Question: How can someone become a multi-disciplinary researcher?

For example, can one study a multi-disciplinary domain that combines signal processing, artificial intelligence (neural net, machine learning), robotics, instrumentation and control engineering, and embedded systems? Is there a path that could make a candidate a marketable researcher across all these domains?

Answer: 
To answer the general question: You can be a interdisciplinary researcher by getting multiple degrees in different fields, getting a single interdisciplinary degree, or by getting a degree in one field and, over the course of your career, working your way into another. 

Most academic jobs are hired by departments, and the wide majority of departments are single-disiplinary, though interdisciplinary programs are fashionable right now. 

To be a marketable researcher in a given discipline, you would generally need at least a phd in that discipline, possibly a interdisciplinary phd that centrally involved it (marketability depends a lot on the specific interdisciplinary program, but in general, these will be less appealing than an phd in the actual discipline), or, in very rare cases, a a phd in a different discipline but VERY extensive research in that discipline. When it comes to the latter, things are probably more flexible in the humanities than in the sciences, and often only in one direction (ex. there are philosophy phds in rhetoric departments, but not rhetoric phds in philosophy departments). In general, you need to be able to teach introductory courses in that discipline as well as in your particular area. 

Some universities do have particular interdisciplinary departments or other interdisciplinary lines, but these are in established interdisciplinary subjects—cognitive science, peace studies, asian cultures, environmental studies...

There are also "cluster hires," where universities look to give a researcher appointments in multiple departments for work on topics like diaspora studies and agroecology that are appealing to administrators but too small to support entire departments. Cluster hires are rare and are not something you can plan a career around. 

There are no lines for unspecified "interdisciplinary" researchers. You need to be able to market yourself under a specific discipline or under an established interdisciplinary program. In general, the latter will be harder.
There are two groups of researchers relevant to your question. The inter-disciplinary ones, and the multi-disciplinary ones.

I know one or two hundred inter-disciplinary researchers. With a couple of exceptions (so now we're down to a tiny tiny proportion of all researchers), they nevertheless all have a single specialism: in each case, it's a specialism that spans more than one traditional topic. Typically, they did one (or occasionally two) Masters' degree(s) in fields different to their first degree, and then did an inter-disciplinary PhD.

Only the exceptions are multi-disciplinary. We became that through many years of working across different fields. We're not specialists in all of those fields. But we know enough to be able to work in teams that consist of specialists from any combination of them. None of us planned it this way - it just emerged as a consequence of our (lack of) career path.

Many fields see the multi-disciplinary researcher as something of a luxury. In the first instance, most principal investigators and other research leaders seem to prefer single-discipline experts. An enlightened few see the benefits of creating the best team, rather than just selecting the best individuals; and for inter-disciplinary work, a multi-disciplinary researcher can be the catalyst that enhances the performance of the rest of the team, as well as doing research in their own right.