多様体上の軌道最適化：理論保証付き埋め込み逐次凸計画法
Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach
幾何学的埋め込みを用いて多様体制約付き軌道最適化問題をユークリッド空間上の等価問題に変換し、既存の逐次凸計画法を多様体設定へ拡張した理論保証付き手法を提案した。
著者: Riccardo Bonalli, Andrew Bylard, Abhishek Cauligi, Thomas Lew, Marco Pavone
分類: math.OC, cs.RO
原文アブストラクト
Sequential Convex Programming (SCP) has recently gained popularity as a tool for trajectory optimization due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are restricted to Euclidean settings, which precludes their application to problem instances where one must reason about manifold-type constraints (that is, constraints, such as loop closure, which restrict the motion of a system to a subset of the ambient space). The aim of this paper is to fill this gap by extending SCP-based trajectory optimization methods to a manifold setting. The key insight is to leverage geometric embeddings to lift a manifold-constrained trajectory optimization problem into an equivalent problem defined over a space enjoying a Euclidean structure. This insight allows one to extend existing SCP methods to a manifold setting in a fairly natural way. In particular, we present a SCP algorithm for manifold problems with refined theoretical guarantees that resemble those derived for the Euclidean setting, and demonstrate its practical performance via numerical experiments.
