There are a variety of x86 products with Coreboot support, if what you are looking for is firmware openness. If what you are looking for is PCB design openness, the options are much fewer, but at that point you are probably optimizing for an overly niche objective.
> Part of the point of this for me is to see what's possible with open hardware (down to chip level at least)
I appreciate the idea, but this is essentially saying "this project will prioritize a specific choice of one (core) piece of hardware to the detriment of everything else, users included". Approximately none of your potential users are going to benefit from the "openness" of the SBC versus that of a more broadly-supported platform (I say "openness" because the reality of SBCs is that actually finding a usefully performant one that is completely blob-free is almost impossible). Open hardware means very little if it isn't running an upstream kernel and userland.
The South-Korean Hardkernel ODROID H4 models are open hardware. There is no need to send one to you, as you can order one yourself from their on-line shop or from local shops.
You get their schematics/PCB documentation and their BIOS has features that are missing in most mini-PCs and laptops with Alder Lake N/Twin Lake, e.g. you can enable in-band ECC for the memory. You can choose various variants of the SBC and you can buy cheaply various accessories, e.g. several case variants and additional peripheral interfaces. Those ODROID H4 SBCs are also correctly designed for cooling inside a box like that used in this project, because the PCB is attached to a big heatsink and you can attach the heatsink directly to an aluminum wall from inside the box, ensuring good thermal contact with pads or grease, so that the electronics will be cooled well.
Most technical information can be found in their Korean site, but there is a UK distributor (though the prices appear greatly inflated here; so much that it might be cheaper to buy from South Korea, depending on shipping costs and applicable taxes):
Also the Chinese Radxa has a Raspberry Pi sized SBC with an Intel N100, which is open hardware, with complete schematics/PCB documentation (but unlike ODROID H4, which has excellent cooling and it can be used without a fan, it is unclear how easy is to cool the Radxa SBC).
Moreover, unlike for many Intel/AMD CPUs, which no longer have public documentation, for Alder Lake N Intel still provides public datasheets, which contain e.g. the thousands of control registers for the on-chip peripherals. Most ARM Cortex-A based CPUs are undocumented, with few exceptions like Rockchip RK3588 and the very expensive NVDIA Orin/Thor (or the obsolete Xavier). All Cortex-A based CPUs have secret boot loaders, so you can never be certain that your programs really run on bare metal, as the CPU vendor can implement the equivalent of the Intel System Management Mode, where the proprietary vendor firmware can take control from your own operating system whenever it wants.
There are somewhat more ARM-based SBCs than Intel-based SBCs that are open hardware, but there are also plenty of undocumented ARM SBCs that are much worse from this PoV than the Intel/AMD based computers, where at least the IBM PC standards and the later standards pushed by Intel, e.g. ACPI/UEFI, apply. The Allwinner CPU used in this robot has almost non-existent documentation, in comparison with Intel Alder Lake N, so it is much farther from "open hardware".
You have mentioned the NVIDIA Jetson modules, which are based on Thor/Orin/Xavier. Those have excellent documentation, but you have to register at NVIDIA, for a free account, in order to access it. The documentation is not the problem with them, but the fact that they are greatly overpriced, like almost anything made by NVIDIA. Unless your application critically depends on some feature provided by NVIDIA, for which no acceptable alternatives exist, choosing Jetson is a very bad decision, because the alternatives are usually both better and cheaper.
The SBCs based on Cortex-A55 are the cheapest for the purpose of running Linux that still have a decent performance and they may be sufficient for many applications.
However, the SBCs based on either Intel Alder Lake N or on ARM Cortex-A7x cores are in a completely different class of performance, so they are more future-proof as they can enable the implementation of applications that were not taken into consideration in the beginning. Moreover, as pointed by the other poster, none of the Cortex-A55 SBCs implements any kind of standard, so migration to any different SBC may require significant work, unlike with the Intel/AMD SBCs, which are mostly interchangeable.
The Intel Alder Lake N/Twin Lake cores (Gracemont cores) have a performance similar to the ARM Cortex-A78 cores, which for now can be found only in few SBCs, which use Qualcomm, Mediatek or NVIDIA CPUs. The Cortex-A76 cores, which are used in Rockchip 3588 and in the latest Raspberry Pi, have a speed of only around 2/3 of the Gracemont/Cortex-A78 speed, at the same clock frequency.
Cortex-A55 cores are many times slower than any of these bigger cores. A single Intel SBC (or Cortex-A7x based SBC), can replace both Cortex-A55 SBCs of this design, at about the same cost, improving the cooling and probably lowering the power consumption, while also providing a significant performance headroom for future extensions.
While using 1 Cortex-A55 SBC for minimum cost may make sense, using 2 is a definite mistake, as they should be replaced by 1 better SBC.
I have mentioned the open-hardware Intel-based ODROID H4. The same company makes several models of ARM-based SBCs, which I would trust much more in an outdoors robot, than the choice done in the parent article, because the cooling behavior of all of them is carefully tested and reported on their site, and because it is a company that has been around for many years, demonstrating reliable hardware. Avaota provides much less information about their product than Hardkernel, i.e. they only give schematics/PCB information, without any information about power consumption, and especially about thermal behavior, which is essential in a robot application.
Part of the point of this for me is to see what's possible with open hardware (down to chip level at least)