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We propose a novel single-shot motion-planning algorithm based on adaptive random walks. The proposed algorithm turns out to be simple to implement, and the solution it produces can be easily and efficiently optimized. Furthermore, the algorithm can incorporate adaptive components, so the developer is not required to specify all the parameters of the random distributions involved, and the algorithm itself can adapt to the environment it is moving in. Proofs of the theoretical soundness of the algorithm are provided, as well as implementation details. Numerical comparisons with well-known algorithms illustrate its effectiveness.