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.

翻译：将规划作为推理问题的运动目标，被表述为因子图上耦合随机变量的联合分布。利用优化-推理对偶性，可通过最小二乘优化快速求解因子图的最大后验估计。该方法的计算效率可用于竞技性自动驾驶赛车中寻找最小曲率赛车线。赛车线规划被归类为全局规划问题，需要计算赛车的最小曲率路径，该路径能为给定赛道提供最高弯道速度，从而缩短单圈时间。本文提出了一种新方法，将最小曲率赛车线规划问题表述为因子图上的概率推理。通过利用最小曲率规划问题固有的切向几何特性与结构性质，我们将其表征在因子图上，随后通过稀疏最小二乘优化求解。与基于二次规划的对比方法的分析结果表明，所提方法展现了优越的计算性能：在实现相近单圈时间缩减的同时，计算效率提升了四倍。