This work addresses motion planning under uncertainty as a stochastic optimal control problem. The path distribution induced by the optimal controller corresponds to a posterior path distribution with a known form. To approximate this posterior, we frame an optimization problem in the space of Gaussian distributions, which aligns with the Gaussian Variational Inference Motion Planning (GVIMP) paradigm introduced in \cite{yu2023gaussian}. In this framework, the computation bottleneck lies in evaluating the expectation of collision costs over a dense discretized trajectory and computing the marginal covariances. This work exploits the sparse motion planning factor graph, which allows for parallel computing collision costs and Gaussian Belief Propagation (GBP) marginal covariance computation, to introduce a computationally efficient approach to solving GVIMP. We term the novel paradigm as the Parallel Gaussian Variational Inference Motion Planning (P-GVIMP). We validate the proposed framework on various robotic systems, demonstrating significant speed acceleration achieved by leveraging Graphics Processing Units (GPUs) for parallel computation. An open-sourced implementation is presented at https://github.com/hzyu17/VIMP.

翻译：本研究将不确定性条件下的运动规划问题建模为随机最优控制问题。最优控制器导出的路径分布对应于具有已知形式的后验路径分布。为逼近此后验分布，我们在高斯分布空间中构建优化问题，这与\cite{yu2023gaussian}提出的高斯变分推断运动规划（GVIMP）范式一致。该框架的计算瓶颈在于评估密集离散化轨迹上的碰撞代价期望值以及计算边缘协方差。本研究利用稀疏运动规划因子图的特性，通过并行计算碰撞代价与高斯置信传播（GBP）边缘协方差计算，提出了一种计算高效的GVIMP求解方法。我们将这一新范式命名为并行高斯变分推断运动规划（P-GVIMP）。我们在多种机器人系统上验证了所提框架的有效性，结果表明通过利用图形处理器（GPU）进行并行计算可实现显著的加速效果。开源实现发布于https://github.com/hzyu17/VIMP。