A Ball Balancing Robot (BBR) is a highly agile machine which is an unstable system. To stabilize, it uses three omni wheels connected to motors as an input of the system. Since it has less inputs than outputs, the BBR is an underactuated system. Due to the underactuated character and the non-minimum phase plant, the BBR is an interesting mechanism to study the effectiveness of control design.

An adaptive controller will be designed for the BBR such that it can cope with a changing environment, for example added mass to the robot or change of the surface it rides on. Due to the non-minimum phase characteristic of the plant, an Adaptive Pole Placement Controller (APPC) is the most suitable adaptive controller for the BBR.

In order to study which adaptive law in combination with the APPC gives the best performance simulations are done. For these simulations a 2D planar model is derived, which is compared and verified with the actual system.