Can Control Hierarchies be Developed and Optimised Progressively?

Hierarchical structures are used in robots to achieve effective results in control problems. Hierarchical structures are found in a wide array of applications of AI and robotics, making them a key aspect of control. Even though they hold an integral part in control, such structures are typically produced heuristically, resulting in inconsistent performance. This means that effective control tasks or controllers perform poorly due to the hierarchy being badly defined, limiting what controllers can do. Complex control problems that require adaptive behaviour or autonomy remain challenging for control theorists, with complex problem domains making the heuristic process of producing complex hierarchies harder.

It is evident that the heuristic process must have some form of procedure that could be turned into a methodology. By formalising or automating this process, control hierarchies can be produced with consistently effective results without relying on the heuristic production of a control engineer which can easily fail. This thesis proposes an algorithmic approach (inspired by Perceptual Control Theory) known as \ac{DOSA}. \ac{DOSA} produces heirarchies automatically using real world experience and the inputs the system has access to. This thesis shows that DOSA consistently reproduces effective hierarchies that exist in the literature, when billions of possible hierarchies were available.

Furthermore, this thesis investigates the value of using hierarchies in general and their benefits in control problems. The computational complexity of hierarchies is compared, showing that while hierarchies do not have a computational advantage, the parameter optimisation procedure is aided greatly by hierarchical parameter optimisation. The thesis then proceeds to study th hierarchical optimisation of parameters and how hierarchies allow this process to be performed more consistently for better results, concluding that hierarchical parameter optimisation produces more consistent controllers that also transfer better to an unseen problem domain. Parameter optimisation is a challenge that also limits otherwise effective controllers and limits the use of larger structures in control.

The research described in this thesis formalises the process of generating hierarchical controllers as well as hierarchically optimising them, providing a comprehensive methodology to automate the production of robust controllers for complex problems.