneralized ORangE are shown in Fig. 6.
Fig. 6:
Range estimation error for ArDrone. Plot showingerror in operational range calculated using the offline andonline models along with corresponding standard deviation.
Across multiple trials, the average accuracy of the offline approach was . while that of online was . .For brevity, only limited results are showcased here for thegeneralized ORangE approach, but additional results can befound in [10, 12].. C ONCLUSION
The aim of this paper was to summarize our recent findingsin operational range estimation . Operational range estimationis an important system consideration for exploration of ex-treme environments such as underwater and benthic habitats,hot-springs, volcanoes, asteroids, and planetary surfaces. Inmost of these cases, recharging of batteries is not feasible, and,hence, the robots must be able to optimize the area exploredon a single discharge cycle. To this end, we briefly presentedour recent works which describe two range estimators withdifferent levels of generality and model fidelity. Additionally,we presented arguments as to why one should use this settingas a potential mission characterization metric as opposed tothe conventional energy & endurance estimation methods.Model performance metrics were presented to empiricallyvalidate the proposed estimators on physical robot platformsfor both indoor and outdoor settings. We believe that ourORangE framework can be utilized as an important missioncharacteristic for applications like environmental monitoring,precision agriculture, and disaster response where robots areincreasingly being deployed.Both the simplified and generic ORangE approaches pre-sented herewith rely on the system calibration parameterswhich need to be calibrated a priori . As the robots operatein the field and undergo wear-and-tear, these parameters alsovary over time. Continued monitoring of these parameters isa labor-intensive task, thus, in the future works, we wouldlike to investigate mechanisms to reduce the reliance onsuch parameters. It would also be of interest to validate ourgeneralized ORangE on other robot platforms, e.g., marinerobots that are tasked with monitoring the marine ecology asshown in the works like [4, 15].R
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