Solar Based Navigational Planning for Robotic Explorers Kimberly Shillcutt Robotics Institute, Carnegie Mellon University October 2, 2000.

Solar Based Navigational Planning for Robotic Explorers

Kimberly Shillcutt

Robotics Institute, Carnegie Mellon University

October 2, 2000

Thesis Statement

Sun and terrain knowledge can greatly improve the performance of remote

outdoor robotic explorers.

Preview of Results

New navigational abilities are now possibleSun-following, or sun-synchronous driving

Sun-seeking, Earth-seeking driving

Solar-powered coverage

Time-dependent, environmental modeling is incorporated in navigational planning

Prediction of solar power generation

Robot performance improvements

OutlineMotivation & GoalsApproach

Sun Position CalculationSolar NavigationCoverage PatternsEvaluation Algorithms

ResultsField WorkSimulations

Conclusions & SignificanceFuture Work

Motivation

Robotic exploration of remote areasAutonomous

Close, continual contact not available – emergency assistance may not even be possible

Motivation

Robotic exploration of remote areasAutonomous

Self-powered

Critical need for power – solar energy is a prime source, but is highly dependent on environment and terrain

Motivation

Robotic exploration of remote areasAutonomous

Self-powered

Navigation-intensive

Systematic exploration is best served by methodical coverage patterns, while extended exploration requires long-range paths

Goal #1

Enable navigation throughout region while remaining continually in sunlight.

Polar regions:Continual sunLow sun angles • Long shadows• Vertical solar panels

Goal #2

Long-range navigation

Improve the efficiency, productivity and lifetime of solar-powered robots performing coverage patterns.

Fixed solar panels

Emergency battery reserves

Goal #3

Long-range navigation

Regional coverage

Enable autonomous emergency recovery by finding short-term paths to locations with sun or Earth line-of-sight.

On-board information

Approach

Sun Position Calculation

Solar NavigationShadow maps

Coverage PatternsTask simulation

Solar power generation

Pattern selection

Sun Position Calculation

Surface location planet latitude & longitude

Latitude & longitude + time Sun (and Earth) position

Sun position + terrain map shadowing

Lunar Surface Example

Input: time and date

Input: robot location

Shadow Map

Shadowing determined for each grid cell of map, for given date and time

Shadow snapshots combined into animation

Example:

Lunar South Pole, summer (April 2000)

Sun elevation ~ 1.5 degrees at pole

Earth

Sun-Synchronous Driving

Solar Navigation

Time-dependent search through terrain map, grid cell by grid cell, identifying whether locations are sunlit as the simulated robot arrives

Guided sun-synchronous search circumnavigates terrain or polar features

Can access pre-calculated database of shadow maps

Sun-seeking (or Earth-seeking) search finds nearest location to be lit for required time

Utilizes a sunlight (Earthlight) endurance map

Coverage Patterns

Evaluation of navigational tasksTasks occur over time

Robot position changes over time

Sun and shadow positions change over time

Need to predict changing relationship between robot, environment, and results…

Task Simulation

Coverage patternsStraight rows, spiral

Sun-following

Variable curvature

Task Simulation

Simulate set of potential navigational tasks under the applicable conditions

Coverage patterns

Evaluate attributes of the tasksPower generation

Power consumption

Area coverage, etc.

Select best task based on desired attributesfor the robot’s mission

Predicting Solar Power Generation

Robot coordinates surface latitude & longitude

Latitude & longitude + time + map sun and shadow positions

Sun position + solar panel normal incident sunlight angle θ

Solar power = cos(θ) * power/panel

Other Evaluation Models

Power consumptionmodeled on statistical field data

Area coverage and overlapgrid-based internal map keeps trackof grid cells seen

Timesimple increment each pass throughsimulation loop

Wind power generationassumes predictable wind speed and

direction

Pattern Selection

Implementation

Sun position algorithm

Coverage pattern algorithms

Evaluation algorithms

On-board planning library used infield work and simulations

Results

Field WorkAccuracy of solar power prediction

SimulationsPattern characteristics

Effect of pose uncertainty

Potential numerical improvements

Examples of solar navigation

Robotic Antarctic Meteorite Search

Solar panel normal is 40°

above horizontal

Field Results

Nomad tested inPittsburgh

Williams Field

Elephant Moraine

Straight rows & spiral patterns performed at each location

Recorded ValuesDGPS positionRoll, pitch, yawSolar panel current outputMotor currents & voltagesTimestampWind speed & direction

Modeled output of:

Solar power generationArea coverage & overlap

Field Results - Pittsburgh

Nomad tested inPittsburgh

Williams Field

Elephant Moraine

32+ days of data at slag heaps, 1998-1999

Coverage pattern development

Maneuvering tests

Initial solar panel testing

Field Results - Antarctica

Nomad tested inPittsburgh

Williams Field

Elephant Moraine

8 days of test data, Dec 1999-Jan 2000

Image segmentation tests

Final search integration

Pattern trials

Field Results - Antarctica

Nomad tested inPittsburgh

Williams Field

Elephant Moraine

17 days of test data, Jan 2000

10 official meteorite searches

5 meteorites autonomously identified

Pattern trials

Solar Power Predictability

Two types of simulations:Concurrent simulation, real-time, based on actual robot pose and model of solar panels

A priori simulation, predictive, based on pattern parameters and starting time

How does a priori simulation match actual power generated? Is it sufficient to distinguish between pattern types?

Actual vs. Concurrent SimulationS

trai

ght R

ows

Spi

ral

A Priori Prediction Accuracy

Time (s) Time (s)

Straight Rows Spiral

mean error0.65%

mean error1.25%

Simulation Results

Pattern characteristics eliminate unnecessary simulations

Simple heuristics

Analytical evaluations

Including terrain shadowing

Effect of pose uncertainty

Potential numerical improvements

Pattern Evaluation Heuristics

Over 80 pattern variations evaluated

Heuristics for limiting evaluation setsStraight rows solar power generation varies sinusoidally with initial heading

Spiral pattern direction makes little difference in evaluations

Analytical Evaluations

Variable Curvature PatternsMost evaluation category totals can be approximated as analytical functions of curvature, for given row lengthsSolar energy generation depends on location and latitude also

Resulting equations can be used in an optimization function, given desired weighting of each evaluation category, without complete simulation of each pattern

Area Coverage and Overlap

Sharper curvature combined with longer rows produces less coverage and more overlap

Area Coverage and Overlap

x position (m)

y po

siti

on (

m)

Area AreaCoverage Overlap

-200m curvature

Area Coverage and Overlap

-40m curvature

y po

siti

on (

m)

x position (m)Coverage Overlap

Area Area

Area Coverage

100m row length, 5m row width,3000m total length

Area = -878,395 ρ-2 + 87 ρ-1 + 1655ρ = radius of curvature, [-300, 300]m

max δ < 5.8%(using 4th order polynomial, max δ < 0.9%)

Solar Energy Generated

Patterns start with optimal sun heading

Sharper curvatures (small radii) remain in optimal heading for shorter time, reducing power generation

Terrain Shadowing

Straight rows patterns covering two regions, with variable starting positions, headings, and times

Terrain Shadowing

Start Times

Pattern Characteristics Summary

Reduction of simulation set by using heuristics to eliminate near duplicates

Analytical evaluation of variable curvature patterns without complete simulation

Identification of similarities between starting locations for patterns in shadowed terrain

Pose Uncertainty

Pose variations

relative robot-sun angle variations

power generation variations

How unpredictable can the solar power variations be?

Pose Uncertainty

Simulations vary robot pitch and roll with a randomized Gaussian distribution:

1° 2° 5° 8°

Multiple pattern runs with each value of uncertainty, at each location

Minor Power Generation Effects

Power varies as cosine of angle large angular deviations required to produce noticeable drop-off in results

Replaying actual field data without pitch/roll results in evaluation differences of < 1.3% from original

Differences between straight rows and spiral patterns in Elephant Moraine were > 50%

Mission Scenarios

Power model:Solar power generationBattery reserve charging/dischargingPower consumption

Mission:Total driving time/path length specifiedRandomized target stops lasting about 5 minutes each, with/without point turns to optimal headings

When battery state < 20% capacity, robot stops, point turns to best heading, recharges to 99%

0

2000

4000

6000

8000

10000

12000

14000

Lif

etim

e (s

)

80S, Earth

Sample Results

Lifetime = time until firstrecharging stop

Straight Spiral Sun-Following Curved

Mission Time = total time tocompletion

Results: 60-89ºS range

Lifetime improvements, no targets23%-143%, Earth123%-161%, Moon

Productivity improvements, Earth16%-51% savings, with target stops14%-24% savings, no target stops

Time savings, Earth21%-58% savings, with target stops18%-31% savings, no target stops

Solar Navigation Results

Sun-synchronous, long-range paths

Sun-seeking, emergency recovery paths

Sun-Synchronous Navigation

Haughton Crater, Arctic, July 15, 2001

75° 23’ N latitude

Sun elevation ~ 7-36 degrees

Autonomous path search inputs:Starting point and time

Direction of travel

Robot speed

NN

Sun-Seeking Navigation

Hypothetical, deep crater at 80S, Earth

Robot must find nearest location which will be lit by the sun for at least 3 hours after robot arrives

Sun-Seeking Navigation

Conclusions

Knowledge of sun and terrain enables continual, autonomous operation at poles.

Continually sunlit paths

On-board identification of recharging and communication locations

Modeling of environment enhances efficiency of robotic explorers.

Lifetime improvements of over 160%

Productivity improvements of over 50%

Time savings of over 50%

Conclusions

Coverage pattern results can be accurately predicted.

Solar panel modeling errors insignificant

Pose uncertainty effects << pattern differences

Number of patterns to be simulated can be reduced by heuristics or analytical equations.

Significance of Research

New robotic navigational abilities are possible for the first time.

Sun-synchronous paths

Sun-seeking, Earth-seeking paths

On-board robotic planning structure uses time-dependent environmental modeling, including solar power generation.

Expandable to new models

Step-by-step evaluation for temporal aspects

Significance of Research

Solar position algorithm is integrated with robotic planners and terrain elevation maps.

Precise prediction and evaluation toolAny Earth and moon locations, dates and timesConfirmation of observational data

Detailed analysis performed of new coverage patterns.

Sun-following polar patternCharacteristics and heuristics for reducing evaluation set

Future Work

Solar NavigationMore efficient path searches

3-D search space, variable robot speed

Identifying slopes and obstacles from terrain knowledge

Autonomously select multiple waypoints

More accurate modeling: for example, power consumption and wind resistance

Future Work

Automatic sky condition monitoring, for adapting solar power predictions and vision algorithms

Solar ephemeris for Mars, Mercury and other planetary surface locations

The End

Appendices

Solar algorithm

Other evaluation details

Elephant Moraine patterns, path following

Wind power generation modeling

Further calibration details

Solar Algorithm - Earth

Coordinate system transformations

Solar Algorithm - Moon

Coordinate system transformations

Solar Algorithm

Terrain ray-tracing

Terrain Elevation and Occlusions

Evaluating Power Consumption

Modeled on field data – statistical resultsBase locomotion power290 W

Base steering power 65 W

Point turns +88 W

Changing turning radii +15 W

High/low pitch ±60 W

Evaluating Area Coverage

Grid-based

Depends on sensor parameters

Elephant Moraine patterns

Evaluating Wind Power Generation

Power = * e * A * δ * v3 * cos θe = turbine efficiency

A = turbine area

δ = air density

v = air speed

θ = angle between wind direction and turbine

How predictable is wind power generation?

Wind Predictability

Antarctic regularity is predictable

Multiple-Parameter Evaluations

Varied initial angles between sun azimuth and robot heading, and between sun azimuth and primary wind directionOther variables are wind speed, pattern length, and latitude

Wind turbine is assumed fixed, with 1m radius blades

Only Earth locations and straight rows patterns are considered

Wind vs. Solar Energy Generation

0 20 45 70 90

3000s, 5 knots10000s, 5 knots

3000s, 15 knots10000s, 15 knots

0

10

20

30

40

50

60

70

80

90

Bes

t S

un

/Ro

bo

t A

ng

le

Sun/Wind Angle

80 S, Earth 160% more

power than

alternatives

Cloudy Day Calibration

Diffuse lighting conditions

Reflective snow and ice

Insignificant Modeling Error

Time (s)

Cum

ulat

ive

Sol

ar E

nerg

y (k

J)

Spiralmean error 1.25%

Straight Rowsmean error 0.65%

Patterndifferenceof 16.37%