連続リーマン力学による分散ポーズグラフ最適化
Distributed Pose Graph Optimization via Continuous Riemannian Dynamics
ポーズグラフ最適化をリー群上の連続時間力学系として定式化し、分散・並列に解く新しい最適化アルゴリズムを提案した。
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著者: Jaeho Shin, Maani Ghaffari, Yulun Tian
分類: cs.RO
原文アブストラクト
We present a framework for distributed Pose Graph Optimization (PGO) by formulating the problem as a second-order continuous-time dynamical system evolving on Lie groups. By modeling pose variables as massive particles subject to damping, the equilibrium points of the resulting Riemannian dynamics coincide with first-order critical points of the original PGO problem. Using the governing damped Euler--Poincar\'e equations and a semi-implicit geometric integrator, we design an optimization algorithm that generalizes existing algorithms such as Riemannian gradient descent and Gauss--Newton. In multi-robot settings, we present a fully distributed and parallel method based on block-diagonal mass and damping matrices, where each robot solves an ordinary differential equation for its own poses with minimal communication overhead. Moreover, modeling both state and velocity enables principled neighbor prediction that significantly improves convergence under delayed communication. Theoretically, we present an analysis and establish sufficient condition that ensures energy dissipation under the employed geometric discretization scheme. Experiments on benchmark PGO datasets demonstrate that the proposed solver achieves superior performance compared to state-of-the-art distributed baselines in both synchronous and asynchronous regimes.
