Vectorisation of robotran equations through FPGA

This thesis aims at characterising the potential of parallel computation for multibody systems and the consequential reduction of simulation time, understanding the limitations, boundary conditions which we are currently facing and the future improvements that could take place in order to push further away these boundaries. Parallel computing in multibody dynamics is pushed by multiple causes: the increasing complexity of multibody systems, the need for real-time applications, the use of parallel computing in other research areas, the democratisation of multi-core CPU. During this thesis we develop a dedicated parallel architecture on a FPGA in order to implement and test a multibody system. This implementation allows to characterise the limitations, challenges and benefits of such an architecture. Given the architecture we develop and in parallel to this, we create an algorithm that is able to handle the multibody systems equations to extract the fine-grain parallelism of these equations. As multibody dynamic systems vary both in size and in morphological characteristics, we make a study case of multibody systems with the variation of these characteristics. These are on size, system with 23-, 50-, 70-, 100- and 130-dof and on topology, with either a serial, a semi-serial or a parallel multibody system. We will use these in order to compare their potential differences and similarities. To further increase the extraction of the fine-grain parallelism, we propose three methods in order to modify the equations, exploiting the following two concepts: the atomisation into a binary expression tree and the critical path of the equations.