I am the National Technical Chair for the SkillsUSA Mobile Robotics Competition. Our committee designs the contest each year and it is released in early October.
Mobile Robotics is a 2 student team contest that compete alone on the field (no contact with other robots). There is a 60 second autonomous period followed by a 60 second operator controlled period. The team is judged on how well they perform during the given challenge, their engineering notebook and a oral presentation. The robot must also built from a fixed kit of parts detailed in the Mobile Robotics rules in the link below.
Teams must be registered with their state Skills USA chapter in order to compete at the state contest. The state contests are typically in March time frame, but this varies by state. The winner represents their state at the national contest in June in Kansas City. This contest is open to both secondary and post secondary schools.
Here is link to last year's rules.
http://intelitekdownloads.com/skills...tics/index.htm
The Vex Robotics Competition (VRC) is a completely different competition. Teams are typically 2-5 students, but there is no stated limit like Mobile Robotics. The game is played in a head to head 2 vs. 2 format on a 12x12 field with alliances similar to FRC. The matches are 15 seconds of autonomous followed by 1:45 seconds of operator control. The robot can be built from any VEX legal part. Please review the contest rules in the link below.
Teams can go to variety of VRC competitions in their area. There is no limit on the number of competitions a team can attend. There are regional, national and worldwide competitions that teams can qualify for if they perform well at local events. VRC also has a middle school division.
Here is a link to this year's VRC game
http://www.vexforum.com/wiki/index.php/Sack_Attack
I am active in both competitions and I live in NH, so PM me and I will get you connected with the right people.
Good Luck this year!