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This thesis is concerned with the detection of loop closing in a Simultaneous Localisation arid Mapping (SLAM) application. The loop closing detection problem asks how a robot can 'recognise' it has returned to a previously visited location after completing a long circuitous path. Many SLAM implementations look to internal map and pose estimates to make decisions about whether a robot has closed a loop. Approaches that rely on these estimates are generally unreliable in detec:ting loop closure when true and estimated robot poses diverge greatly. The aim of this thesis is to produce a loop closing detection algorithm that is independent of pose estimates, sensor modality and estimation techniques, and works across a spectrum of workspaces. A key competency required is appearance-based place recognition. In order to achieve this goal, some significant issues pertinent to place recognition, namely perceptual variability and aliasing, have to be resolved. Viewpoint invariant descriptors are derived from observations used to represent local scenes. An efficient retrieval system coupled with indexing techniques allows for rapid comparison between observations based on a similarity function. Similarity relationships between local scenes are then encoded within a similarity matrix. The loop closing problem is then addressed as a sequence detection problem within a similarity matrix. Exploiting the phenomenon that loop closing events occur as off-diagonals within a similarity matrix, a sequence detection algorithm is developed to extract such sequences. Instead of finding matching pair of observations, matching sequences are detected so as to e>.-ploit the topological relationships between scenes to reduce false positives. To further tackle the perceptual aliasing problem, spectral decomposition of a similarity matrix is carried out. The effects of repetitive and ambiguous artefacts found within an environment are removed through rank reduction based on an entropy maximisation criterion. Sequence detection is achieved in these rank reduced matrices. A principled manner to determine the probability of sequence occurring randomly allows the evaluation of the significance of such sequences before loop closing is triggered. The practical implementation of the loop closing technique is demonstrated in a variety of challenging scenarios and experimental settings.

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Scheduling research has mainly focused on development of efficient· algorithms for solving deterministic and single criterion models to overcome the associated computational time complexity. However, scheduling in practice, demands development of effective approaches in order to fill the gap between the theory and practice. As many other decision processes, scheduling usually involves imprecisely defined problem parameters and multiple conflicting criteria in real-life domains. This thesis aims to put forward novel methodologies for solving some real-life production scheduling problems. In particular two problems have been tackled that are faced in the production process of the collaborating establishment Denby Pottery Ltd: an integrated loading and scheduling problem of a batch processing kiln that is used to fire glazed products and scheduling of parallel flow-lines where products to be input to the firing kiln are glazed. The first problem concerns both short-term criteria of relevance to the shop-floor and criteria that are related to the longer term objectives of the firm. The short-term objectives, which are reduction of energy consumption and work-in-process inventories, can be modelled using crisp objective functions. The longer-term objectives of meeting financial targets of the firm and attaining balanced end-product inventory levels constitute imprecise goals to be achieved. Moreover, the relative importance of criteria is also iniprecisely defmed. A novel fuzzy goal programming method is developed for solving the kiln loading and scheduling problem. This method takes into account not only fuzzy goals but also fuzzy •importance relations among the goals. A new fuzzy goal programming model of the problem is built. A prototype decision support system is developed that involves this model as its model base. The effectiveness of the developed methodolo.gy in producing different non- .dominated solutions has been demonstrated. The second problem considers scheduling of a set ofjobs on parallel non-identical flow.~ ines with respect to sequence dependent set-ups, flow-line eligibilities and fuzzy due-dates. A hierarchical optimisation approach is proposed for solving the problem. In the first phase a s~redule maximising the minimum satisfaction degree with respect to the fuzzy due-dates is ·~ought. This is accomplished using a novel fuzzy mixed integer linear programming model :3f~~;problem. In the second phase further optimisation ofmachine utilisations is carried out '. ;Und~r co~sideration of the solutions obtained in the first phase using a secondary model. The .,c~.T~utational analysis of the models and their effectiveness in producing optimal solutions ''th~real-life instances ofthe problem are presented.

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