Seeking Advice: Robotics Art Project - $25 Reward

well, you have been warned that this is subject on safety. with that i will leave it to you to worry about safety and we can move on to feasibility and possible implementation. i would propose using some low cost controller, 12V car battery couple of relays, some geared motors and of course few sensors to avoid running into things.

geared motors are needed to get correct (reduced) speed and higher torque needed to move such heavy payload. with sufficiently high gear ratio even small motor can be used. i am thinking two motors would be enough and controlling when and how long they are powered will give you sufficiently random path pattern. there are different ways to go about this. for unit that mostly moves in one direction, one motor can be used for propulsion and other for steering (like in a regular car). for unit that moves at random, in both directions and can turn on a dime, it is better to put both motors on opposite wheels that are parallel to each other, for example one on left, one on right side. then you place one caster in front and one in the back and you are golden.

note that automotive motors are high current so you would need pair of inverting relays (SPDT) for each motor. so for two motors you would need 4 relays and therefore 4 outputs from the the controller. for example windhield wiper motors are very powerful and already have pretty substantial gearbox.

this is how each of motors would be wired:

i would also put diodes (a bridge rectifier really) to as a suppressor since every time you turn off one of motor, they would produce high voltage spike. this will not only erode relay contacts prematurely (which you may not care about if project is short life) but more importantly this could give you nasty jolts and wreak havoc on the controller. for that reason it would be a good idea to keep controller powered from separate battery (few AA cells for example).

as a controller you can use pretty much anything, smart relay (if it can be powered by 12V), some PLC (plenty of knockoffs for mitsubishi FX series), or Arduino etc. anything really would be fine.

the last item is sensors to detect obstacles. really there are two options - ultrasound or optical sensors, since the range you want is of 0.5-1m is too long for contact switch or inductive type. Amazon and hobby sites have tons of them. if using Arduino or whatever microcontroller (but not PLC), cheap sensors are something like this: ($2 a piece or so):

btw, regardless what you think or feel is needed (even with no humans present) i would consider at the very least adding a pullcord around the perimeter of the unit, and wire it to a simple 1-channel EStop circuit. (needs one more relay).

btw, Arduino or any microcontroller will not be able to drive relay coils directly and high current relays to control motor would need driver logic. cheap solution is to simply use additional intermediate weaker relays that already have built in drivers. they interface to Arduion etc easily and will have no problem driving the bigger relays.

here are typical automotive relays for high current that can easily control those motors

logic can be simple, drum sequencer or lookup table driven state machine.

here is an example wiring for high current section (motor circuit)