  Mobile robots are becoming increasingly important both for individuals and
industries. Mobile robotic technology is not only utilised by experts in this
field but is also very popular among amateurs. However, implementing a mobile
robot to perform tasks autonomously can be expensive because of the need for
various types of sensors and the high price of robot platforms. Hence, in this
paper we present a mobile robot localisation and navigation system which uses a
LEGO ultrasonic sensor in an indoor map based on the LEGO MINDSTORM NXT. This
provides an affordable and ready-to-use option for most robot fans. In this
paper, an effective method is proposed to extract useful information from the
distorted readings collected by the ultrasonic sensor. Then, the particle
filter is used to localise the robot. After robot's position is estimated, a
sampling-based path planning method is proposed for the robot navigation. This
method reduces the robot accumulative motion error by minimising robot turning
times and covering distances. The robot localisation and navigation algorithms
are implemented in MATLAB. Simulation results show an average accuracy between
1 and 3 cm for three different indoor map locations. Furthermore, experiments
performed in a real setup show the effectiveness of the proposed methods.
