The cadence of proximity operations for the OSIRIS-REx mission may have an extra induced challenge given the potential of the detection of a natural satellite orbiting the asteroid Bennu. Current ground radar observations for object detection orbiting Bennu show no found objects within bounds of specific size and rotation rates. If a natural satellite is detected during approach, a different proximity operation cadence will need to be implemented as well as a collision avoidance strategy for mission success. A collision avoidance strategy will be analyzed using the Wald Sequential Probability Ratio Test

Carpenter, J. Russell

Mashiku, Alinda K.

NASA Technical Reports Server

A Collision Avoidance Strategy for a Potential Natural Satellite around the Asteroid Bennu for the OSIRIS-REx Mission

Carpenter, Russell

Mashiku, Alinda

THE UNIVERSITY OF ARIZONA – NASA GODDARD SPACE FLIGHT CENTER – LOCKHEED MARTIN - KINETX
A COLLISION AVOIDANCE STRATEGY 
FOR A POTENTIAL NATURAL 
SATELLITE AROUND THE ASTEROID 
BENNU FOR THE OSIRIS-REX MISSION
ALINDA MASHIKU*
RUSSELL CARPENTER**
*NASA GSFC – Flight Dynamics Team
**NASA GSFC - Navigation Advisory Group
AIAA/AAS Astrodynamics Specialist Conference
Long Beach, CA
SEPTEMBER 16, 2016
https://ntrs.nasa.gov/search.jsp?R=20160011510 2019-08-29T16:22:34+00:00Z
AGENDA
• Introduction to the OSIRIS-REx mission
• Proximity Operations Concept
• Current status of Natural Satellites
• Approaches to Collision Avoidance
• Wald Sequential Probability Ratio Test (WSPRT) 
• Conjunction analysis Example 1: 8 hr prediction
• Conjunction analysis Example 2: 3 hr prediction
• Summary
INTRODUCTION TO THE OSIRIS-REX MISSION
• The OSIRIS-REx mission launched on Sept 8th 2016 at Cape Canaveral, FL
onwards to the asteroid Bennu.
• Bennu is a carbonaceous asteroid and a potentially hazardous asteroid with a 
probability of impacting the Earth in the late 22nd century. The determination of 
Bennu’s physical and chemical properties are of key importance in the event an 
impact mitigation mission will be required.
• OSIRIS-REx’s key science objectives include(1):
• Return and analyze a sample of Bennu’s surface
• Map the asteroid
• Document the sample site
• Measure the orbit deviation cause by non-gravitational forces (the Yarkovsky effect)
• Compare observations at the asteroid to ground-based observations
(1) www.asteroidmission.org
INTRODUCTION TO THE OSIRIS-REX MISSION
• Equatorial Diameter: ~500m
• Polar Diameter: ~510 m
• Average Speed: 63,000 mph
• Rotation Period: 4.3 hrs
• Orbital Period: 1.2 yrs
• Orbital Inclination: 6 degrees
• Earth Approach: Bennu comes close to Earth every 6 yrs
BENNU FACTS
PROXIMITY OPERATIONS
• There are various phases of the OSIRIS-REx mission proximity operations in which 
specific scientific campaigns at specified cadences are in place.
• Eventually, there is a safe home orbit in which OSIRIS-REx remains in a terminator 
orbit as the staging point for all subsequent activities.
• The terminator orbit is a plane that is perpendicular to the sun vector: 
• For OSIRIS-REx, minimizes solar radiation pressure (SRP) perturbations 
• Relatively large perturbation due to the small size of Bennu
Terminator Orbit
OPERATIONS CONCEPT FLOWCHART
Characterize satellite ephemeris 
and physical properties*
Is object in 
the vicinity of  
Proximity Ops
< 10km
Proceed with cadence of 
operations with 
situational awareness**
No
Yes
Is the object in 
an orbit < 2km 
radius ?
• Hill Sphere: 31.7 +3.3/-4.2 km (2)
(2) D.S. Lauretta et al.,“The OSIRIS-Rex target asteroid (101955) Bennu: constraints on its physical, geological, and dynamical nature from astronomical observations” Meteoritics & Planteary Science, Vol 50, No 4, pg 
834-849
** Based on the Hill Sphere, 
proceed with caution of potential 
objects cruising within vicinity
No Characterize object with 
predictions for Prelim. 
Survey (7km) etc
Yes
Does the 
object pose a 
threat to the 
S/C?
No Continue with 
Preliminary Survey  
1. Determine Cadence of object observations (OpNav)
1. How does this interfere mission ops
2. Implement Collision avoidance scheme
Yes
Is the orbit a 
terminator 
orbit?
Yes
No
1. Determine Cadence of object observations (OpNav)
1. How does this interfere prox. Ops (Orbit A and B, 
Recon phasing, TAG timings etc.)
2. Implement Collision avoidance scheme
1. Determine Cadence of 
object observations 
(OpNav)
1. How does this 
interfere prox. 
Ops in the off-
terminator orbit 
(Recon, TAG)?
2. Implement Collision 
avoidance scheme
CURRENT STATUS OF BENNU NATURAL SATELLITES
• The presence of natural satellites depend on the rotation rates of the primary 
body. Bennu’s rotation rate is 4.29 hrs for a Bennu sidereal day (3)
• Most NEA of spheroidal shapes and rapid rotation rates have been found to be 
primaries of a binary system.
• About 16% of Near Earth Asteroids (NEA) with diameters larger than 200m may 
belong to binary systems.(4)
(1)
• Based on radar albedo of Bennu and a tidally locked rotation period,  the largest 
undetected satellite within 300km of Bennu is 2m.(1)
Potential Stable Natural 
Satellites size
Bennu’s Hill Sphere
Diameters 1m Out to 26 km
Diameters 10cm Out to 16 km
Diameters 1cm Out to 5km
(1) D.S. Lauretta et al.,“The OSIRIS-Rex target asteroid (101955) Bennu: constraints on its physical, geological, and dynamical nature from astronomical observations” Meteoritics & Planetary Science, Vol 50, No 4, pg 
834-849
(3) M.C. Nolan, “Shape model and surface properties of the OSIRIS-Rex target Asteroid (101955) Bennu from radar and lightcurve observations,” Icarus, Vol.226, 2013, pp.629-640
(4) J.Margot et al.,”Binary asteroids in the Near-Earth object population,” Science, Vol.296, No. 5572, 2002. 
APOLLO ASTEROIDS SIMILAR TO BENNU
• Apollo asteroids are Earth-crossing asteroids with
• Semi-major axes, a > Earth’s semi major axis (1 AU)
• Perihelion distances < Earth’s aphelion (1.017 AU)
• There are 55 known NEAs with moons
• (14 Amor, 34 Apollo, and 7 Aten) with a total of 57 moons
http://en.wikipedia.org/wiki/List_
of_Apollo_asteroids (5)
Name of 
Asteroid
Diameter (km) Name of Moon Diameter (km) Separation
1999 DJ4 0.43+/- 0.08 S/2004 0.21+/- 0.05 0.8
2002 AM31 0.45+/- 0.05 S/2012 0.11 1.5
2004 DC 0.36 S/2006 0.07 0.75+/- 0.045
* Note: No rotation rate information is included here
(5) Wikipedia. “Minor-planet moon” 2015
STANDARD APPROACH TO COLLISION AVOIDANCE (CA)
Collision Probability, Pc
• Compute Pc (might be hard)
• Compare to some threshold
Potential Issues with Pc
(5)
• Often integrating PDF in the tail 
region
• Must project PDF into future
• Is PDF even Gaussian?
• Pc might “roll-off” – when to 
decide?
(5) R.Carpenter, L. Markley and D. Gold, “Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data”, GNC , August 19-22 2013
WALD SEQUENTIAL PROBABILITY RATIO TEST
(WSPRT) FOR CA
• Test for true miss distance at time of closest approach: r* = rca
• Given set of observations at times tk prior to t* = tca: 1:k
• H0: fixed* hypothesis that true miss distance is unsafe (||r*|| ≤ R, hard body radius)
• H1: fixed* hypothesis that true miss distance is safe
• Form ratio of conditional PDF’s:
• Compare ratio to decision limits A & B:
• If Lk ≥ A, reject H0 and dismiss conjunction
• If Lk ≤ B, accept H0 and maneuver
• Otherwise, if possible, seek another observation
• Targeted Pmd (missed detection) and targeted Pfa (false alarm) are values that need to be 
pre-determined based on apriori statistics and/or Monte Carlo analysis
A
B
* Fixed hypotheses imply that there are no 
random disturbances, e.g. process noise, 
that can change a hit into a miss; if this 
can occur, must use a different test, such 
as Shirayeyev SPRT
(6) R.Carpenter, L. Markley and D. Gold, “Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data”, GNC , August 19-22 2013
WSPRT ALGORITHM
The conditional probabilities are 
calculated as:
The time series relative position vector and its covariance:
Therefore:
Simplifies to :
Likelihood ratio of WSPRT:
CONJUNCTION ANALYSIS EXAMPLE 1: 8 HR PREDICTION
• Simulated range, azimuth and elevation 
measurements for 4 hrs 
• Epoch 18 Feb 2019 12:00:00.000 UTC
• 500 Monte Carlo runs
• Natural Satellite
• Po = [σ2xx=(2/3 HBR)
2km2, σ2vv=(10e-6)
2 km2/s2]
• R = 0.01km
• Pc|0 = 0.052075
FAR (False Alarm Rate)
MDR (Missed Detection Rate)
Low Pfa
- High Alarm Limit
- Low Alarms
- Low False Alarms 
Hi  Pmd
- Hi Dismissal 
Limit 
- Affects No 
Decisions (f(Pfa))
How to decide based 
on one parameter only 
or two?
CONJUNCTION ANALYSIS EXAMPLE 1: 8 HR PREDICTION
• The decision is made 
depending on the 
values of the targeted 
Pfa and Pmd and 
calculated Pc|k.
• The required balance 
is a quick decision vs
accuracy 
requirements.
• This can be 
implemented 
dependent on the 
mission phase.
(a)   Pfa = 0.2 and Pmd = 0.2
(d)   Pfa = 0.01 and Pmd = 0.2(c)   Pfa = 0.2 and Pmd = 0.01
(b)   Pfa =0.01 and Pmd = 0.01
Pc|k ≥ Pc Alarm
Pc Alarm = Pc|0 (B+ (1-B)Pc|0)
-1
Pc|k < Pc Dismiss
Pc Dismiss = Pc|0 (A+ (1-A)Pc|0)
-1
CONJUNCTION ANALYSIS EXAMPLE 2: 3 HR PREDICTION
• Simulated range, azimuth and elevation 
measurements for 4 hrs + Prediction for 3 hrs
• Epoch 18 Feb 2019 12:00:00.000 UTC
• 500 Monte Carlo runs
• Natural Satellite
• Po = [σ2xx=(2/3 HBR)
2km2, σ2vv=(10e-6)
2 km2/s2]
• R = 0.01km
• Pc|0 = 0.052075
Low Pfa
- High Alarm Limit
- Low Alarms
- Low False Alarms 
-Similar value patterns to 8 hr
-Noticeably reduced FAR and 
MDR
Hi  Pmd
- Hi Dismissal 
Limit 
- Affects No 
Decisions (f(Pfa))
CONJUNCTION ANALYSIS EXAMPLE 2: 3 HR PREDICTION
(a)   Pfa = 0.2 and Pmd = 0.2
(d)   Pfa = 0.01 and Pmd = 0.2(c)   Pfa = 0.2 and Pmd = 0.01
(b)   Pfa =0.01 and Pmd = 0.01
• The decision is made 
depending on the 
values of the targeted 
Pfa and Pmd and 
calculated Pc|k.
• With 19 hits, still notice 
Pc|k < Pc Dismiss 
overtime .
Pc|k < Pc Dismiss
Pc Dismiss = Pc|0 (A+ (1-A)Pc|0)
-1
Pc|k ≥ Pc Alarm
Pc Alarm = Pc|0 (B+ (1-B)Pc|0)
-1
SUMMARY
• There exists a trade in False Alarm Rates and Missed Detection Rates accuracies with the prediction
duration to the time of Closest approach (TCA).
• Desired Pfa and Pmd can be tailored based on the mission phase and the available time of prediction to
TCA.
• This preliminary study will be useful in determining the correct approaches for each mission phase during
proximity operations
WORK TO GO:
• Complete build of generating a range of targeted Pfa and Pmd using a representative number of Monte
Carlo runs.
• Run examples of specific mission phase scenarios.
8 hrs Prediction to Close approach
Hi Pfa /Hi Pmd Low Pfa /Low Pmd Hi Pfa /Low Pmd Low Pfa /Hi Pmd
FAR 45.11% 13.72% 46.78% 13.31%
MDR 10.53% 10.53% 10.53% 15.79%
3 hrs Prediction to Close approach
Hi Pfa /Hi Pmd Low Pfa /Low Pmd Hi Pfa /Low Pmd Low Pfa /Hi Pmd
FAR 37.42% 16.01% 36.80% 16.84%
MDR 5.26% 5.26% 5.26% 5.26%
THE UNIVERSITY OF ARIZONA – NASA GODDARD SPACE FLIGHT CENTER – LOCKHEED MARTIN - KINETX
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A Collision Avoidance Strategy for a Potential Natural Satellite around the Asteroid Bennu for the OSIRIS-REx Mission

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