The motion objectives of a planning as inference problem are formulated as a joint distribution over coupled random variables on a factor graph. Leveraging optimization-inference duality, a fast solution to the maximum a posteriori estimation of the factor graph can be obtained via least-squares optimization. The computational efficiency of this approach can be used in competitive autonomous racing for finding the minimum curvature raceline. Finding the raceline is classified as a global planning problem that entails the computation of a minimum curvature path for a racecar which offers highest cornering speed for a given racetrack resulting in reduced lap time. This work introduces a novel methodology for formulating the minimum curvature raceline planning problem as probabilistic inference on a factor graph. By exploiting the tangential geometry and structural properties inherent in the minimum curvature planning problem, we represent it on a factor graph, which is subsequently solved via sparse least-squares optimization. The results obtained by performing comparative analysis with the quadratic programming-based methodology, the proposed approach demonstrated the superior computing performance, as it provides comparable lap time reduction while achieving fourfold improvement in computational efficiency.

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