- It don't want the system to detect any person going near by, just detect the cat
The right type of dog will have different sensor inputs for various stimuli, and the resulting outputs can be coordinated with practice. With the right code, it will only trigger the wagTail() and destroyCat() interrupts when appropiate.
- the detection distance should be at least 40cm
Most models of dogs' sensors should be more than adequate for the task, Check the datasheet for specifics though.
- it has to be low cost as there is at least 5 or 6 places where she scratches.
Initial startup costs to a dog can be minimal if found from the right second hand reseller. Some might have some hidden bugs in the code that might need some expert attention, and that consultant may charge a bit more. Long term maintenance of dogs can be quite affordable, and usually the extra benefits outweigh any accrued costs. Depending on the exact make and model of your dog, you can pair it up with another dog module and create a series of Dog 2.0 breakouts, which may allow to offset more cost.
- it neads to be waterpoof has it's outside and if possible discret
Err.. well... that depends on the make and model again. Check the specific datasheet on weather proofness of your dog. My shepherd was miserable at this, but my retriever was amazing in bad weather. Discreet.... umm.....
I think the other guys are right about trimming the toe nails. However, for general purposes, you might experiment with cheap PIR detectors. Normally, they are made to detect larger warm bodies, like humans, at 10-20 feet, but they may work for smaller bodies at 'short' range. IOW, mount them low to the ground near where the cat goes. You can also use black electrician's tape to mask off the detection zone of the sensor. It might work.
you could probably design something with a Light Dependent Resistors and a buzzer . the ldr could be placed on the floor or the area which gets covered by the cat.you could design it with a small (and cheap)micro controller and with a piezoelectric buzzer(to scare the cat) the total cost would be very low($5-$10).you can also do it without the micro controller directly with a couple of resistor and transistors . the cost would be even lower
The LDR thing might work ok, if you compensate for general luminance changes, like day/night, lights-on/off, etc. So, look for somewhat "quick" changes in intensity against an ambient background. There might be problems with shadows when you walk by.
Probably work better as a photo-interruptor, ie Led on one side and LDR pickup on the other side of the cat spot. BTW, cyberneticzoo is a really great site, see the guy getting into the elevator at 5:00 into the video!