Legged locomotion is a discrete event system (DES) due to the ever changing contact states of each leg. As such, it requires a nonlinear modelling method to predict the trajectory of a legged robot. One such robot has been focused on throughout this thesis; the six legged "Zebro''. With its half-circular legs, the Zebro is well suited for traversing uneven terrain and even climbing up small steps, making it the robot of choice for a lunar mission in the near future. A previous attempt at modelling the trajectory of a Zebro kinematically fell short when it came to modelling a curved path, with the reasoning behind this being how the Zebro's legs can visibly be seen slipping over the ground as it walks, the effect of which is never taken into account. A combination of kinematics and dynamics was used for the model in this thesis. The reason for this is that the Zebro's legs are actuated using position controlled motors, so the information available is the leg's angle and the speed at which the leg is rotating, rather than the torque. Therefore, kinematics were used to estimate the vertical motion of the Zebro due to the rotational speed of each leg, which could then be used to estimate the normal contact force on each leg. The traction forces could then be estimated using the normal force and a slippage model which has been experimentally identified in collaboration with a different research team at the TU Delft. With these forces, and the Newton-Euler equations of motion, the Zebro's path could be predicted. Applying a slippage model to a half-circular leg, rather than a wheel, required a new method of calculating the slip ratios which was based on Pacejka's formula, but adapted to also account for the case where a leg is standing on its toe. Furthermore, a contact detection algorithm was designed to kinematically predict which leg(s) lift off of the ground during a touchdown event. This was used to kinematically model the orientation of the Zebro during a tetrapod gait and was shown to correctly predict the complicated contact transitions during said gait. Another product of the research in this thesis is a new and improved algorithm for a turning tripod gait, which achieves smoother turning than beforehand by guaranteeing a smooth contact transition between two leg groups. That being said, it cannot yet be applied to the tetrapod gait, so the current gait scheduling algorithm is still required for a turning tetrapod gait. The results of the simulations showed the Zebro walking as expected, both in a straight line and when turning, but the simulations could not be validated quantitatively due to current events regarding COVID-19. For a qualitative review of the model, photographs were taken of the Zebro during walking gaits to compare to the simulations and showed that, while straightforward walking was predicted well, the turning circle of the model was significantly sharper than in reality. The reason for this is most likely a problem in the calculation of the slip ratios, since they were consistently unrealistically low, therefore requiring further research in future.

Correction techniques, such as tangential iterative projections (TIP), were developed to reconstruct the image for the whole field of view. However, due to the three dimensional nature of biological tissues, induced aberrations are different throughout the field of view. This Master of Science thesis shows the development of four algorithms. These algorithms apply TIP to deconvolve images locally. Thereafter, the local results are combined in order to restore images from anisoplanatic aberrations. The difference between the the algorithms developed during this research is the complexity in the spatial domain and in the Fourier domain. It was found that adaptive limited support in the spatial domain increases the im- age quality of the estimated object. A novel approach for multi-frame deconvolution in the Fourier domain has shown to be a promising modification. The use of weighted multi-frame deconvolution in the Fourier domain has lead to improved image quality.

The ZeBRo (Dutch abbreviation: Zesbenige Robot, six-legged robot), is a walking robot designed by the TU Delft, with its foundations on the RHex. The current version of the ZeBRo project, the DeciZebro, is made for the research to swarming in robotics, and is about the size of an A4-paper.
To counter these shortcomings of CPG (a method to determine gait movement), Max-Plus algebra can be used for the timing of the legs of walking robots. This can be done by modeling a walking cycle as two discrete events. These events are the times of the lift-off and touchdown and can be determined by using a Max-Plus Discrete Event System (DES) framework. The main purpose of these events is to determine two separate periods; the stance period, and the swing or flight period.
Max-Plus algebra is defined as a semi-ring over the union of real numbers and minus infinity. The standard binary operations are taking the maximum and addition which can be used for scalar and matrix operations.
The Max-Plus linear system contain the gait matrix A, and the vector v(k) containing the lift-off and touchdown times of vector instance k. One of the strengths of this method is the ability to change gaits, by simply changing the A-matrix. This then results in the switching Max-Plus linear (SMPL) system:
This SPML system determined in only contains gaits with successive recirculating leg-groups, where the synchronization of the lift-off of a certain leg-group I relies on the touchdown of the leg-group i-1. This allows for gaits like walking for humans, or a slow trot for horses, where a leg-group remains on the ground until the previous leg-group has recirculated.
To increase the number of possible gaits, the synchronization of successive leg-groups is extended to not only contain the previous leg-groups' touchdown times, but also their lift-off times. This extension allows for gaits containing multiple rotation leg-groups at the same time, making gaits like the gallop possible. Because of the desired stable situation of grounded legs, the synchronization is chosen to not extend the timing of the touchdown, as delays should not hinder the return of the legs to their grounded position.
The performance of different gaits is tested on different surfaces, to determine the influence of the amount of legs on the ground and determining whether gait changes could influence the success rate of the system regarding traversing rough terrain. Inertia measurement units (IMU) are used for detecting rough terrain, and tests show that the body movement of a ZeBRo on both flat and rough terrain are heavily influenced by the gaits used.
Because of several limitations regarding the actuation of the legs, gaits containing moments of static instability could not be tested. However, the framework for implementation regarding the Max-Plus is lain and tested using simulations.

A challenging task in synchronization of multi-agent systems is steering the network towards a coherent solution when the dynamics of the constituent systems are heterogeneous and residing in a possibly large uncertainty set. In this situation, synchronization can be achieved via adaptive protocols (with adaptive feedback gains, or adaptive coupling gains, or both). However, as state-of-the-art synchronization methods adopt a distributed observer architecture, they require to communicate extra local observer variables among neighbors, in addition to the neighbors' states (or outputs). The distinguishing feature of this work is to show that synchronization in heterogeneous and uncertain multi-agent systems is possible without the need for any distributed observer. This can be achieved by designing adaptive distributed synchronization protocols, based on homogenization reasoning. Specifically, ideal gains are defined (feedback and coupling gains) that could lead all the heterogeneous agents to a desired homogeneous behavior and thus synchronization. However, since these gains are unknown in view of the unknown dynamics, we design adaptive laws for these gains that lead the agents toward synchronization. In this thesis, different control protocols are designed to address both leaderless and leader-follower synchronization of linear multi-agent systems. The protocols are then extended to achieve synchronization over a special class of nonlinear multi-agent systems, whose units are modeled as Kuramoto-like systems. Throughout this work, convergence of the synchronization error to zero is shown via Lyapunov analysis, and numerical examples demonstrate the effectiveness of the proposed protocols.

Proton therapy is an increasingly popular form of radiotherapy that uses high energy protons for the treatment of cancer. It results in a lower integral dose than the classical photon radiotherapy. This makes it suitable for the treatment of tumors close to critical organs such as in the head and neck. To minimize alignment errors the head and neck are immobilized during treatment. Current immobilization methods are uncomfortable and unable to correct local misalignments between the head and the body. Therefore, an adaptive immobilization device is designed that can correct the local misalignments of the head and neck.