Yes, both sentences are correct, and the meaning is slightly different in each.

So far, they... have contributed greatly to improved vehicle design

Here, they have contributed to a [new] vehicle design that has been improved. The object of to is vehicle design, and it is modified by improved ("what kind of vehicle design? an improved vehicle design"). Here, improved is a past participle acting as an adjective to modify vehicle design.

So far, they... have contributed greatly to improving vehicle design

Here, they have contributed to the goal/act of making improvements on [the study/science of] vehicle design. The object of to is improving, i.e., the action or goal of making improvements. In particular, it is the act of making improvements to vehicle design. Here, improving vehicle design is a gerund phrase, where improving is the gerund noun and vehicle design is its object.

It's also possible to read this as they have contributed to the study/science of vehicle design, which is currently improving. A similar use might be "We invested in the growing company": we invested in the company, which was growing.

I see absolutely no reason why you can't do this. However, perhaps you shouldn't depending on what you are writing for.

Firstly, two Google searches give us a much higher return of results for "improved" than "improving".

Why? Well, I'd hasten to say it's pretty simple. As language objects, the "-ed" past participle screams completion whilst its cousin the "-ing" participle resonates with "in progress". You will likely find that the vast majority of cases similar to the one you provide will prefer "-ed" over "-ing" because it provides that sense of completion; i.e. "The vehicles design has already been improved". Think of advertising, research or a variety of other fields. Giving the impression that the results of your test/products have already been implemented gives the consumer/reader a greater sense of satisfaction thanif you imply you are still working on things.