What was the earliest date a home-computer or home-robot could be interfaced with a tv-camera or digital-camera .
Depends on the definition of 'interfaced', as a case can easily be made for the 1975 Altair Cyclops Camera/TV-Dazzler set, as it combines a TV input with modifiable output.
There were many more before the Cyclops, but it would hard to make a case about the associated computers as home computers(*1). In the following years an incredible number of video input devices for microcomputers were developed(*2,3).
The most notable one may be the Sony HB-701FD MSX computer of 1984, as it is essentially the first consumer grade machine (*4) to include a video digitizer and real-time superimposing by default.
With MSX2 (and later the HBI-V1 module) video capture became a standard OS feature of MSX.
Robots were often based on home-computers.
Not really - not even nearly a historical fact. Sure, there were some robotic devices for home computers, robots themselves were either based on distinct microprocessor systems or microcontrollers.
*1 - Well, a case could be made even against S-100 as being mostly business systems, and the genuine home computer not being invented until the TI99 and Atari 400. Then again, its founding system, the Altair, was definitely targeted to hobbyists, so maybe we just read home computer as hobby computer and go along with that.
*2 - Just check this blog-post showing four different digitizers for the C64.
*3 - Including one by yours truly in 1983 - not for the C64, rather targeted at a professional audience.
*4 - Upper end that is - with some variations targeted at professional video/small TV stations.