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 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
Outline
Motivation & Goals
Approach
Sun Position Calculation
Solar Navigation
Coverage Patterns
Evaluation Algorithms
Results
Field Work
Simulations
Conclusions & Significance
Future Work
Motivation
Robotic exploration of remote areas
Autonomous
Close, continual contact not available –
emergency assistance may not even be possible
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
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
Goal #1
Enable navigation throughout region while
remaining continually in sunlight.
Polar regions:
Continual sun
Low 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 Navigation
Shadow maps
Coverage Patterns
Task 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: robot location
Input: time
and date
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 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…
Task Simulation
Coverage patterns
Straight rows, spiral
Sun-following
Variable curvature
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 attributes
for 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 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
Pattern Selection
Implementation
Sun position algorithm
Coverage pattern algorithms
Evaluation algorithms
On-board planning library used in
field work and simulations
Results
Field Work
Accuracy of solar power prediction
Simulations
Pattern 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 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
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
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
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
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?
Spiral
Actual vs. Concurrent Simulation
A Priori Prediction Accuracy
mean error
0.65%
mean error
1.25%
Straight
Rows
Time (s)
Spiral
Time (s)
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 sets
Straight rows solar power generation varies
sinusoidally with initial heading
Spiral pattern direction makes little difference
in evaluations
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
Area Coverage and Overlap
Sharper curvature combined with longer rows
produces less coverage and more overlap
y position (m)
Area Coverage and Overlap
x position (m)
-200m curvature
Area Area
Coverage Overlap
Area Coverage and Overlap
x position (m)
-40m curvature
Area Area
Coverage Overlap
Area Coverage
100m row length, 5m row width,
3000m total length
Area = -878,395 ρ-2 + 87 ρ-1 + 1655
ρ = 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 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 < 20% capacity, robot stops,
point turns to best heading, recharges to 99%
Sample Results
Lifetime = time until first
recharging stop
80S, Earth
14000
Lifetime (s)
12000
10000
8000
6000
Mission Time =
total time to
completion
4000
2000
0
Straight Spiral
Sun-Following
Curved
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
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
N
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 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
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
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 results
Base locomotion power
Base steering power
Point turns
Changing turning radii
High/low pitch
290 W
65 W
+88 W
+15 W
±60 W
Evaluating Area Coverage
Grid-based
Depends on sensor parameters
Elephant Moraine patterns
Evaluating Wind Power Generation
Power =  * e * A * δ * v3 * cos θ
e = 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 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
Wind vs. Solar Energy Generation
80 S, Earth
Best Sun/Robot
Angle
90
80
160% more
power than
alternatives
70
60
50
40
30
20
10000s, 15 knots
3000s, 15 knots
10000s, 5 knots
3000s, 5 knots
10
0
0
20
45
70
Sun/Wind Angle
90
Cloudy Day Calibration
Diffuse lighting conditions
Reflective snow and ice
Cumulative Solar Energy (kJ)
Insignificant Modeling Error
Pattern
difference
of 16.37%
Straight Rows
mean error 0.65%
Spiral
mean error 1.25%
Time (s)