Solar Based Navigational Planning for Robotic Explorers

1
Solar Based Navigational Planning for Robotic
Explorers

• Kimberly Shillcutt
• Robotics Institute, Carnegie Mellon University
• October 2, 2000

2
Thesis Statement

• Sun and terrain knowledge can greatly improve the
  performance of remoteoutdoor robotic explorers.

3
Preview of Results

• New navigational abilities are now possible
• Sun-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

4
Outline

• Motivation Goals
• Approach
• Sun Position Calculation
• Solar Navigation
• Coverage Patterns
• Evaluation Algorithms
• Results
• Field Work
• Simulations
• Conclusions Significance
• Future Work

5
Motivation

• Robotic exploration of remote areas
• Autonomous

Close, continual contact not available
emergency assistance may not even be possible
6
Motivation

• Robotic exploration of remote areas
• Autonomous
• Self-powered

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

• Robotic exploration of remote areas
• Autonomous
• Self-powered
• Navigation-intensive

Systematic exploration is best served by
methodical coverage patterns, while extended
exploration requires long-range paths
8
Goal 1

• Enable navigation throughout region while
  remaining continually in sunlight.

• Polar regions
• Continual sun
• Low sun angles ?
• Long shadows
• Vertical solar panels

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Goal 2

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

• Fixed solar panels
• Emergency battery reserves

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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

11
Approach

• Sun Position Calculation
• Solar Navigation
• Shadow maps
• Coverage Patterns
• Task simulation
• Solar power generation
• Pattern selection

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Sun Position Calculation

• Surface location ? planet latitude longitude
• Latitude longitude time ? Sun (and Earth)
  position
• Sun position terrain map ? shadowing

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Lunar Surface Example
Input robot location
Input time and date
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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

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Earth
16
Sun-Synchronous Driving
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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

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Coverage Patterns

• Evaluation of navigational tasks
• Tasks 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

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Task Simulation

• Coverage patterns
• Straight rows, spiral
• Sun-following
• Variable curvature

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Task Simulation

• Simulate set of potential navigational tasks
  under the applicable conditions
• Coverage patterns
• Evaluate attributes of the tasks
• Power generation
• Power consumption
• Area coverage, etc.
• Select best task based on desired attributesfor
  the robots mission

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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 ?
• Solar power cos(?) power/panel

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Other Evaluation Models

• Power consumption modeled on statistical field
  data
• Area coverage and overlap grid-based internal
  map keeps track of grid cells seen
• Time simple increment each pass
  through simulation loop
• Wind power generation assumes predictable wind
  speed and direction

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Pattern Selection
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Implementation

• Sun position algorithm
• Coverage pattern algorithms
• Evaluation algorithms
• On-board planning library used infield work and
  simulations

25
Results

• Field Work
• Accuracy of solar power prediction
• Simulations
• Pattern characteristics
• Effect of pose uncertainty
• Potential numerical improvements
• Examples of solar navigation

26
Robotic Antarctic Meteorite Search
Solar panel normal is 40 above horizontal
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Field Results

• Nomad tested in
• Pittsburgh
• Williams Field
• Elephant Moraine
• Straight rows spiral patterns performed at each
  location

Recorded Values DGPS position Roll, pitch,
yaw Solar panel current output Motor currents
voltages Timestamp Wind speed direction Modeled
output of Solar power generation Area coverage
overlap
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Field Results - Pittsburgh

• Nomad tested in
• Pittsburgh
• Williams Field
• Elephant Moraine
• 32 days of data at slag heaps, 1998-1999
• Coverage pattern development
• Maneuvering tests
• Initial solar panel testing

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Field Results - Antarctica

• Nomad tested in
• Pittsburgh
• Williams Field
• Elephant Moraine
• 8 days of test data, Dec 1999-Jan 2000
• Image segmentation tests
• Final search integration
• Pattern trials

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Field Results - Antarctica

• Nomad tested in
• Pittsburgh
• Williams Field
• Elephant Moraine
• 17 days of test data, Jan 2000
• 10 official meteorite searches
• 5 meteorites autonomously identified
• Pattern trials

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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?

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Actual vs. Concurrent Simulation
Straight Rows
Spiral
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A Priori Prediction Accuracy
mean error0.65
mean error1.25
Straight Rows
Spiral
Time (s)
Time (s)
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Simulation Results

• Pattern characteristics ? eliminate unnecessary
  simulations
• Simple heuristics
• Analytical evaluations
• Including terrain shadowing
• Effect of pose uncertainty
• Potential numerical improvements

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Pattern Evaluation Heuristics

• Over 80 pattern variations evaluated
• Heuristics for limiting evaluation sets
• Straight rows solar power generation varies
  sinusoidally with initial heading

• Spiral pattern direction makes little difference
  in evaluations

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Analytical Evaluations

• Variable Curvature Patterns
• Most evaluation category totals can be
  approximated as analytical functions of
  curvature, for given row lengths
• Solar 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

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Area Coverage and Overlap

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

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Area Coverage and Overlap
y position (m)
x position (m)
Area Area
Coverage Overlap
-200m curvature
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Area Coverage and Overlap
y position (m)
x position (m)
Area Area
Coverage Overlap
-40m curvature
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Area Coverage

• 100m row length, 5m row width,3000m total length
• Area -878,395 ?-2 87 ?-1 1655
• ? radius of curvature, -300, 300m
• max d lt 5.8
• (using 4th order polynomial, max d lt 0.9)

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Solar Energy Generated

• Patterns start with optimal sun heading
• Sharper curvatures (small radii) remain in
  optimal heading for shorter time, reducing power
  generation

42
Terrain Shadowing

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

43
Terrain Shadowing
Start Times
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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

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Pose Uncertainty

• Pose variations relative robot-sun angle
  variations power generation variations
• How unpredictable can the solar power variations
  be?

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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

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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 lt 1.3 from
  original
• Differences between straight rows and spiral
  patterns in Elephant Moraine were gt 50

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Mission Scenarios

• Power model
• Solar power generation
• Battery reserve charging/discharging
• Power consumption
• Mission
• Total driving time/path length specified
• Randomized target stops lasting about 5 minutes
  each, with/without point turns to optimal
  headings
• When battery state lt 20 capacity, robot stops,
  point turns to best heading, recharges to 99

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Sample Results
Lifetime time until first recharging stop
Mission Time total time to completion
Straight
Spiral
Sun-Following
Curved
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Results 60-89ºS range

• Lifetime improvements, no targets
• 23-143, Earth
• 123-161, Moon
• Productivity improvements, Earth
• 16-51 savings, with target stops
• 14-24 savings, no target stops
• Time savings, Earth
• 21-58 savings, with target stops
• 18-31 savings, no target stops

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Solar Navigation Results

• Sun-synchronous, long-range paths
• Sun-seeking, emergency recovery paths

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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

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N
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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

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Sun-Seeking Navigation
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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

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Conclusions

• Coverage pattern results can be accurately
  predicted.
• Solar panel modeling errors insignificant
• Pose uncertainty effects ltlt pattern differences
• Number of patterns to be simulated can be reduced
  by heuristics or analytical equations.

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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

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Significance of Research

• Solar position algorithm is integrated with
  robotic planners and terrain elevation maps.
• Precise prediction and evaluation tool
• Any Earth and moon locations, dates and times
• Confirmation of observational data
• Detailed analysis performed of new coverage
  patterns.
• Sun-following polar pattern
• Characteristics and heuristics for reducing
  evaluation set

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Future Work

• Solar Navigation
• More 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

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Future Work

• Automatic sky condition monitoring, for adapting
  solar power predictions and vision algorithms
• Solar ephemeris for Mars, Mercury and other
  planetary surface locations

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The End
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Appendices

• Solar algorithm
• Other evaluation details
• Elephant Moraine patterns, path following
• Wind power generation modeling
• Further calibration details

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Solar Algorithm - Earth

• Coordinate system transformations

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Solar Algorithm - Moon

• Coordinate system transformations

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Solar Algorithm

• Terrain ray-tracing

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Terrain Elevation and Occlusions
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Evaluating Power Consumption

• Modeled on field data statistical results

• Base locomotion power 290 W
• Base steering power 65 W
• Point turns 88 W
• Changing turning radii 15 W
• High/low pitch 60 W

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Evaluating Area Coverage

• Grid-based
• Depends on sensor parameters

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Elephant Moraine patterns
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Evaluating Wind Power Generation

• Power ? e A d v3 cos ?
• e turbine efficiency
• A turbine area
• d air density
• v air speed
• ? angle between wind direction and turbine
• How predictable is wind power generation?

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Wind Predictability

• Antarctic regularity is predictable

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Multiple-Parameter Evaluations

• Varied initial angles between sun azimuth and
  robot heading, and between sun azimuth and
  primary wind direction

• Other 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

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Wind vs. Solar Energy Generation
160 more power than alternatives
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Cloudy Day Calibration

• Diffuse lighting conditions
• Reflective snow and ice

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Insignificant Modeling Error
Patterndifferenceof 16.37
Straight Rows mean error 0.65
Cumulative Solar Energy (kJ)
Spiral mean error 1.25
Time (s)