Generalised Motions in Active Inference by finite differences

Abstract

This thesis is a contribution to the research on Active Inference for Robotics. Active Inference is an intricate, intriguing theory from neuroscience, a field in which it has already gained a greater following and popularity. This theory, based on the underlying Free Energy Principle, provides a unified account of perception, action and learning in the biological brain. It has great explanatory power of the function of the biological brain and furthermore it is mathematically well-defined. This property makes the theory suitable for a translation to robotics, in which it can also provide a unified account of action and perception. This is not only elegant, but potentially very powerful too. The research for Active Inference in robotics is young, but the current research already shows that Active Inference indeed has great potential for robotics control. Literature on Active Inference is narrow and complex, and provides a lot of concepts to work with in a translation to robotics control. Once such concept are the generalised coordinates of motion, which are the instantaneous derivatives of a dynamic variable. The incorporation of generalised coordinates, especially in combination with the assumption that the noise encountered in a dynamic environment is coloured, has great potential to be beneficial for both action and perception when it comes to robot control in real environments. Generalised coordinates provide a reference frame for the gradient descent that is applied to provide the action and perception laws, which in a dynamic setting has to `hit a moving target'. Furthermore, in combination with coloured noise the generalised coordinates are advantageous for dealing with such noise. In this thesis, detailed research is provided with regards to the application of generalised coordinates in Active Inference for robotics. Current research for robotics in which Active Inference has been applied doesn't exploit the full potential of generalised coordinates. Therefore, this research aims to explore the constructs necessary to apply generalised coordinates of motion in an on-line Active Inference control loop of an LTI State Space system. A detailed derivation of the generalised precision, which relates generalised coordinates and coloured noise, is provided. A method for obtaining generalised output by means of finite differences is proposed, that constructs generalised coordinates from the on-line data in scenarios in which the environment does not provide the required generalised coordinates naturally. The method is implemented in the simulation of a one degree of freedom SISO LTI State Space scenario which highlights the potential but also the difficulties still faced when applying Active Inference for on-line robotics control. Besides the detailed derivations of some aspects of Active Inference for robotics, open problems are identified and suggested for future research that can potentially yield methods to apply Active Inference in robotics at full capacity, providing a true biologically plausible robot control method.