Making it remote conrtolled wouldn't be that hard. Buy a tank R/C from Wal Mart. Rip it apart for the electronics, wheels, & tracks. Build a chassis out of aluminum. Once those bugs are works out & you have the ca$h for a multi channel radio you can animate the arms & head with servos.

Once you get all that done, if you're feeling brave, make it an actual robot! There are all kinds of tutorials on the net that would tell you how they use those wires sticking out of it's chest as bump sensors. When you turn it on it would control itself. LEDs are super easy.