Abstract
This paper studies the symmetries of the extension to three points of the Dubins problem, the Three-Point Dubins Problem (3PDP), which consists of finding the shortest curvature-constrained 𝐶1 path passing through three waypoints, which are the first and last oriented. In the literature, the optimal solution is selected by enumerating 18 possible candidates: the best is elected as the global solution of the instance of the 3PDP. To reduce the need of this enumeration, we exploit the symmetries of the problem to improve the solution strategy by using a Machine Learning (ML) framework. We show how to map an arbitrary configuration into a canonical domain and significantly reduce the parameter space, without a loss of generality. Then, we use this method to construct a compact yet comprehensive dataset of over 17 million valid cases. The reduction in the input dimensionality leads to a faster and more robust learning approach; we investigate both regression and classification neural networks, where the regression model estimates the optimal intermediate angle, and the classification model predicts the path type. The classification network achieved a top-1 accuracy of 97.5% and 100% accuracy within the top-5 predictions (instead of testing all 18 cases), whereas the regression model attained a mean angular error of about 2∘. A detailed case study illustrates how the proposed method can complement existing analytic approaches by providing accurate initial guesses, thus accelerating iterative solvers. Our results demonstrate that ML-based methods can serve as efficient and reliable alternatives for solving the 3PDP, with direct implications for other motion planners in robotics and autonomous systems.