This thesis deals with safety verification analysis of collision avoidance systems for unmanned vehicles. The safety of the vehicle is dependent on collision avoidance algorithms and associated control laws, and it must be proven that the collision avoidance algorithms and controllers are functioning correctly in all nominal conditions, various failure conditions and in the presence of possible variations in the vehicle and operational environment. The current widely used exhaustive search based approaches are not suitable for safety analysis of autonomous vehicles due to the large number of possible variations and the complexity of algorithms and the systems. To address this topic, a new optimisation-based verification method is developed to verify the safety of collision avoidance systems. The proposed verification method formulates the worst case analysis problem arising the verification of collision avoidance systems into an optimisation problem and employs optimisation algorithms to automatically search the worst cases. Minimum distance to the obstacle during the collision avoidance manoeuvre is defined as the objective function of the optimisation problem, and realistic simulation consisting of the detailed vehicle dynamics, the operational environment, the collision avoidance algorithm and low level control laws is embedded in the optimisation process. This enables the verification process to take into account the parameters variations in the vehicle, the change of the environment, the uncertainties in sensors, and in particular the mismatching between model used for developing the collision avoidance algorithms and the real vehicle. It is shown that the resultant simulation based optimisation problem is non-convex and there might be many local optima. To illustrate and investigate the proposed optimisation based verification process, the potential field method and decision making collision avoidance method are chosen as an obstacle avoidance candidate technique for verification study. Five benchmark case studies are investigated in this thesis: static obstacle avoidance system of a simple unicycle robot, moving obstacle avoidance system for a Pioneer 3DX robot, and a 6 Degrees of Freedom fixed wing Unmanned Aerial Vehicle with static and moving collision avoidance algorithms. It is proven that although a local optimisation method for nonlinear optimisation is quite efficient, it is not able to find the most dangerous situation. Results in this thesis show that, among all the global optimisation methods that have been investigated, the DIviding RECTangle method provides most promising performance for verification of collision avoidance functions in terms of guaranteed capability in searching worst scenarios.

The particular study case in this thesis is the shock test performed on the LISA Pathfinder satellite conducted in a laboratory environment on a dedicated test bed: Vega Shock Test Apparatus (VESTA). This test is considered fully representative to study shock levels produced by fairing jettisoning event at Vega Launcher Vehicle, which induces high shock loads towards the satellite. In the frame of this thesis, some transient response analyses have been conducted in MSC Nastran, and a shock simulation tool for the VESTA test configuration has been developed. The simulation tool is based on Nastran Direct Transient Response Analysis solver (SOL 109), and is representative of the upper composite of Vega with the LISA Pathfinder coupled to it. Post-processing routines of transient response signals were conducted in Dynaworks which served to calculate Shock Response Spectra (SRS). The simulation tool is a model of forcing function parameters for transient analysis which adequately correlates with the shock real test data, in order to understand how the effect of shock generated by the launcher is seen in the satellite and its sub-systems. Since available computation resources are limited the parameters for analysis were optimised for computation time, file size, memory capacity,  and model complexity. The forcing function represents a release of the HSS clamp band which is responsible for fairing jettisoning, thus the parameters which were studied are mostly concerning the modelling of this event. Among many investigated, those which visibly improved SRS correlation are radial forcing function shape, implementation of axial impulse, clamp band loading geometry and refined loading scheme. Integration time step duration and analysis duration were also studied and found to improve correlation.  From each analysis, the qualifying shock environment was then derived by linear scaling in proportion of the applied preload, and considering a qualification margin of 3dB. Consecutive tracking of structural responses along shock propagation path exposed gradual changes in responses pattern and revealed an important property that a breathing mode (n = 0) at the base of a conical Adapter translates into an axial input to the spacecraft. The parametrisation itself was based on responses registered at interfaces located in near-field (where the clamp band is located and forcing function is applied) and medium-field with respect to the shock event location. Following shock propagation path, the final step was the analysis of shock responses inside the satellite located in a far-field region, which still revealed a very good correlation of results. Thus, it can be said that parametrisation process was adequate, and the developed shock simulation tool can be qualified. However, due to the nature of shock, the tool cannot fully replace VESTA laboratory test, but can support shock assessment process and preparation to such test. In the last part of the thesis, the implementation of some finite element model improvements is investigated. Majority of the panels in spacecraft interior exhibited shock over-prediction due to finite element model limitation. Equipment units modelled as lump masses rigidly attached with RBE2 elements to the panel surface are a source of such local over-predictions. Thus, some of the units were remodelled and transient responses were reinvestigated. It was found that remodelling with either solid elements, or lump mass connected to RBE3 element and reinforced by RBE2 element, can significantly improve local transient responses. This conclusion is in line with conclusions found in ECSS Shock Handbook.