Asynchronous Distributed Smoothing and Mapping via On-Manifold Consensus ADMM

TL;DR

This paper develops a CSLAM back-end based on Consensus ADMM called MESA (Manifold, Edge-based, Separable ADMM), which exhibits superior convergence rates and accuracy compare to existing state-of-the art CSLAM back-end optimizers.

Abstract

In this paper we present a fully distributed, asynchronous, and general purpose optimization algorithm for Consensus Simultaneous Localization and Mapping (CSLAM). Multi-robot teams require that agents have timely and accurate solutions to their state as well as the states of the other robots in the team. To optimize this solution we develop a CSLAM back-end based on Consensus ADMM called MESA (Manifold, Edge-based, Separable ADMM). MESA is fully distributed to tolerate failures of individual robots, asynchronous to tolerate communication delays and outages, and general purpose to handle any CSLAM problem formulation. We demonstrate that MESA exhibits superior convergence rates and accuracy compare to existing state-of-the art CSLAM back-end optimizers.

Figures (5)

• Figure 1: Example multi-robot factor graph (gray) and its corresponding distribution between agents (blue, green, and orange) in MESA. When asynchronously communicating (arrows), the robots send only their solutions for shared variables (A, C, E). These are used to construct "Biased Priors" (purple factors) incorporated into each robot's local graph to enforce consistency across the team.
• Figure 2: Ground-truth from example synthetic datasets. Colors represent different robots.
• Figure 3: Comparison of MESA variants derived from Geodesic ($\mdblkcircle$), Split ($\mdblksquare$), Approximate-Geodesic ($\blacktriangle$) and Chordal () constraints on 20 synthetic 3D pose graph datasets. Split and Geodesic constraints significantly outperform the alternatives.
• Figure 4: Performance of Geodesic MESA ($\mdblkcircle$) and Split MESA ($\mdblksquare$) compared to Centralized ($\bigstar$) and Independent ($\mathrm{\textit{I}}$) baselines under a variety of conditions. The MESA variants consistently converge to the centralized solution indicating they are accurate and generalize across different conditions found in CSLAM problems.
• Figure 5: Accuracy vs. Communications of Geodesic MESA ($\mdblkcircle$) and Split MESA ($\mdblksquare$) compared to prior works [DGS (), ASAPP (), MB-ADMM ($\blacklozenge$), DDF-SAM2 ($\pentagonblack$)] and baselines [Centralized ($\bigstar$), Independent ($\mathrm{\textit{I}}$)] on 200 synthetic 3D pose graph datasets. Ellipses depict $3\sigma$ uncertainty bounds. Methods that require only one round of communication are shown as horizontal lines. MESA outperforms prior works both with respect to accuracy and convergence speed.

Theorems & Definitions (4)

• Remark 1: MESA Initialization
• Remark 2: MESA Theoretical Guarantees
• Remark 3: Hyper-Parameters
• Remark 4: Prior Work Implementation Details