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# ACMD Seminar: Rendezvous Search on a Sphere: The Astronaut Problem

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Drew Henrichsen*Ph.D. Candidate, Johns Hopkins University*

Tuesday, February 6, 2024, 3:00-4:00 PM ET (1:00-2:00 PM MT)

In person at: Gaithersburg Bldg. 101 **LR C** with VTC to Boulder 1-**1203D**Online at: ZoomGov

Add this talk to your calendar: https://inet.nist.gov/calendar/ics/2276311

**Abstract**: In a rendezvous search problem, the goal is to find an optimal strategy for two agents in a specified region to use in order to meet in the minimum expected time. The astronaut problem considers two agents on a sphere representing a featureless planet. The agents can see everything within a detection radius *r* and have a maximum allowed speed of movement. Although the problem is decades old, there are no published results. We consider multiple strategies, providing both theoretical bounds and Monte Carlo simulation estimates. Some of the strategies are iterative, restarting if the agents have not met, so they involve geometric waiting time distributions. Although one might expect the optimal meeting time to vary inversely with the detection area, which is of the order of *r2*, upper bounds that vary inversely with *r* are obtained in both the symmetric and asymmetric settings.

**Bio**: Drew Henrichsen graduated with a degree in Applied and Computational Mathematics with an emphasis on Biology from Brigham Young University. He worked in industry for a few years in software, data, and AI, then returned to school at Johns Hopkins University as a PhD student. While there, he published a paper on Rendezvous Search on a Sphere and was instructor of record for the Data Mining course in Fall 2023. Drew is currently focusing on research on Bayesian Statistics for strengthening the control arm in clinical trials and following up on loose ends in rendezvous search.

**Host**: Tony Kearsley

**Note**: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

**Note**: Visitors from outside NIST must contact Meliza Lane at least 24 hours in advance.

Information technologyComputational scienceMathematics and statisticsTransportationAerospace

## Contacts

                -  Anthony J. Kearsley  anthony.kearsley@nist.gov      (301) 975-6103   
                -  Zachary Grey  zachary.grey@nist.gov      (303) 497-5920   
                -  Elsie Lane  elsie.lane@nist.gov      (303) 497-5356   

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