arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节(Veterans Day),12 日无更新
arXiv 2308.04071cs.ROcs.AIcs.LG
收藏

概率轨迹优化中用于多样性的路径签名

Path Signatures for Diversity in Probabilistic Trajectory Optimisation

The University of Sydney(悉尼大学);CSIRO(联邦科学与工业研究组织);NVIDIA(英伟达)

Lucas Barcelos, Tin Lai, Rafael Oliveira, Paulo Borges, Fabio Ramos

AI总结:

本文提出基于路径签名和希尔伯特空间表示的并行轨迹优化算法,通过促进解多样性避免模式坍缩,在导航和机械臂任务中取得更低平均代价。

摘要:

运动规划可以被表述为一个轨迹优化问题,其中代价作为所生成轨迹的函数被最小化。在具有多个障碍物和复杂几何形状的复杂环境中,该优化问题通常难以求解,并且容易陷入局部极小值。然而,计算硬件的最新进展允许并行轨迹优化,其中同时获得多个解,每个解从不同的起点初始化。不幸的是,如果没有一种策略来防止两个解相互坍缩,朴素的并行优化可能会遭受模式坍缩,从而降低该方法的效率以及找到全局解的可能性。在本文中,我们利用粗糙路径理论的最新进展,设计了一种并行轨迹优化算法,该算法在解的范围内促进多样性,从而避免模式坍缩并获得更好的全局性质。我们的方法建立在路径签名和轨迹的希尔伯特空间表示之上,并将用于轨迹估计的并行变分推断与促进多样性的核连接起来。我们通过实验证明,在从二维导航到在杂乱环境中操作的机器人机械臂等一系列问题上,该策略比竞争性替代方案实现了更低的平均代价。

英文摘要:

Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem is usually difficult to solve and prone to local minima. However, recent advancements in computing hardware allow for parallel trajectory optimisation where multiple solutions are obtained simultaneously, each initialised from a different starting point. Unfortunately, without a strategy preventing two solutions to collapse on each other, naive parallel optimisation can suffer from mode collapse diminishing the efficiency of the approach and the likelihood of finding a global solution. In this paper we leverage on recent advances in the theory of rough paths to devise an algorithm for parallel trajectory optimisation that promotes diversity over the range of solutions, therefore avoiding mode collapses and achieving better global properties. Our approach builds on path signatures and Hilbert space representations of trajectories, and connects parallel variational inference for trajectory estimation with diversity promoting kernels. We empirically demonstrate that this strategy achieves lower average costs than competing alternatives on a range of problems, from 2D navigation to robotic manipulators operating in cluttered environments.

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。

↑