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State-of-the-art autonomous cars use various algorithms for path planning in different environments. The design of these algorithms is difficult when the nonlinear and the nonholonomic aspect of the vehicle dynamics are dominant. These aspects are small at high speeds and for simple maneuvers at low speeds, so effective algorithms exist. However, path planning for more complex maneuvers at low speeds, especially in tight and cluttered environments, remains a difficult challenge. This paper proposes a new approach to this problem. The presented algorithm performs a tree-search on a discretized state space using dynamic programming. It is shown in simulation and experiments that even complicated paths can be computed very efficiently. Since a path is composed of a sequence of simple arcs, it is easy to track by a linear controller.