For a wide range of people with limited upper- and lower-body mobility, interaction with robots remains a challenging problem. Due to various health conditions, they are often unable to use standard joystick interface, most of wheelchairs are equipped with. To accommodate this audience, a number of alternative human-machine interfaces have been designed, such as single switch, sip-and-puff, brain-computer interfaces. They are known as low throughput interfaces referring to the amount of information that an operator can pass into the machine. Using them to control a wheelchair poses a number of challenges. This thesis makes several contributions towards the design of robotic wheelchairs controlled via low throughput human-machine interfaces: (1) To improve wheelchair motion control, an adaptive controller with online parameter estimation is developed for a differentially driven wheelchair. (2) Steering control scheme is designed that provides a unified framework integrating different types of low throughput human-machine interfaces with an obstacle avoidance mechanism. (3) A novel approach to the design of control systems with low throughput human-machine interfaces has been proposed. Based on the approach, position control scheme for a holonomic robot that aims to probabilistically minimize time to destination is developed and tested in simulation. The scheme is adopted for a real differentially driven wheelchair. In contrast to other methods, the proposed scheme allows to use prior information about the user habits, but does not restrict navigation to a set of pre-defined points, and parallelizes the inference and motion reducing the navigation time. (4) To enable the real time operation of the position control, a high-performance algorithm for single-source any-angle path planning on a grid has been developed. By abandoning the graph model and introducing discrete geometric primitives to represent the propagating wave front, we were able to design a planning algorithm that uses only integer addition and bit shifting. Experiments revealed a significant performance advantage. Several modifications, including optimal and multithreaded implementations, are also presented.