This thesis is about how a vehicle can, without human intervention, be navigated and guided in its movements through its environment. To move a real mobile robot so that it traces out a desired path, 'commands' need to be dispensed to the control systems of the actuators that drive the wheels that move the vehicle. Algorithms which issue such commands are called guidance algorithms. These can cause the vehicle to move about at the desired speed, in the desired direction, and can change the direction of motion, or can achieve some other 'complex' manoeuvre. As commands from guidance algorithms are physically realised, and become the sensible motion of the mobile robot, the desired 'intentions' embodied in them become corrupted. To combat this corruption the mobile robot needs to keep track of where it is in relation to some reference system. This is navigation. The mobile robot needs to navigate so that 'commands' to the actuation systems can then be reformulated in terms of its navigated 'location', given the task it is doing, and where it has been commanded to go to. In this thesis three navigational phases are distinguished for a wheeled 'robotic' vehicle. Their utility was tested and confirmed by experiment, using a 0.5 tonne mobile robot equipped with the relevant sensors, and actuation systems. The three phases of navigation are:- 1) Deduced reckoning based on the intrinsic motion of the vehicle to produce an initial estimate of the vehicle's position and heading. 2) The use of an absolute measurement of the vehicle's bearing to correct errors in the estimated heading. 3) The use of sonar range measurements to objects in the surroundings to correct errors in the estimated position. The positional coordinates, orientation, and extent of these objects being held in a 'world map'. Two guidance algorithms to control a mobile robot's movement are needed, correctly sequenced and coordinated, to enable it to perform a range of useful activities. This thesis has examined 1) Guidance to achieve motion with zero curvature, for a specified distance, and orientated relative to some specified direction in the environment. 2) Guidance to achieve the reorientation of a vehicle, that has to move in order to turn, so that it can move forward again with zero curvature in a different direction. Finally, a new technique that modulates the steering wheel angle with a time dependent Gaussian envelope is given. This technique is able to produce desirable changes in the position and heading of a path curvature limited vehicle, as it moves. Examples of manoeuvres possible with this technique are illustrated.