The robot eats antennas? I would feed it something less expensive.
Are you using 2.4Ghz Wi-Fi or something else? Perhaps it would be useful if you disclose what hardware and software you have to work with and in what environment you plan to use the robot.
I've helped with a few 2.4GHz wireless robots. It's amazing how much RFI (radio freq interfernce) a high power motor controller can generate. 2.4Ghz works just fine as long as there is no interference and your traffic is minimal. If you're running 30fps video over Wi-Fi, give up now.
Since you didn't specify a distance requirement, I can't really offer any specific suggestions. Up to about 50 ft, with no obstructions, almost any omni antenna will work. If you plan on going farther, you'll need to make some changes. Since you don't know the robots orientation, I suggest you move the omni to the robot. Yeah, I know it's a big long antenna. At the control point, I suggest anything between a 12dBi panel antenna, which should have about a 45 degree beamwidth. Any more gain will require some form of tracking. I've done this for model airplanes using 2.4GHz Spektrum RC hardware:
You might find this interesting for your bot: "World Smallest Longest Range 2.4 Ghz Radio Remote Control Wireless RC Camera": $70. If you pick your channels carefully, it sorta coexists with Spektrum and Wi-Fi radios.
 We staged a private autonomous maze run at the local university and had to disarm the wireless access point in the room. If we pulled the plug, alarms would go off all over place. So, I just unscrewed both antennas on 3 access points.