ABSTRACT WHEN IS MORE NOT BETTER

WHEN IS MORE NOT BETTER?Karen T.SutherlandDepartment of Computer ScienceUniversity of Wisconsin–La CrosseLa Crosse,WI56401ABSTRACTIt is often assumed that when sensing in autonomous robot navigation,the more measurements taken,the better.In many cases,this is indeed true.However,we have found that in an outdoor, unstructured environment where the number of possible measurements one can take is limited and error is not normally distributed,additional measurements may cause more harm than good.These “rogue”measurements are not interpreted as outliers due to the fact that there is no observed central tendency in the measurements as a whole.This paper describes ongoing work in determining how a qualitative rating can be used with sparse data to weight measurements and how these weighted measurements can best be combined with map data to produce a good estimate of location.Exper-iments have been run using U.S.Geographical Survey Digital Elevation Map(DEM)data from mountainous terrain in eastern Utah.INTRODUCTIONFinding one’s own location in the environment is a critical skill for a robot navigator,especially in an outdoor unstructured environment.Localization errors outdoors tend to have more severe consequences than those indoors.In an indoor environment,proximity sensors can warn of impend-ing disaster.Outdoors,it is possible,with a small error in localization measure,to send oneself off a cliff.Problems which occurred with nonconvergence of measurements taken to self locate in such an environment caused us to look more closely at the assumptions under which we were expecting that convergence.The result was a realization that merely taking more measurements is not always a wise move.It shouldfirst be made clear what is meant by an unstructured environment.Any indoor envi-ronment,regardless of clutter,is,by our definition,structured.An outdoor environment containing buildings,roads,light beacons and other such items is,by our definition,structured.An outdoor, unstructured environment has no man made objects to use for landmarks.It is also the type of en-vironment in which the Global Positioning System(GPS)and instruments such as a compass or barometric altimeter may fail to give valid location ndmarks are naturally occurring physical terrain features such as mountain peaks or ridgelines.Due to the large distance between viewpoint and feature,proximity sensors are useless.Measurements are taken from camera images.The foundation for the assumption that more measurements are better lies in the Law of Large Numbers.If we let be a sequence of mutually independent random variables with a common distribution and if the expectation exists,then for every asFigure1:When the number of pixels in the image is constant,the larger the actual area covered by the image,the greater the error due to discretization.One pixel represents4meters on the left and 0.2inches on the right.Errors in discretization of the image become worse as distance to landmarks increases.Fig-ure1shows two typical images used in navigation tasks,one outdoors and the other indoors.The scale of the mountain view is such that one pixel represents about4meters,while one pixel along the right door jam in the indoor scene represents approximately0.2inches.Al-though an outdoor navigator can,in general,allow more room for maneuvering than if navi-gating indoors,it is usually not at this level of magnitude.Figure2:A rendering of the DEM data showing the smooth contour which results from the30meter square averaging.Much more significant is the error in the map.Whereas maps of structured environments can, in general,be made quite exact,the USGS DEM data is made up of measurements averaged over a grid of cells of30meters square.Most of the USGS DEM’s were produced by running paper contour maps through a drum scanner,extracting the contour lines and interpolating to estimate elevations.This averaging produces a type of inverse discretization which is,for the outdoor example shown in Figure1,approximately ten times that which is caused by dis-cretization in the image.The smoothing which results from this operation can be seen in therendering in Figure2.Features which may be very sharp in the actual view are smoothed out in the map data and the resultant rendering.Since these are the very features which would be taken from the view to use as landmarks,the smoothing significantly affects accuracy.Errors in elevation deception,as shown in the diagram in Figure3,where a subpeak or sub-ridge in the image is mistaken for a peak or ridgeline on the map,are not common indoors or in a structured outdoor environment.An observer located between B and C will see peak or ridge1as the highest point while an observer located between A and B will see peak or ridge 2as the highest point.Not until the observer moves beyond point A will the true summit be observed.Errors such as these add large inaccuracies to localization measurements.Figure3:Misidentifying a subridge or subpeak as the true landmark is a common error in navigation in unstructured environments.The true summit will be seen only by an observer located to the left of point A.Most importantly,the number of landmarks from which to take readings is extremely limited in this environment.The contour map in Figure4shows one area approximately21kilo-meters by14kilometers.The navigator’s path is shown by the heavy black line.The black dots are located at the only visible,distinguishable mountain peaks which could be used for landmarks.Only four tofive of them were visible at any one time.A navigator in such an environment cannot simply add more beacons from which to take readings.Figure4:The number of distinguishable landmarks is small at any one time.INTERACTIVE MEASUREMENTSWe have developed a strategy for measuring in environments with few natural landmarks which analyzes the map data in the area of each landmark in addition to the measurements which are taken. These“interactive”measurements are meshed together to produce a more robust result.The exam-ple presented here uses mountain peaks as point landmarks.As in the method described by Suther-land and Thompson,self localization is determined by measuring the angle between pairs of three point landmarks which have been identified on the map.The strategy focuses on errors in elevation deception,as described in the previous section,since these were the errors which could most easily be addressed.Although misidentifying a subpeak for a nearby given peak is a distinct possibility, we assume that there is no misidentification of one landmark peak for another.We know which three peaks we are using and we know which is which.The navigator is moving toward a goal, measuring as it moves.The process is as follows:Step1:Sweep peaks and record elevations.Thefirst step in this process is to search the map data around each landmark peak for possible nearby subpeaks.These searches are in the form of a sweep around the peak while measur-ing the elevations at each30meter interval.Although the map data has been averaged,any average elevation close to the elevation of the peak is a candidate for a mismatch.The sweep is done only half way around each peak on the side on which the navigator is located.The ra-dius of the sweep is arbitrarily set.It follows that the shallower the inclination up to the peak, the higher the probability of a mismatch.Any distinguishable point with elevation close to that of the peak will later be tagged for analysis.Step2:Estimate navigator location.The angles between landmark pairs as well as the angles of elevation from the navigator to each of the three landmarks are then measured.This results in an initial estimate of location.Step3:Check elevations.An arbitrary error threshold is set for the angle of elevation to each peak.Each elevation at location recorded for each of the three peaks in Step1is tested as follows: IfIf or,candidate is culled from the pool.The pool of tagged eleva-tions for each peak now consists of locations which could be misidentified as the landmark peak and which lie within the line of view from the navigator to the peak.A“probability of occlusion”,based on the elevation of the subpeak,is associated with each candidate in the pool.The navigator now moves.The direction and distance of this move is calculated as a linear pro-gramming problem with the following goals:1.The move is toward the goal.2.The move removes candidates with high probability of occlusion in each landmark pool fromthe line of view.3.The move is of minimal distance.At this point,the process repeats.However,the sweep needn’t be complete.Indeed,it is often un-necessary to sweep at all on a subsequent move.Likewise,the elevation checks are not completely repeated,but only augmented whenever additional sweeping is required.Candidates which were culled in an earlier pass may move into a line of view and candidates which were previously in a line of view may be culled.Consequently,the process involves for most moves only reprocessing the candidates for each peak and reassigning probabilities.#Subpeaks Peak2Initial pool5Culled pool3Advantages of this strategy:Rather than measurements being taken at specific time intervals or after specific distances traveled,they are only taken when the navigator has moved to a position where the measure-ment has a chance of adding to the accuracy of the localization.Numerous measurements incorporating the very same elevation deception errors are not being averaged into the calcu-lations of location.The necessary elevations and angles can be calculated quickly.After thefirst pass,incremen-tal calculations are minimal.The moving and recalculating also address the discretization error in the image.Moving the minimal distance to remove the candidates for occlusion from the line of view prevents the navigator from missing a good measurement situation.The navigator is always moving toward the goal.Drawback of the strategy:The radius of the area scanned around each landmark peak must be preset,as must both and .If set too small,occluding subpeaks will not be picked up.If set too large,determining probabilities of occlusion and removing from the pool of candidates with high probabilities of occlusion on a move will be difficult if not impossible to do.Work is ongoing on how best to determine these values.CONCLUSIONWe have shown that,when used in simulation,a strategy which combines measurement analysis of the view with measurement analysis of the map data as opposed to simply taking random mea-surements can significantly improve localization in outdoor,unstructured environments with few landmarks.This method has served to compensate for the inability to make numerous useful mea-surements by taking advantage of the few good measurements which can be made.At the present time,this strategy is being tested in an actual outdoor environment,using both peak and ridgeline 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