Navigation in mobile robotics involves two tasks, keeping track of the robot's position and moving according to a control strategy. In addition, when no prior knowledge of the environment is available, the problem is even more difficult, as the robot has to build a map of its surroundings as it moves. These three problems ought to be solved in conjunction since they depend on each other. This thesis is about simultaneously controlling an autonomous vehicle, estimating its location and building the map of the environment. The main objective is to analyse the problem from a control theoretical perspective based on the EKF-SLAM implementation. The contribution of this thesis is the analysis of system's properties such as observability, controllability and stability, which allow us to propose an appropriate navigation scheme that produces well-behaved estimators, controllers, and consequently, the system as a whole. We present a steady state analysis of the SLAM problem, identifying the conditions that lead to partial observability. It is shown that the effects of partial observability appear even in the ideal linear Gaussian case. This indicates that linearisation alone is not the only cause of SLAM inconsistency, and that observability must be achieved as a prerequisite to tackling the effects of linearisation. Additionally, full observability is also shown to be necessary during diagonalisation of the covariance matrix, an approach often used to reduce the computational complexity of the SLAM algorithm, and which leads to full controllability as we show in this work.Focusing specifically on the case of a system with a single monocular camera, we present an observability analysis using the nullspace basis of the stripped observability matrix. The aim is to get a better understanding of the well known intuitive behaviour of this type of systems, such as the need for triangulation to features from different positions in order to get accurate relative pose estimates between vehicle and camera. Through characterisation the unobservable directions in monocular SLAM, we are able to identify the vehicle motions required to maximise the number of observable states in the system. When closing the control loop of the SLAM system, both the feedback controller and the estimator are shown to be asymptotically stable. Furthermore, we show that the tracking error does not influence the estimation performance of a fully observable system and viceversa, that control is not affected by the estimation. Because of this, a higher level motion strategy is required in order to enhance estimation, specially needed while performing SLAM with a single camera. Considering a real-time application, we propose a control strategy to optimise both the localisation of the vehicle and the feature map by computing the most appropriate control actions or movements. The actions are chosen in order to maximise an information theoretic metric. Simulations and real-time experiments are performed to demonstrate the feasibility of the proposed control strategy
