Actually it is possible to build a robot with only hardwired logic, (no software) but nobody would consider such a solution these days. Sometimes it is important enough that safety systems and over-rides are done all in hardware.
Actually there are Robotic competitions where one of the main requirements (or restrictions) is that there is no micro controller or software involved. Even an Untrasonic Distance sensor that are typically used in bots are off limits. Only discrete components and mechanical parts are allowed. You can make a line follower easily without a micro.
Then again there are the BEAM-bot that use something like a Solar Panel and a Capacitor as it's power source and are typically made out of resistors and transistors and a micro motor.
To comment on your earlier post from awhile back:
"without software hardware is doing nothing"
Actually, Hardware does not need software to run; that is non micro controller type hardware does not need software.
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