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.
This is a tough question. I will set aside the issues of whether it is "interdisciplinary," "multidisciplinary," "cross-disciplinary" or any of a number of other terms that some people get very emotional about. I have heard some people give definitions of all of these terms that overlap, and my humanities friends definitely have strong opinions about them, while my science friends often just can't see the point of using any of the terms or keep them straight. 

This sort of work is intrinsically hard to support in academic settings. Many departments actively punish people who do inter-, cross-, multi-disciplinary work in promotion decisions, by either downgrading the importance of that work in the promotion decision or completely removing it from the calculation; effectively saying "focus on what **we** do, here." Most interdisciplinary workers I know believe that they are behind the curve on promotions and advancement.

So programs that are truly interdisciplinary are rare. (There are some great exceptions, "Energy Studies" was mentioned in comments, and "Neuroethics" exists at my school -- there are others. Basically once a set of topics get pushed together often enough they can form their own field or discipline.)

You seem to be interested in the student or taking-classes side of this, so I will focus on that. 

First, look at the topics you are trying to combine and see if they exist in that combination. For instance, you mentioned neural nets and machine learning which 20+ years ago were semi-independent fields (the former often in computer science departments and the latter often in engineering), and are now the inter-disciplinary "artificial intelligence" (at least at some schools; your local history may vary). Likewise, instrumentation and control engineering, embedded systems, and robotics will all include strong signal processing components. So signal processing may be covered in the others.

So start by picking as a central field one that combines the maximum number of interests you have.

Then, pick your second majors and minors carefully to fill in more, if you can. You may end up getting multiple degrees along the way, all in different fields. That is what happened to me, I have a BA/BS, three masters degrees, and a PhD; all in different fields, and all important to the work I do these days.

Just as importantly as degrees and classes are projects. Often part of education is doing projects and you usually get to pick topics that interest you. Pick things that combine topics you want to combine. To do projects you will need a lot of self-study, a skill you will need a lot of if you are serious about being multi/inter/cross-disciplinary in your working life.

**But** a lot of inter/cross/multi-disciplinary work only comes into existence once you get to work. So expect to keep learning well past the degree phase. That may be where you get the most of the stuff that makes your work interdisciplinary.