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Hydrogen + oxygen fuel cells powered the week-long Apollo missions to the Moon and Shuttle missions to orbit, and there is a industry trying to build itself around hydrogen-fed fuel cell-based road vehicles.

Cryogenic methane + oxygen deep space vehicles are probably coming, and missions could go well beyond Mars, to moons of Jupiter or Saturn possibly at some point, where solar power is only a few percent as strong as it is circa 1 AU. (see How far from the Sun can solar power be used as a reliable energy source?) Just look at Juno's giant solar panels and its fear of eclipses and Rosetta's need to hibernate when furthest from the Sun for examples.

Question: There is hydrogen in methane, so there is some potential for a fuel cell, but I'd like to know if there are any designs or research into a methane + oxygen based fuel cell for electrical power.

Yes, there are also proposed internal combustion space-engines and one could just use a natural gas powered electrical generator, but for the purposes of this question let's stick to conversion from chemical to electrical power using fuel cell technology.

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    $\begingroup$ Good question! Answer: Theoretically possible, but it's in the early stage of development. This might be helpful. Further in Solid oxide fuel cell, lighter hydrocarbons can be internally reformed. Simply methalox-based fuel cell is possible it's but under development. $\endgroup$
    – Vishnu
    Commented Nov 5, 2019 at 5:46
  • $\begingroup$ @Intellex okay that's good news! $\endgroup$
    – uhoh
    Commented Nov 5, 2019 at 6:37
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    $\begingroup$ Note: the correct terms would be methox or hydrox, the fuel cell doesn't run on liquid oxygen and gaseous fuel. And usually the oxygen is left assumed. $\endgroup$
    – Christopher James Huff
    Commented Nov 5, 2019 at 14:22
  • $\begingroup$ @ChristopherJamesHuff that's a really good point! The fuel cell doesn't know it's on an interplanetary voyage aboard a big rocket with cryogenic storage. It only sees gas phase reactants that are probably pre-heated before reaching the catalysts. I've adjusted the wording accordingly. Thanks! $\endgroup$
    – uhoh
    Commented Nov 5, 2019 at 18:28

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This 2018 release from Georgia Tech describes one such - claimed to be more practical than previous methane-fueled cells because it operates at a lower temperature. It is a solid-oxide cell.

It appears to work by catalytically cracking the methane to hydrogen, and it seems that the advance is in the cracking part.

https://www.news.gatech.edu/2018/10/29/finally-robust-fuel-cell-runs-methane-practical-temperatures

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    $\begingroup$ Thank goodness, it's about time somebody got cracking on this. $\endgroup$
    – uhoh
    Commented Nov 5, 2019 at 12:58

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