Global Optimality of Pose Graph Optimization

Shuan Ding; Ruishuang Chen; Mengfan Cao; Zaiyue Yang

cs.ROOct 10, 2026

Global Optimality of Pose Graph Optimization

Authors: Shuan Ding, Ruishuang Chen, Mengfan Cao, Zaiyue Yang

Organizations: Guangdong Provincial Key Laboratory of FullyActuated System Control Theory and Technology, and the School of Automation and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen 518055, China · Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

Abstract

Pose Graph Optimization (PGO) is a classical and widely applied problem in state estimation for robotics, playing a fundamental role in localization, mapping, and navigation. Yet, it is nonconvex in nature and may have many local minimizers, thus difficult to analyze. In this paper, we investigate the optimization landscape and establish a sufficient condition of global optimality for PGO. The ultimate goal of this paper is to theoretically confirm that the optimization landscape is benign and attractive around the global minimizer, if noise is smaller than an explicit and a priori bound. To reveal such an insight, this paper develops three main technical results. First, we identify a proper basin of attraction (BOA) containing global minimizer, and characterize its geometric property by showing that its radius is controlled by noise in an explicit way. Then, by exploring the first order optimality conditions of PGO, we prove that a local minimizer is globally optimal if a noise-controlled criterion is satisfied. Finally, by combining above two results, we prove that one and only one local minimizer exists in the BOA and this minimizer is globally optimal, when the noise is smaller than an explicit bound that can be verified a priori. Numerical simulations validate the proposed theory under various random cases, showing that the obtained conditions provide an effective criterion for certifying the global optimality of PGO.

Figures & tables

Fig. 1: Illustration of PGO.

Parameter	Description	Value
$\gamma^{\star}$	Spectral gap	$2.229$
$d$	Orbit radius ( $2$ -norm)	$0.065$
Eq. ( 20 )	Bound of $d$	$0.615$
$d_{\infty}$	Orbit radius ( $\infty$ -norm)	$0.048$
Eq. ( 31 )	Bound of $d_{\infty}$	$0.482$
$\eta_{\infty}(\left\\|\Delta\mathcal{Q}\mathbf{r}^{\star}\right\\|_{\infty})$	Bound of noise acting on truth	$0.229$

TABLE I: Parameters and simulation results for 4 robot nodes

Fig. 2: PGO for 4 robot nodes.

Fig. 3: Evaluation of the proposed bound under varying noise intensities.

Fig. 4: Margins of Theorem 4 and Theorem 5 .

Fig. 5: Success rate of optimality condition in Theorem 4 .

Fig. 6: Success rate of optimality condition in Theorem 5 .

Fig. 7: Distribution of optimality condition satisfaction in Theorem 4 .

Fig. 8: Distribution of optimality condition satisfaction in Theorem 5 .

Pose Graph Optimization

Pose graph optimization estimates globally consistent positions and orientations by reconciling relative-pose measurements in a graph.

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May 11, 2026J/K move · Enter open · S save

Distributed Pose Graph Optimization via Continuous Riemannian Dynamics

Jaeho Shin, Maani Ghaffari, Yulun Tian

University of Michigan Ann Arbor, MI 48109, USA

Riemannian Optimization Multi-Robot Systems Distributed Optimization Pose Graph Optimization

Open paper AskPDF arXiv

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--Poincaré 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.

Abstract

Pose Graph Optimization

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