Sampling-based motion planners (SBMPs) are widely used for robot motion planning with complex kinodynamic constraints in high-dimensional spaces, yet they struggle to achieve \emph{real-time} performance due to their serial computation design. Recent efforts to parallelize SBMPs have achieved significant speedups in finding feasible solutions; however, they provide no guarantees of optimizing an objective function. We introduce Kino-PAX$^{+}$, a massively parallel kinodynamic SBMP with asymptotic near-optimal guarantees. Kino-PAX$^{+}$ builds a sparse tree of dynamically feasible trajectories by decomposing traditionally serial operations into three massively parallel subroutines. The algorithm focuses computation on the most promising nodes within local neighborhoods for propagation and refinement, enabling rapid improvement of solution cost. We prove that, while maintaining probabilistic $δ$-robust completeness, this focus on promising nodes ensures asymptotic $δ$-robust near-optimality. Our results show that Kino-PAX$^{+}$ finds solutions up to three orders of magnitude faster than existing serial methods and achieves lower solution costs than a state-of-the-art GPU-based planner.

翻译：采样运动规划器被广泛应用于高维空间中具有复杂运动学约束的机器人运动规划，但由于其串行计算设计，难以实现实时性能。近期并行化SBMPs的研究在寻找可行解方面取得了显著加速，但未能提供优化目标函数的保证。我们提出了Kino-PAX⁺，一种具有渐近近乎最优保证的大规模并行运动学SBMP。Kino-PAX⁺通过将传统串行操作分解为三个大规模并行子程序，构建了一个稀疏的动态可行轨迹树。该算法将计算集中在局部邻域内最有希望的节点上进行传播和细化，从而实现解成本的快速改进。我们证明，在保持概率δ-鲁棒完备性的同时，这种对有希望节点的聚焦确保了渐近δ-鲁棒近乎最优性。我们的结果表明，Kino-PAX⁺寻找解的速度比现有串行方法快三个数量级，并且实现了比最先进的基于GPU的规划器更低的解成本。