So you would like to build your own omnidirectional robots with Arduino? This 4WD Omni-Directional Arduino Robot Kit can help. It has an aluminum alloy frame and can move in any direction. It comes mostly assembled and can achieve speeds up to 0.6m/s. The board is based on the Arduino 328 microcontroller board. It has 14 digital pins and 8 analog inputs.
You have the option to add sensors, servos, and other components to build even smarter robots.