http://www.ifirobotics.com/radio_modem.shtml
9600bps Full Duplex. Not sure if that helps. For the bit parity, I would say just brute force it and try all of the available options.
I hope you're going to have some kind of local object detection system on the robot, or at least some kind of emergency shut-off in case of packet drop. The last thing you want is a router to shut off and your robot to slam into a person in the hall.