Batteries for 3v gearbox
You need to measure the current drawn by your load. Insert a multimeter on A (amps) range in series with the battery circuit somehow. Start the robot and measure the current drawn.
You can then compare the Ah (ampere-hour) specifications of various batteries and get an estimate of run time by dividing Ah by the multimeter amps reading. \$ Run~hours = \frac {battery~Ah}{multimeter~A} \$. Note that Ah rating is usually at a specified current draw. If you increase the current the batteries will give less Ah due to power lost as heat in the battery cells.