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An algorithm for dynamic trajectory generation employing numerical multi-objective optimisation is presented. The crucial innovations are the description of the trajectory through velocity and curvature on the one hand and the restriction of the otherwise infinite function space to a set of basis functions on the other hand. A number of boundary conditions and inequality constraints ensuring the feasibility of the planned trajectory for real vehicles are adhered to. This algorithm is embedded in a rudimentary map-building scheme and an efficient path-planning concept working with incomplete environment information. The performance of the system is demonstrated by application to randomly generated environments.