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This paper presents a novel approach to kino-dynamic trajectory generation for non-circular omnidirectional platforms that can be combined with existing path planners. We use quintic Bézier splines to specify position and orientation of the holonomic robot for every point in time. To fully exploit the capabilities of the holonomic robot we propose a novel path representation. It allows for continuous variation of path shapes in the spectrum between straight-line paths with turns on the spot and smooth paths with independent rotations and translations. Using this representation our method optimizes trajectories according to a user-defined cost function, considering the constraints of the platform. This way, it generates fast and efficient trajectories in an anytime fashion. The experiments carried out on an industrial robot show that our approach generates highly efficient and smooth motion trajectories that can be tracked with high precision and predictability. Furthermore, the system operates in real-world environments containing unmapped obstacles and narrow passages.