確率的軌道最適化における多様性のためのパスシグネチャ
Path Signatures for Diversity in Probabilistic Trajectory Optimisation
ラフパス理論のパスシグネチャとヒルベルト空間表現を活用し、並列軌道最適化で解の多様性を促進してモード崩壊を防ぐ手法を提案。2Dナビゲーションからロボットマニピュレータまで平均コストを低減。
著者: Lucas Barcelos, Tin Lai, Rafael Oliveira, Paulo Borges, Fabio Ramos
分類: cs.RO, cs.AI, cs.LG
原文アブストラクト
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.
