高效迭代近端变分推断运动规划
Efficient Iterative Proximal Variational Inference Motion Planning
AI总结：
本文提出P-GVIMP方法，通过并行计算和变分推断解决非线性随机系统的运动规划问题，实现高效规划与不确定性下的成功解决方案。
摘要：
我们将不确定性下的运动规划视为一个随机最优控制问题，其中最优后验分布具有显式形式。为近似此后验，本文在高斯分布空间中框架了一个优化问题，通过在路径分布空间中求解变分推断（VI）来实现。对于线性-高斯随机动力学，提出了一种近端算法，通过迭代求解最优高斯提案。计算瓶颈是评估提案相对于路径的梯度，针对此问题，利用稀疏规划因子图和高斯信念传播（GBP），允许在图形处理单元（GPU）上并行计算这些梯度。我们称这种新的范式为\textit{并行高斯变分推断运动规划（P-GVIMP）}。基于线性高斯系统的高效算法，我们进一步提出基于统计线性回归（SLR）技术的迭代范式，用于解决非线性随机系统的规划问题，其中P-GVIMP在每次迭代中作为线性化时变系统的子程序。所提出的框架在各种机器人系统上得到验证，证明了通过利用并行计算实现的显著速度提升，以及在不确定性下为非线性系统成功规划解决方案。一个开源实现已发布在\href{https://github.com/hzyu17/VIMP}{https://github.com/hzyu17/VIMP}。
英文摘要：
We cast motion planning under uncertainty as a stochastic optimal control problem, where the optimal posterior distribution has an explicit form. To approximate this posterior, this work frames an optimization problem in the space of Gaussian distributions by solving a Variational Inference (VI) in the path distribution space. For linear-Gaussian stochastic dynamics, a proximal algorithm is proposed to solve for an optimal Gaussian proposal iteratively. The computational bottleneck is evaluating the gradients with respect to the proposal over a dense trajectory. To tackle this issue, the sparse planning factor graph and Gaussian Belief Propagation (GBP) are exploited, allowing for parallel computation of these gradients on Graphics Processing Units (GPUs). We term the novel paradigm the \textit{Parallel Gaussian Variational Inference Motion Planning (P-GVIMP)}. Building on the efficient algorithm for linear Gaussian systems, we then propose an iterative paradigm based on Statistical Linear Regression (SLR) techniques to solve planning problems for nonlinear stochastic systems, where the P-GVIMP serves as a sub-routine for the linearized time-varying system at each iteration. The proposed framework is validated on various robotic systems, demonstrating significant speed acceleration achieved by leveraging parallel computation and successful planning solutions for nonlinear systems under uncertainty. An open-sourced implementation is presented at \href{https://github.com/hzyu17/VIMP}{https://github.com/hzyu17/VIMP}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
