Can I use a car battery to power my robot?
To get 24 V at 8 amps, you'll need to supply 12 volts at 16 amps minimum. Add some inefficiency in the converter, and 20 amps is a good starting point. If, as you say, the motor will run half the time (and that may not be the case, depending on your control algorithm), average battery current will be 10 amps. A regular car battery will run about 45 amp-hr, so in theory you should be good for 4 or 5 hours. Of course, if you do this you won't be able to start your car, so you won't be able to recharge your battery.

So, if you really have 50% duty cycle, and the weather is warm, you might go 2 hours. 3 at the most. Anything more is really taking a risk. And if the motor is actually running full time (which it may), trying for more than about an hour is pushing your luck.

Of course, this assumes a new car battery. If your battery is getting old, you should expect an even shorter run time before you get in trouble.