For the mobile (robot) we have several alternatives. We probably want a pattern which doesn't put much power straight up or down, since, in general, the base station end of the link is likely to also be at ground level. A simple omni whip is a first approach. Some form of colinear omni (i.e. several dipoles arranged in a line with appropriate phasing) is popular with cellular antennas (the "spring" in the middle is the phasing between the dipoles). Another advantage is that, for the 900 MHz band, at least, commercial cell phone antennas are readily available, and already tuned to the right frequency (since the 900 MHz band sits right between the Base-to-Mobile and Mobile-to-Base cellular bands.
These antennas are vertically polarized. There may be an advantage in circular polarization, due to the reduction in multipath induced fading. Intersymbol interference might also be an issue at higher bit rates. Certainly, on a non-digital video link from a model airplane to ground (roughly horizontally polarized), I have noticed severe fades from multipath. One technique might be to use circularly polarized antennas at both ends of the links. The multipath signals (being reflected, and of opposite sense) are then rejected by the antenna.
Some alternatives are things like Lindenblads, turnstiles, and helicals. Helicals would work fine at the base station, where you could point it at the mobile and, if you need tracking, probably use an Az-only positioner.
Another alternative would be to have several high gain antennas (or a single antenna and a positioner) on the robot, which is then pointed back to the base station. The look angle (pointing direction) could either be done by calculation from known positions, or by some sort of measurement and/or tracking. This approach was used on NOMAD for the high gain link, and is also used on various and sundry planned Mars rovers. NOMAD used a Suhner flat panel antenna in 2.4GHz band: 16.5dBi gain, beamwidth was 27 H and 25V, and there is a paper by Bapna, Rollins, Foessel, and Whittaker describing the pointing hardware and algorithms. (They claim needing 2.5 degree pointing accuracy, which doesn't mesh well with the 20+ degree beamwidth on the antenna)
My 5 gallon plastic Bucket Lindenblad (although, it's starting to look a lot like a short quad helix radiating in "sidefire" mode).
http://www.amsat.org/amsat/articles/w6shp/lindy.html - construction details for 2m and 70cm bands
http://laws.lp.findlaw.com/getcase/us/vol/getcase/US/306/86.html - oddly,Lindenblad was involved in a Supreme Court Case, although dealing more with Rhombics.
Masters Superturnstile (or Batwing turnstile) http://www.qsl.net/kd2bd/batwing.html
A design for a 900MHz band helical antenna based on 3" PVC pipe, pizza pans, etc. Big and heavy for the robot (at least for a small one), but probably will work for the base station. I'll try it and put the results up. (I must say, though, that it looks like some sort of science fiction death ray projector...)
"A slot-array antenna on a coaxial cylinder" Iigusa, K.; Yamamoto, S.; Tanaka, M.; Teshirogi, T. Antennas and Propagation Society International Symposium, 1998. IEEE , Volume: 3 , 1998 Page(s): 1434 -1437 vol.3
"The circularly polarized cylindrical patch" Sipus, Z.; Herscovici, N.; Bonefacic, D. Antennas and Propagation for Wireless Communications, 1998. 1998 IEEE-APS Conference on , 1998 Page(s): 145 -148
"A circularly polarized omnidirectional antenna" Sakaguchi, K.; Hasebe, N. Antennas and Propagation, 1993., Eighth International Conference on , 1993 Page(s): 477 -480 vol.1
"Antenna Pointing for High Bandwidth Communications from Mobile Robots",
Bapna, D; Rollins, E:, Foessel, A.;Whittaker, R., Proceedings IEEE Conference
on Robotics and Automation, (ICRA '98), Leuven, Belgium, 1998
(on web at:
http://www-2.cs.cmu.edu/afoessel/publications/antenna_pointing.icra1998.pdf)