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Distributed Pose-graph Optimization with Multi-level Partitioning for Collaborative SLAM (2401.01657v3)

Published 3 Jan 2024 in cs.RO and cs.MA

Abstract: The back-end module of Distributed Collaborative Simultaneous Localization and Mapping (DCSLAM) requires solving a nonlinear Pose Graph Optimization (PGO) under a distributed setting, also known as SE(d)-synchronization. Most existing distributed graph optimization algorithms employ a simple sequential partitioning scheme, which may result in unbalanced subgraph dimensions due to the different geographic locations of each robot, and hence imposes extra communication load. Moreover, the performance of current Riemannian optimization algorithms can be further accelerated. In this letter, we propose a novel distributed pose graph optimization algorithm combining multi-level partitioning with an accelerated Riemannian optimization method. Firstly, we employ the multi-level graph partitioning algorithm to preprocess the naive pose graph to formulate a balanced optimization problem. In addition, inspired by the accelerated coordinate descent method, we devise an Improved Riemannian Block Coordinate Descent (IRBCD) algorithm and the critical point obtained is globally optimal. Finally, we evaluate the effects of four common graph partitioning approaches on the correlation of the inter-subgraphs, and discover that the Highest scheme has the best partitioning performance. Also, we implement simulations to quantitatively demonstrate that our proposed algorithm outperforms the state-of-the-art distributed pose graph optimization protocols.

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Summary

  • The paper presents a new distributed pose graph optimization algorithm that uses multi-level partitioning to balance computation and reduce inter-robot communication.
  • It reformulates the non-convex problem into a Low-Rank Convex Relaxation and solves it via an Improved Riemannian Block Coordinate Descent method without relying on Lipschitz constants.
  • Simulations confirm that the Highest partitioning scheme enhances convergence speed and scalability, achieving globally optimal solutions in collaborative SLAM.

Introduction to Distributed Pose Graph Optimization

In multi-robot systems applied to diverse domains such as search and rescue, and environmental mapping, collaborative localization and mapping are essential. These systems employ a technology known as Collaborative Simultaneous Localization and Mapping (CSLAM), which enhances autonomy and intelligence. Distributed CSLAM Systems (DCSLAM) rely on local resources without central coordination and face the challenge of Distributed Pose Graph Optimization (DPGO), a computational model requiring optimization in a specific mathematical space, the special Euclidean group. However, distributed Riemannian optimization methods currently in use can be further improved in terms of balancing computation and communication efficiency.

Novel Contributions

To address these challenges, a novel DPGO algorithm is put forth, incorporating multi-level graph partitioning with an acceleration method. By preprocessing the pose graph, a balanced multi-level partitioning is produced, which allows each robot to hold a balanced pose subgraph and reduces communication overhead. The method reformulates the non-convex DPGO problem as a Low-Rank Convex Relaxation (LRCR) and employs an Improved Riemannian Block Coordinate Descent (IRBCD) algorithm to solve it, without relying on the Lipschitz constant of the objective function. An extensive comparison of partitioning performance was conducted, manifesting that the Highest scheme yields the best partitioning. Simulations also showed this novel algorithm outperforming current distributed PGO methods. Importantly, the algorithm’s convergence to a first-order critical point is proven to be globally optimal.

Graph Partitioning and Performance Analysis

Examining different graph partitioning methods on standard and complex datasets demonstrated the superiority of the Highest scheme. The ultimate synthesis of this graph partitioning approach with the IRBCD algorithm was then evaluated in depth. Results indicated a significant reduction in communication volume between robots compared to benchmark techniques and faster convergence to high-quality solutions even as the number of robots scaled.

Concluding Remarks

The proposed algorithm uniquely solves DPGO by leveraging multi-robot collaboration, achieving balance in optimization subproblems and hastening convergence. The communication volume is notably lowered, and the algorithm is proven to yield globally optimal solutions. The versatility of this approach holds promise for future applications in real-world multi-robot tasks and other optimization problems on manifolds. The authors express intentions to validate this method in practical scenarios and possibly extend it to distributed on-manifold model predictive control.

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