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: 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 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, 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 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 Simulation Straight Rows Spiral

A Priori Prediction Accuracy Time (s) Straight Rows Spiral mean error 0.65% mean error 1.25%

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 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

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

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

Area Coverage 100m row length, 5m row width, 3000m total length Area = -878,395 ρ ρ ρ = radius of curvature, [-300, 300]m max δ < 5.8% (using 4 th 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 StraightSpiralSun-FollowingCurved Mission Time = total time to completion

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, ° 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 power290 W Base steering power65 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 * v 3 * 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 160% more power than alternatives

Cloudy Day Calibration Diffuse lighting conditions Reflective snow and ice

Insignificant Modeling Error Time (s) Cumulative Solar Energy (kJ) Spiral mean error 1.25% Straight Rows mean error 0.65% Pattern difference of 16.37%