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This paper describes an algorithm to calculate near-optimal minimum time trajectories for omnidirectional vehicles, which can be used as part of a high-level path planner. The basis is an optimal control algorithm with relaxations to reduce the required computational effort. It takes limited friction and vehicle dynamics into account, as encountered in high-performance omnidirectional vehicles. The algorithm is written with modest computational resources in mind, so that it is possible to control an omnidirectional vehicle in real time in a fast paced environment.