Personally, I wouldn't bother fannying about with either a 433mhz system nor with a hand-built rx/tx pair.
Although, I could never read mention of Forest Mims without remembering with fondness the series of
electronics notebooks of his I have. Also, the time I nuked everyone's tv reception in the neighborhood as
a kid because I left a ~100Mhz transmitter running on batteries for a week and a half on the same breadboard
that was flashing an led. I realized after about 10 days that a new and funny band that was appearing on the
screen co-incided with the flash of the led. When I removed the batteries, the reception cleared back up.
The kicker was when a neighbor asked later that day or the next if we'd had any trouble with our tv for
the past week and a half.
Building that radio was the best electronics fun I had since dad
helped me make a radio-bug that fitted in a matchbox a decade earlier.
Since you've asked for cheapest-radio, I'd just go with an industry standard nrf24L01+ set.
Not only can you get the modules with varying output power, they're 'all' pin-compatible with one-another
and cheaper than chips. You should be able to get a pair of them delivered for less money than
either 1/2 of the 434mhz solution CrossRoads suggested.
You should be able to have them delivered to your door for around $2 ea - $4 in total for two transceivers.
So, they're cheaper and are bidirectional. You could receive messages back from your robot as well as
being able to control it.
If you'd like more range than the 24L01+ chipsets give, you could just get a pair of A7105 modules. I've bought and
had a pair of them delivered for $6. They're more sensitive and have a lower data-rate, which translates into
better range performance.
Also, each of the ones I mention handle ID, pairing and noise rejection in hardware. No need to waste time and effort
re-implementing what can be (and is) done in hardware.
434mhz Tx : US $3.95
434mhz Rx : US $4.95
(link provided earlier in thread)
nRF24L01+ TRx : AUD $1.47 ea (need 2)http://www.ebay.com.au/itm/1X-NRF24L01-2-4GHz-Antenna-Wireless-Transceiver-Module-Microcontroller-WST-/300951649158
A7105 TRx: AUD $6.57 pr (need 1)http://dx.com/p/xl7105-sy-diy-2-4ghz-a7105-nrf24l01-wireless-module-for-arduino-green-2-pcs-149253
The 24L01 is in all kinds of industrial equipment, while r/c gear made by Hobby King, Husban, FlySky and others all use the a7105 module. There are threads at rcgroups.com on making your own Tx or Rx that's compatible with commercially available
Rx or Txs. Turning on a laser pointer from over 200 meters away was a giggle one night. Having 10 simultaneous 16-bit channels
(65536 values used to represent 0-100%) with either of the transcievers is no more difficult than a single 1 (very easy).
Depending on the output requirements - PWM or simple on/off - It's usually harder to drive the arduino outputs than send the channel info.
Commercial units (FlySky) transmit at intervals as low as 1.5ms, which is great for responsiveness and low-jitter operation.
There's no requirement for you to do so as often, many wireless temperature sensors only transmit a packet every 30 seconds.