Charging 15 AA battery Pack
A battery's charge current is not determined by the basic battery size (eg: AA). The battery's capacity specification (in AH, mah) needs to be considered.  A simple AA battery can have a wide range of capacity values, some are low cost low capacity while other are high cost high capacity.  The best way to start with a charger design is to consult the manufacturer's specifications, most quality battery manufacturers provide this.  In the specifications the required charge current, voltage, safety, and other charging parameters are often given.

In regard to building up a 20v assembly:  Did you consider that battery packs in this range already exist?  For example manufacturers such as Black &amp; Decker have battery packs available for many of their portable products.  20v units are quite common. If you were to use one of these packs the charger could also be a standard Black &amp; Decker part.  If the large interface connector is a problem for your project you may be able to remove/modify it as needed.  If you start with a known matched up pair of battery and charger you can save yourself a lot of time and effort.  Not to mention you would know they work well together. 

Note that many of the newer B&amp;D battery products use Li battery types, though some other brands still use NiMH battery types. Some commercial battery packs are actually made up from stacks of several AA batteries.

Even if you choose not to use a commercial battery pack and charger for your project, looking at the manufacturer's specifications (and other hacks) of such a systems can give you a lot of good ideas on making your own.