The original design for the GPS dog collar includes the use of Li-ion batteries.  The batteries are rechargeable and have significant power capacity to weight ratio which is ideal for this mobile application.  The only issue is that there is no way to know how much charge the battery has.  I am working on integrating a "fuel gauge" IC that will allow monitoring of battery status so that the battery won't just go out and you lose your furry friend.  It will likely be included in board V009.  Board V008 will be posted soon and includes the 555 timers instead of the 556 timers.