The Free Energy Principle, which underlies Active Inference (AI), is a way to explain human perception and behaviour. Previous literature has hinted at a relation between AI and Linear-Quadratic Gaussian (LQG) control, the latter being a textbook controller. AI and LQG are, however, defined with different settings in mind: LQG has access to inputs, whereas AI estimates these; LQG is optimal for White Gaussian Noise, whereas noise needs to be coloured for AI, in order to make derivatives. Therefore, a comparison is provided on two bases: the setting of LQG control; and the setting of AI. The optimal LQG controller is obtained for both settings, and AI is applied to both settings as well. When AI is reduced to the setting of LQG, an equivalent expression can be obtained by a proper choice of tuning parameters. This entails choosing a matrix such that the closed-loop is stable, which contrasts LQG control, which is always a stabilizing controller. When LQG is extended closer to the normal AI setting, we find that tuning of AI becomes harder for more complex systems, but that AI is mostly able to show optimal behaviour.

Active inference is a process theory arising from neuroscience which casts perception, action, planning and learning under one optimisation criterion: minimisation of free energy. Current literature on the implementation of discrete state-space active inference focuses on scalability, the comparison to reinforcement learning and its performance to learn the state-observation mapping of the environment. In these implementations, active inference is supplied with accurate predefined information (knowledge) about the transition dynamics (controlled state transitions) of the environment. However, it is likely that in practical settings, knowledge gaps about controlled state transitions are involved. This thesis analyses the influence of knowledge gaps about controlled state transition on the active inference process. First, we provide a comprehensive overview of active inference and related principles. Secondly, we expand current active inference formulations with the power to actively evaluate the consequences of actions in their ability to resolve transition knowledge gaps. Thirdly, we analyse the behaviour of this expanded version of active inference once concerned with uncertain transition knowledge in a pure explorative setting (no task set). We found that active inference can deal with minor transition uncertainty, however, fails to operate when no initial transition knowledge is supplied due to a failing parameter updating mechanism. After proposing an alternative parameter updating mechanism, we found that active inference can deal with total uncertainty. Finally, we analysed the performance of active inference (with alternative parameter updating mechanism) to reach goals, starting without knowledge about transitions. We found that the resulting behaviour is a trade-off between exploration and exploitation and that the active inference agent gains transition knowledge while reaching the goals. In short, by investigating the influence of knowledge gaps in controlled state transitions, we aim to bring discrete state-space active inference one step closer to practical applications.

A fundamental task of intelligent and autonomous robots is to infer from observations the state of the world. This inference is generally achieved by employing a filter, which consists of a model and filtering law. Learning this model and filtering law from observations is another fundamental part of robotics, and is generally referred to as system identification.

Neuroscientist K.J. Friston has developed a relatively novel theory on biologically plausible human brain inference called the Free-Energy Principle. One of the theories within the Free-Energy Principle, namely that Dynamic Expectation Maximization (DEM), has been suggested as a novel method for filtering and system identification. This method is expected to outperform standard Expectation Maximization (EM) in terms of hidden state and parameter estimation in settings where noise is correlated. However, in order for this neuroscientific theory to be properly used for robot inference, two problems must first be solved.

The first of these problems is the fact that the theory is defined in the continuous-time domain, whereas data available for system identification is always discrete. In this thesis I will suggest three discrete-time interpretations for DEM-based system identification. The major difference between the three methods is the information that is embedded in the generalized signals: predictions, derivatives and past data.

The second problem is that the filtering method corresponding to the Free-Energy Principle depends on data which is not available: the derivative signals of measured in- and outputs. I introduce two fundamentally different solutions to this feasibility issue: a numerical differentiator and a stable filter. Both of these solutions are shown to find an estimate for the unavailable data. However, the former is shown to significantly outperform the latter.

Furthermore, the theory described in this thesis is implemented into a novel python toolbox for system identification. This toolbox can be used as a basis for further research and be approved along with it, until at some point it is ready to be used for real applications.

Using the toolbox, the DEM-based identification and filtering methods are tested though various numerical simulations and the results are compared with the EM method. Results show that with the implemented settings none of the suggested discrete-time filtering methods outperforms the conventional Kalman filter. The main cause of this inferior performance is shown to be instability in the filtering method. I make some suggestions for overcoming this problem. As a result of the inferior performance, the joint-performance of the suggested DEM-based parameter- and state- estimation methods also proves to be inferior in terms of parameter estimation accuracy.

However, results show that the theoretical parameter optima of the Free-Energy as determined from known hidden states are in fact close on the real parameters, and furthermore show to be invariant to noise correlation. This suggests that should the instability issue as some point be solved and a better means to approximate the theoretical optimum be found, the DEM-based methods might in fact outperform EM both in terms of hidden-state and parameter accuracy in settings with correlated noise.

This research focuses on proving the presence of coloured noise on the longitudinal, lateral and rotational velocity in steady-state cornering of a skid steer mobile robot. Furthermore, it also focuses on the creation of a Gaussian filter which is able to recreate the characteristics of the measured coloured noise. This is done to determine the characteristics of the Gaussian filter based on real-life experimental values, which defines the Gaussian filter that creates coloured process noise in the Active Inference algorithm. To accomplish the main research goal, the following is done: - Create a linear dynamical model of the jackal robot and optimize the model in such a way that its velocity states resemble the experimental values of the velocities for the given experimental inputs. - Show the presence of coloured noise in the dynamical behaviour of the jackal robot. - Create a Gaussian filter and determine its characteristics, which can recreate the coloured noise found in the velocity states of the jackal robot in steady state turning. To accomplish this, experiments are done capturing the linear acceleration, rotational ve- locities, position and heading of the skid steer mobile robot using both the internal sensors of the robot as well as an external motion capturing system. A linear model of the jackal robot is constructed and discretised as the noise is a function of the difference between the experimental value for the next step state [k + 1]exp and the prediction of the next step state [k + 1]est. The prediction is made by inputting the experimental values for step [k] into the discretised linear model together with the model input. The difference between [k + 1]exp and [k+1]est is the noise on the velocities during the steady-state cornering experiments. Optimal values for Gaussian filter are found by fitting the autocorrelations of coloured noise which is made by filtering white noise with a range of Gaussian filters on the autocorrelation of the measured coloured noise. The result of this research is proof of the presence of coloured noise in skid steer mobile robots which in turn indicates that using Active Inference on these types of robots is a worthwhile approach to control and state estimation.

The trajectory tracking efficiency of a quadrotor Micro Aerial Vehicle (MAV) position controller is decreased by discrete jumps in the pose estimate provided by a localization algorithm. This paper presents a solution to this problem by first introducing a new quadrotor MAV position control architecture followed by two methods that can compensate for the jumps in the pose estimate. The new control architecture consists of Model Predictive Control (MPC) for the outer position control loop and Incremental Nonlinear Dynamic Inversion (INDI) to control the inner angular accelerations. The attitude itself is controlled with a Proportional-Derivative (PD) controller. The first method that compensates for the jumps in the pose estimate considers an adaptive control law that changes the weights in the MPC cost function when the quadrotor's position is known to be uncertain. The second method applies a filter to the reference signal before providing it to the controller. Simulations validate the proposed controller architecture and show that the adaptive controller and the controller with reference filter decrease the covered distance during a flight mission by 6.7% and 7.0%, respectively, compared to the controller without these enhancements. Therefore, the efficiency of the trajectory tracking is increased.