Spatial Coverage Planning and Optimization for a Planetory Exploration Rover

Daniel M. Gaines and Tara Estlin and Caroline ChouinardJet Propulsion Laboratory

4800 Oak Grove DrivePasadena, California 91109

{firstname.lastname}@jpl.nasa.gov

AbstractWe are developing onboard planning and executiontechnology to support the exploration and characteriza-tion of geological features by autonomous rovers. Inorder to generate high quality mission plans, an au-tonomous rover must reason about the relative impor-tance of the observations it can perform. There are a va-riety of criteria that may contribute to the importance ofan observation such as how well the observation is ex-pected to contribute to different scientific themes (e.g.geology, atmospheric studies) or to engineering tasks.In this paper we look at the scientific criteria of selectingobservations that improve the quality of the area cov-ered by samples. Our approach makes use of a prioriinformation, if available, and allows scientists to marksub-regions of the area with relative priorities for ex-ploration. We use an efficient algorithm for prioritizingobservations based on spatial coverage that allows thesystem to update observation rankings as new informa-tion is gained during execution.

IntroductionOur goal is to increase the onboard decision-making capabil-ities of planetary exploration rovers. Currently, each morn-ing of the Mars Exploration Rover (MER) mission the sci-entists and engineers meet to discuss the observations theywould like the rover to perform. A subset of these obser-vations are selected that are predicted to fit within the timeand resource (e.g. energy, onboard memory) constraints ofthe rover. The engineering team spends the rest of the daypreparing the specific sequences that the rover will performto collect these observations and modeling the plan to ensureit fits within resource constraints.

While the MER mission has been highly successful at ex-ploring Mars, mission operations are manually intensive andtime consuming. And, in some cases, the sequences that areuplinked do not always take full advantage of available op-portunities. For example, if the rover receives more solararray input than expected, it may have energy to preformmore science observations than what was uplinked.

By enabling rovers to perform onboard planning andscheduling, we anticipate greatly reducing the time and ef-fort required to perform mission operations while increasing

Copyright c© 2007, American Association for Artificial Intelli-gence (www.aaai.org). All rights reserved.

the science that is acquired. The science and engineeringteams will be able to uplink observation requests that po-tentially over-subscribe the rover’s resources. The rover willuse observation priorities and its current assessment of avail-able resources to make decision bout which observations toperform and when to perform them.

In order to make effective decisions about which obser-vations to perform, the rover must reason about science pri-orities. In previous work, we have used a single value toindicate science priority and the rover attempted to generateplans the maximized the sum of these priorities. In reality,there are many different factors that determine the scientificimportance of an observation. For example, the MER mis-sion organizes the science team into several themes: geol-ogy, mineralogy, rock/soil properties, atmospheric and longterm planning,. Representatives from these themes evaluatethe quality of the day’s science plan.

In our current work, we are focusing on situations inwhich the rover is exploring large geological features suchas craters, channels or a boundary between two different re-gions. In these cases, another important factor in assessingthe quality of a plan is how the set of chosen observationsspatially cover the area of interest. Thus, one of the con-siderations a rover should make when evaluating which ob-servations should be included in a plan is how well the can-didate observations will increase the spatial coverage of theplan.

The overall goal of this technology is to enable the roverto generate and execute plans that makes an appropriate bal-ance between detailed study and broad coverage of a region.In this paper we describe a technique that allows a rover toevaluate the spatial coverage quality of a plan and gener-ate plans that respect mission and resource constraints whileattempting to maximize the spatial coverage quality of theplan. Our approach must also be efficient as the system mayhave to re-evaluate the coverage quality of the plan and thepotential observations during plan execution.

Exploring Geological FeaturesWe are developing onboard planning and scheduling tech-nology to enable rovers to more effectively assist scientistsin exploring geological features. Figure 1 shows examplesof geological features on Mars illustrating the types of fea-tures rovers may be directed to explore.

(a) Channels (MGS MOC Image) (b) Layers (MGS MOC Image) (c) Craters (MGS MOC Image)

(d) Boundary (MGS MOC Image) (e) Large area characterization (Spirit Image)

Figure 1: Example geological features on Mars.

A scientific campaign for exploring a geological featurewill employ a variety of rover instruments for collecting dataabout the region. For example, each Mars Exploration Roveris equipped with remote sensing instruments including high-resolution panoramic stereo cameras with a variety of fil-ters (Pancam), navigational (Navcam) and hazard avoidance(Hazcam) stereo cameras and a Mini Thermal EmissionsSpectrometer (Mini-TES). Each rover also has an arm witha suite of instruments for close contact measurements: a mi-croscopic imager (MI), two spectrometers and a rock abra-sion tool (RAT) able to remove a few millimeters of a rock’ssurface.

When humans perform mission planning, there may be avariety of reasons why a particular observation is selected ina given plan. The observation may be selected for its scien-tific merit. As discussed previously, this may be further bro-ken down into the observation’s contribution to one or moreof the scientific themes (e.g. atmospheric, geology, . . . ). Anobservation may provide benefit from an engineering per-spective such as collecting data for long-term route planningor assessing atmospheric dust content to facilitate better en-ergy modeling. In addition, an observation may be selectedas it increases the area that has been covered by collecteddata. In many cases, a single observation may contribute toseveral of these criteria in various degrees.

Of course, the mission planning team must also take into

account the limited set of resources that the rovers have toperform observations. The rovers are constrained by limitedenergy, onboard data storage, downlink opportunities andbandwidth and time to complete observations. Each obser-vation places a different set of demands on these resources.Some are very time consuming, such as long-term spectrom-eter integrations, while others are memory intensive, such asPancam acquisitions. And some activities are constrainedto occur at certain periods of the day due to sun angle orambient temperature.

Each observation also varies in the amount of spatial cov-erage that it affords. For example, Navcams and Hazcamshave a wide field of view while Pancams and Mini-TES havea narrow field of view. A further challenge is that terrainfeatures, such as large rocks or hills, may occlude an ob-servation thus limiting the area that it covers. The qualityof coverage afforded by an observation also degrades as afunction of distance from the rover.

Finally, for a given geological feature, scientists may bemore interested in certain sub-regions of that feature thanin others. Thus, observations should also be evaluated basedon the relative importance of the area for which they providecoverage.

The current practice on planetary exploration missionsis to have the science and engineering teams select a sub-set of observations that achieve an acceptable compromise

among these considerations and respect the team’s estimatesof the available resources for accomplishing these tasks. Thedrawback to this approach is that the rover has extremelylimited ability to alter the plan if things do not go as pre-dicted. For example, if tasks take longer than expected, thenlater tasks may get dropped, even if they are deemed higherpriority than earlier tasks. Or, if the rover has extra resources(e.g. more solar array energy than predicted) then it mayhave been able to accomplish more observations than wereuplinked. Our objective is to enable rovers to reason aboutscience quality onboard so that they can appropriately adjustthe plan when state or environment information change.

CASPER Continuous Planning andOptimization Framework

Our objective is to enable onboard planning software to rea-son about the scientific quality of a plan so that it can makemore informed decisions about which observations to per-form. This will enable the ground team to uplink a larger setof observations and let the rover dynamically select amongthem based on the scientific and engineering merit of theresulting plan and the rover’s assessment of available re-sources. During execution, the rover will modify the planbased on the current estimate of its resources.

Our approach is implemented within the CASPER sys-tem (Estlin et al. 2002; Chien et al. 2000). CASPERemploys a continuous planning technique where the plan-ner continually evaluates the current plan and modifies itwhen necessary based on new state and resource informa-tion. Rather than consider planning a batch process, whereplanning is performed once for a certain time period and setof goals, the planner has a current goal set, a current roverstate, and state projections into the future for that plan. Atany time an incremental update to the goals or current statemay update the current plan. This update may be an unex-pected event (such as a new science target) or a current read-ing for a particular resource level (such as battery charge).The planner is then responsible for maintaining a plan con-sistent with the most current information.

A plan consists of a set of grounded (i.e., time-tagged)activities that represent different rover actions and behav-iors. Rover state in CASPER is modeled by a set of plantimelines, which contain information on states, such as roverposition, and resources, such as energy. Timelines are cal-culated by reasoning about activity effects and represent thepast, current and expected state of the rover over time. Astime progresses, the actual state of the rover drifts from thestate expected by the timelines, reflecting changes in theworld. If an update results in a problem, such as an ac-tivity consuming more memory than expected and therebyover-subscribing RAM, CASPER re-plans, using iterativerepair (Zweben et al. 1994), to address conflicts.

CASPER includes an optimization framework for rea-soning about soft constraints such as reducing the distancetraversed by the rover and increasing the value of sciencedata collected. User-defined preferences are used to com-pute plan quality based on how well the plan satisfies theseconstraints. Optimization proceeds similar to iterative re-

pair. For each preference, an optimization heuristic gener-ates modifications that could potentially improve the planscore.

In order to apply CASPER to the described rover domain,we performed a number of steps. These included devel-oping a domain model for rover operations, developing acontrol algorithm geared toward appropriately respondingto problems and opportunities, and integrating the processesfor plan optimization and repair. Figure 2 provides a highlevel description of the control algorithm.

InputA set of prioritized science goals fromEarthTime constraintsResource constraintsPreferences

Repeat:Process any updates from ExecutiveSave current planFor i = 1 to num iterations

If there are conflictsSelect a conflict to work onSelect a repair strategy for thisconflictApply repair strategy

ElseSelect an optimization preferenceSelect an optimization method forthis preferenceApply optimization method

Compute plan scoreIf current plan is best seen so far, save it

Reload plan with highest score

Figure 2: CASPER control algorithm for rover domain.

The algorithm takes as input a set of goals with associ-ated science priorities, a set of time and resource constraintsand a set of user-defined preferences. The main loop of thealgorithm interleaves iterative repair and iterative optimiza-tion to search for a conflict-free plan of high quality. Theloop begins by processing any updates on state and resourcetimelines or on activity status. The current plan is saved. Itthen enters a loop in which it attempts to improve the planby repairing conflicts or performing optimization steps.

If the plan has a conflict, CASPER performs a repair it-eration. Otherwise, CASPER attempts to improve the scoreby performing an iteration of optimize. If the score of the re-sulting plan is higher than the previously saved plan (basedon a set of user-defined preferences), than the current plan isrecorded.

The primary method used to enable the system to reasonabout spatial coverage of science observations was to de-velop an appropriate preference. The preference includes ameans to score a plan based on the spatial coverage qualityafforded by the plan. If the spatial coverage preference isselected to improve the plan score, the optimization methodis to satisfy one of the requested observations that is not yet

in the plan that will provide the biggest improvement to thecoverage quality of the plan.

The next section provides details on how the spatial cov-erage quality of a plan is computed and how observationsare selected to improve this score.

Spatial Coverage PreferenceFigure 3) provides an example region of terrain that we wanta rover to explore and Figure 4 shows an example set ofobservations that are under consideration for the plan.

Figure 3: Digital elevation map of the an example terrain tobe explored.

Figure 4: Set of observations.

With limited available resources, it is unlikely that therover will be able to perform all of these observations. Asdiscussed previously, there are many considerations for de-termining which subset of observations should be includedin a plan. The objective of this work is to develop a prefer-ence to encourage spatial coverage to be one of the consid-erations during plan generation and modification.

In this section we describe our approach to representingand reasoning about the spatial coverage quality of a plan.We begin by describing how we represent a priori informa-tion about the terrain to be explored along with scientists’priorities indicating the relative importance of various sub-regions. We then describe how we model the coverage qual-ity afforded by a given observation. These observation mod-els are used to track the spatial coverage quality of plan, tak-ing into account those observations that have already beenexecuted and those that are scheduled to execute in the fu-ture. When resources and plan space is available, all of thisinformation is then used to select which observations to addto the plan in an attempt to optimize the spatial coverage ofthe plan. Conversely, when resources are over-subscribedand observations must be shed, to select an observation thatwill make the smallest impact on the spatial coverage of theplan if it were to be removed.

Terrain and Terrain Priority RepresentationKnowledge of terrain will enable the system to make bet-ter predictions about the coverage of observations as it willknow about occlusions from terrain features such as rocks orhills.

Scientists typically have a variety of a priori informationthat is used to identify candidate observations that can con-tribute to the initial terrain map. Images from previous ob-servations, such as NAVCAM and PANCAM observations,are the primary source of information for selecting new tar-gets. In addition, images from orbiting spacecraft as wellas images taken during the spacecraft’s descent, provide acoarse view of the geological features.

We represent a priori knowledge of the terrain to be ex-plored as a digital elevation map where each pixel representsthe height of the terrain at that point. Figure 3 shows an ex-ample terrain map.

The resolution of the map has a direct impact on the spaceand time complexity of the algorithm. It is not critical thatwe compute a highly accurate score for the amount of terraincovered by a given observation. Rather, it is important thatthe relative scores of different observations be correctly as-sessed. Thus, we convert the input terrain map into a coarserresolution such as the one in Figure 5. The resolution ofthe terrain map is a parameter that can be tuned to make atrade-off between accuracy of coverage quality predictionsand computational complexity of the system.

Figure 5: Lower resolution version of terrain in Figure 3.

It is also important to note that the approach does not re-quire that a priori knowledge be complete or accurate. Miss-ing or incorrect data in the terrain map will result in incorrectestimates of the spatial coverage that an observation will af-ford which, in turn, could result in lower quality plans. How-ever, as observations are performed the terrain map will beupdated and the coverage quality of upcoming observationswill be re-assessed.

In addition to the terrain map, the system will take as inputa matrix of weights that define the relative scientific impor-tance of sub-regions of the terrain map. The matrix is thesame size and dimensions as the input terrain matrix witheach cell containing a value between 0 (least important) and1 (most important).

Modeling ObservationsIn order to evaluate the coverage quality of a plan, it is nec-essary to compute the coverage afforded by a given observa-

tion. Figure 6 illustrates the key steps in this computation.

(a) compute observation visibility

(b) compute observation coverage quality

Figure 6: Modeling observation coverage quality.

The first step is to determine which cells of the terrain arevisible from the location of the observation. The locationof the observation, the range of the instrument and the el-evation of the terrain determine which cells. For each cellwithin range of the observation’s location (as determined bythe range value for the instrument) we perform an intersec-tion test between the terrain and a line from the location ofthe instrument to the cell using the intersection test (Shapira1990).

Once it has been determined that a cell is visible to anobservation, we compute the coverage quality score whichrepresents how well that cell is covered by the observation.A score of 0 indicates that the cell is not covered at all bythis observation (e.g. it is occluded by the rover body). Ascore of 1 represents “perfect” coverage, in the sense thatanother observation of the cell would not improve upon thecell’s coverage.

This computation of the coverage quality score will varybased on the type of instrument used. In general, cells fur-ther from the origin of the observation are not covered aswell as those closer in. Figure 6 (b) illustrates the coveragequality model for a panoramic image observation. Let d bethe distance of the visible cell from the origin of the obser-vation. The radius r0 represents the diameter of the roverbody. If d ≤ r0 then the cell is occluded by the rover bodyand not covered by this observation. Cells that lie betweenr0 and r1 are within the primary range of this instrument.Coverage is high for cells close to r0 but drops off movingout toward r1.

The range between r1 and r2 is used to encourage“spreading out” of observations. The idea is that, all else be-ing equal, one might prefer to have observations spread outacross the terrain rather than clustered in a small region. Theextend to which spreading out is encouraged can be tuned byincreasing or decreasing r2.

Finally, the coverage of the cell is multiplied by theweight in the scientific priority matrix resulting in the cell’sspatial coverage quality provided by this observation.

Tracking Coverage QualityNow that we have a way of computing the spatial coveragefor a given observation, the next step is to keep track of thespatial coverage provided by a set of observations. We dothis by recording the spatial coverage quality afforded bythe observations into a coverage quality matrix. A coveragequality matrix is the same dimension and resolution as ourterrain matrix with each cell containing a coverage qualityvalue. If multiple observations cover the same cell in thecoverage quality matrix we record the max coverage qual-ity score afforded by these observations. Figure 7 showsan example coverage quality matrix reflecting the coveragequality for a set of observations.

(a) coverage quality for a set of observations

(b) coverage quality overlayed on terrain map

Figure 7: Example coverage quality for a set of observations.

We maintain two separate coverage qualities matrices. Wekeep track of an Executed Coverage Quality Matrix thatkeeps track of the coverage quality afforded by the obser-vations that have already executed. The second matrix is thePending Coverage Quality Matrix and includes the cover-age quality from the executed observations and the predictedcoverage quality that will be obtained after the pending ob-servations in the plan have been executed. As will be seen,maintaining these matrices will improve efficiency when theterrain map is updated and when selecting observations toadd to or remove from the plan.

Each coverage quality matrix has a score which is equalto the sum of the coverage quality of each of its cells.

Ranking ObservationsWe rank observations with respect to how well they are ex-pected to improve the coverage quality of the plan. We main-tain two rankings, one for the requested observations, those

that are not yet in the plan, and the pending observations,those that are in the plan but have not yet executed.

When selecting a requested observation to add to the planwe select the highest ranked observation from the requestedobservations ranking. If we must shed a pending observationto resolve a conflict, we select the lowest observation fromthe pending observations rankings.

In actuality, rather than always selecting the highest ob-servation to add (or lowest when deleting( we perform aprobabilistic selection from the ranked list of observationswith a probability of selecting a particular observation pro-portional to the coverage quality it is expected to contributeto the plan. This probabilistic selection enables the system toavoid getting stuck trying to satisfy an observation for whichthere are insufficient resources to perform.

Because the coverage afforded by observations may over-lap, The coverage quality an observation will contribute toa plan depends in part on the other observation already inthe plan. Thus, when we rank the requested observations wedo so relative to the pending coverage quality matrix. Sim-ilarly, the coverage quality contribution of a pending obser-vation depends on the observations that have already beenexecuted. Therefore, the pending observations are rankedrelative to the executed coverage quality matrix.

Figure 8 shows the algorithm used to rank a set of obser-vation relative to a coverage quality matrix. A contributionscore is computed for each observation which is equal tohow much the score of the coverage quality matrix wouldincrease if this observation were added.

InputUnranked ObservationsInitial Coverage Quality Matrix

For each observation in Unranked Observa-tions

Observation’s contribution score = howmuch the score of the coverage quality ma-trix would improve if this observation wereincluded

Sort observations based on contribution score

Figure 8: Ranking a set of observations relative to a cover-age quality matrix.

Note that the algorithm in Figure 8 ranks only the singlenext observation to add (or remove) and does not indicatewhich order the remaining observations should be added (orremoved). Instead, we use an iterative approach since, giventhe iterative nature of CASPER’s repair and optimizationloop, we will add or remove activities one at a time.

This iterative approach represents a greedy algorithm forselecting observations to add and remove and does not guar-antee an optimal solution except in the case where the ob-servations do not overlap. We have chosen not to attempt anoptimal solution for three main reasons. First, observationsare selected for a variety of reasons, not just spatial cover-age. Thus, we cannot count on the spatial coverage ranking

being honored when observations are added and removed.Second, because we will have to re-rank observations dur-ing execution (when observations are added and removed orwhen the terrain map is updated) we want a fast computa-tion. Finally, we expect that observations will not overlapsignificantly and thus the greedy approach will not be farfrom optimal.

Updating Spatial Coverage During ExecutionDuring the course of executing the plan, the system will needto update its rankings. Through the collection of observa-tions, we will be collecting new information about the ter-rain being explored. We can update the terrain map whenthis happens. Doing so will improve the accuracy of thecoverage quality predictions. However, when the terrain isupdated we will need to re-compute the coverage quality af-forded by each of the observations and re-compute our rank-ings.

We must also re-compute rankings when observations areadded to or removed from the plan since the contributionscore of an observation depends on the order in which it isadded to the plan.

Related WorkThe spatial coverage problem we are solving is similar toa classic computational geometry problem called the ArtGallery Problem (O’Rourke 1987). Given a polygon, repre-senting the floor plan of an art gallery, the problem is to se-lect the minimum number of locations to place guards suchthat every point in the polygon is in view of at least oneguard. It is assumed that guards can see in all directionsand can see out to infinity unless an edge of the polygon ob-structs its view. This has been show to be NP-Hard, but apopular approximation runs in time O(nlogn. The approx-imation triangulates the polygon and then performs three-coloring on the resulting vertices. Guards are posted at thevertices that were colored by the minimum color class (thecolor class that was used the least amount of times to colorvertices).

While similar, there are significant difference between theArt Gallery Problem and the problem we wish to solve.Most significant is that the Art Gallery Problem is restrictedto 2D while we are modeling and selecting observations in3D. The triangulation approximation described above doesnot scale to the 3D case. Furthermore, it is unrealistic tomodel observations the way guards are modeled. Some ob-servations cannot see in all directions and the quality ofthe observation is not constant with respect to the distanceof a point from the origin of the observation. Finally, theArt Gallery Problem does not consider the costs of postingguards.

The ROPE (Rank and Overlap Elimination) system se-lects locations for video cameras for visual surveillance oflarge 3D open spaces (Rana 2005). ROPE discretizes thearea into cells and then uses a greedy algorithm to selectcamera locations by first placing a camera in the cell fromwhich the largest number of other cells are visible. The se-lected cell and the visible cells are removed from the area

and the process is repeated until no cells remain. This greedyapproach is similar to the approach we take in ranking obser-vations. However, like the Art Gallery Problem, ROPE doesnot model the quality of coverage and it does not considercost.

The swath coverage problem for orbital satellites is simi-lar to the spatial coverage problem addressed in this paper. Asatellite collects images as it orbits and may acquire imagesof the same location on subsequent orbits. The problem is toselect which images to downlink to maximize science valuewhile respecting onboard storage and downlink capacities.Knight presents an optimal solution using depth first branchand bound and a network flow formulation for a heuristicreward estimator (Knight & Smith 2005). The ASTER sys-tem uses a greedy approach for selecting images similar toROPE (Muraoka et al. 1998). Both approaches take intoaccount resource cost of observations and can take into ac-count quality of coverage. The heuristic used in Knight as-sumes that the reward for an observation scales with its cost.This is not necessarily the case for rovers where the cost ofan observation may vary independent of the reward due tomany factors such as distance to the observation and terrainconditions. Our greedy algorithm is essentially the same asthat used in ASTER. The main difference in our work is themodeling of instrument observations and the incorporationof this work into surface operations and other optimizationpreferences.

ConclusionsWe have presented a set of algorithms that enable a rover tocompute the spatial coverage quality of a plan and to rankcandidate observations by how well they are expected to im-prove coverage quality. Using this technique, a rover is bet-ter able to assist in the exploration of geological features bygenerating high quality operations sequences that take intoaccount spatial coverage along with other science consider-ations. We have currently implemented and tested these al-gorithms and have tested them in a stand-alone mode. Weare in the process of integrating the preferences into ourrover planning and execution system. In future work, wewill focus on techniques for combining multiple preferencesfunctions so that the system can more effectively trade-offscience and engineering objectives when generating and ex-ecuting plans.

AcknowledgmentsThe research described in this paper was carried out at theJet Propulsion Laboratory, California Institute of Technol-ogy, under a contract with the National Aeronautics andSpace Administration. This work was funded by the JetPropulsion Laboratory Research and Technology Develop-ment program.

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