This robot is unconventional, it has a special kinematic configuration that allows it to move and turn simultaneously, and accelerate in every direction at once (holonomic vehicle) without changing the direction it is facing. This is not true for a car or a differential drive robot, that must change heading while turning. I used tree omnidirectional  wheels made by Rotacaster (thanks Philo for the LDRAW parts!)

I started designing this robot after Xander's Rotacaster One-kit Omniwheel, improving the wheels axis alignment, so they intersect exactly in the middle of the robot. This is important for odometry accurate pose tracking. Xander provided LDD model, while I prefer using LDRAW suite. You can download the instruction at the bottom of the page.

Besides the 3 motors for driving, the robot has a color sensor placed right in the center of it underneath the NXT, and 3 Ultrasonic sensors to scan the environment. To drive perfectly straight even while spinning, I used the MicroInfinity Cruizcore XG1300L.

To program the robot, I chose LejOS NXJ, to maintain the software easily and to exploit the excellent motor control algorithms provided. The robot can follow lines and can be remote controlled, even by an Android phone app I wrote on purpose. The driving-while-spinning feature has been ported to LejOS from Xander's Minifig Vomit Mobile.

You can find the JAVA class to make an omnidirectional robot like this on the LejOS SVN repository, or included in the latest LejOS distribution. Therefore, please don't ask me to send you the source code directly.