As I understand, Canon has been removing USB support for their cameras for a while now... And, I believe there will be no support for any new Powershot cameras going forward.
I believe the compatibility with Canon's SDK (software developer's kit) list shows what cameras you would have a prayer of trying to remote control:
compatibility with Canon's SDK (software developer's kit) listAnd, the SD870 is listed as a NC (not compatible?) with the SDK.
It is possible that with further work, the USB interface can be ported into CHDK--but I would not make any plans (unless you are the one to try it).
Otherwise, the USB interface could be setup with a polling loop and you could try to implement some uBasic functions (zoom in, zoom out, shoot, etc.) with some simple pulse coding on the USB (basically, very slow serial, one way,l interface).
If you want to download photos from the camera without stopping it--perhaps the Eye-Fi card would provide some hope (WiFi SD Card which can download automatically from the camera to your WiFi network).
Automatic transfer of images to PC over USBCHDK Autoboot w/ Eye-FiEye-Fi is a bit of a moving target right now--but if you are into hardware and software--it may be a very interesting project (and do some more searching on the web for the latest news).
-Bill