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This module introduces the theory and practice of optimisation, filtering and fusion techniques. These are all mathematical techniques with widespread practical applications but of particular relevance to robotics and AI. Optimisation is designed to seek the best value for an objective function, possibly subject to some constraints. Filtering can occur in hardware or software and removes unwanted elements of a signal. Fusion is a related process in which the integration of multiple sources of data is used to provide information of greater accuracy or pertinence than is possible for any of the individual sources.

Aims:

The aims of this module are to:

• Provide students with the enabling knowledge to employ practical techniques for optimising systems and for filtering data: the theoretical basis for these, the situations in which they are applicable, their implementation as a practical exercise and the performance characteristics of these implementations.
• Support students in casting robotics and AI problems as mathematical optimisation problems.
• Support students in the subsequent solution of these problems using analysis, self-developed programs and off the shelf optimisation tools.

Intended learning outcomes:

On successful completion of the module, a student will be able to:

1. Describe and use different forms of optimisation, filtering, and fusion techniques, selecting appropriate techniques for problems.
2. Formulate robotics problems as mathematical optimisation problems.
3. Select appropriate analytical and/or computational techniques for solving these problems.
4. Where necessary, implement programs that embody the chosen techniques using both self-developed programs and off-the-shelf optimisation tools.
5. Execute the programs using data from the domain of robotics and AI and report on the results, justifying the choices made and interpreting the results obtained.

Indicative content:

The following are indicative of the topics the module will typically cover:

• Introduction to optimisation
• Linear programming
• Nonlinear optimisation
• Discrete optimisation
• Filtering
• Digital signal processing
• Kalman filters
• Advanced topics in fusion and filtering

Requisite conditions:

To be eligible to select this module as optional or elective, a student must be registered on a programme and year of study for which it is formally available.