Dense reconstruction and differentiable rendering are fundamental tightly connected operations in 3D vision and computer graphics. Recent neural implicit representations demonstrate compelling advantages in reconstruction fidelity and differentiability over conventional discrete representations such as meshes, point clouds, and voxels. However, many neural implicit models, such as neural radiance fields (NeRF) and signed distance function (SDF) networks, are inefficient in rendering due to the need to perform multiple queries along each camera ray. Moreover, NeRF and Gaussian Splatting methods offer impressive photometric reconstruction but often require careful supervision to achieve accurate geometric reconstruction. To address these challenges, we propose a novel representation called signed directional distance function (SDDF). Unlike SDF and similar to NeRF, SDDF has a position and viewing direction as input. Like SDF and unlike NeRF, SDDF directly provides distance to the observed surface rather than integrating along the view ray. As a result, SDDF achieves accurate geometric reconstruction and efficient differentiable directional distance prediction. To learn and predict scene-level SDDF efficiently, we develop a differentiable hybrid representation that combines explicit ellipsoid priors and implicit neural residuals. This allows the model to handle distance discontinuities around obstacle boundaries effectively while preserving the ability for dense high-fidelity distance prediction. Through extensive evaluation against state-of-the-art representations, we show that SDDF achieves (i) competitive SDDF prediction accuracy, (ii) faster prediction speed than SDF and NeRF, and (iii) superior geometric consistency compared to NeRF and Gaussian Splatting.

We propose fast and communication-efficient optimization algorithms for multirobot rotation averaging and translation estimation problems that arise from collaborative simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and camera network localization applications. Our methods are based on theoretical relations between theHessiansof the underlying Riemannian optimization problems and theLaplaciansof suitably weighted graphs. We leverage these results to design a collaborative solver in which robots coordinate with a central server to perform approximate second-order optimization, by solving aLaplacian systemat each iteration. Crucially, our algorithms permit robots to employspectral sparsificationto sparsify intermediate dense matrices before communication, and hence provide a mechanism to tradeoff accuracy with communication efficiency with provable guarantees. We perform rigorous theoretical analysis of our methods and prove that they enjoy (local)linearrate of convergence. Furthermore, we show that our methods can be combined with graduated nonconvexity to achieveoutlier-robustestimation. Extensive experiments on real-world SLAM and SfM scenarios demonstrate the superior convergence rate and communication efficiency of our methods.

This paper revisits Kimera-Multi, a distributed multi-robot Simultaneous Localization and Mapping (SLAM) system, towards the goal of deployment in the real world. In particular, this paper has three main contributions. First, we describe improvements to Kimera-Multi to make it resilient to large-scale real-world deployments, with particular emphasis on handling intermittent and unreliable communication. Second, we collect and release challenging multi-robot benchmarking datasets obtained during live experiments conducted on the MIT campus, with accurate reference trajectories and maps for evaluation. The datasets include up to 8 robots traversing long distances (up to 8 km) and feature many challenging elements such as severe visual ambiguities (e.g., in underground tunnels and hallways), mixed indoor and outdoor trajectories with different lighting conditions, and dynamic entities (e.g., pedestrians and cars). Lastly, we evaluate the resilience of Kimera-Multi under different communication scenarios, and provide a quantitative comparison with a centralized baseline system. Based on the results from both live experiments and subsequent analysis, we discuss the strengths and weaknesses of Kimera-Multi, and suggest future directions for both algorithm and system design. We release the source code of Kimera-Multi and all datasets to facilitate further research towards the reliable real-world deployment of multi-robot SLAM systems.

We present the first distributed optimization al-gorithm with lazy communication for collaborative geometric estimation, the backbone of modern collaborative simultaneous localization and mapping (SLAM) and structure-from-motion (SfM) applications. Our method allows agents to cooperatively reconstruct a shared geometric model on a central server by fusing individual observations, but without the need to transmit potentially sensitive information about the agents themselves (such as their locations). Furthermore, to alleviate the burden of communication during iterative optimization, we design a set of communication triggering conditions that enable agents to selectively upload a targeted subset of local information that is useful to global optimization. Our approach thus achieves significant communication reduction with minimal impact on optimization performance. As our main theoretical contribution, we prove that our method converges to first-order critical points with a global sublinear convergence rate. Numerical evaluations on bundle adjustment problems from collaborative SLAM and SfM datasets show that our method performs competitively against existing distributed techniques, while achieving up to 78% total communication reduction.

Multi-robot simultaneous localization and mapping (SLAM) is a crucial capability to obtain timely situational awareness over large areas. Real-world applications demand multi-robot SLAM systems to be robust to perceptual aliasing and to operate under limited communication bandwidth; moreover, it is desirable for these systems to capture semantic information to enable high-level decision-making and spatial artificial intelligence. This article presents$ \mathsf{{Kimera-Multi}} $, a multi-robot system that: 1) is robust and capable of identifying and rejecting incorrect inter- and intrarobot loop closures resulting from perceptual aliasing; 2) is fully distributed and only relies on local (peer-to-peer) communication to achieve distributed localization and mapping; and 3) builds a globally consistent metric-semantic 3-D mesh model of the environment in real time, where faces of the mesh are annotated with semantic labels.$ \mathsf{{Kimera-Multi}} $is implemented by a team of robots equipped with visual-inertial sensors. Each robot builds a local trajectory estimate and a local mesh using$ \mathsf{{Kimera}} $. When communication is available, robots initiate a distributed place recognition and robust pose graph optimization protocol based on a distributed graduated nonconvexity algorithm. The proposed protocol allows the robots to improve their local trajectory estimates by leveraging inter-robot loop closures while being robust to outliers. Finally, each robot uses its improved trajectory estimate to correct the local mesh using mesh deformation techniques. We demonstrate$ \mathsf{{Kimera-Multi}} $in photo-realistic simulations, SLAM benchmarking datasets, and challenging outdoor datasets collected using ground robots. Both real and simulated experiments involve long trajectories (e.g., up to 800 m per robot). The experiments show that$ \mathsf{{Kimera-Multi}} $: 1) outperforms the state of the art in terms of robustness and accuracy; 2) achieves estimation errors comparable to a centralized SLAM system while being fully distributed; 3) is parsimonious in terms of communication bandwidth; 4) produces accurate metric-semantic 3-D meshes; and 5) is modular and can also be used for standard 3-D reconstruction (i.e., without semantic labels) or for trajectory estimation (i.e., without reconstructing a 3-D mesh).

We present the first fully distributed multi-robot system for dense metric-semantic Simultaneous Localization and Mapping (SLAM). Our system, dubbed Kimera-Multi, is implemented by a team of robots equipped with visual-inertial sensors, and builds a 3D mesh model of the environment in real-time, where each face of the mesh is annotated with a semantic label (e.g., building, road, objects). In Kimera-Multi, each robot builds a local trajectory estimate and a local mesh using Kimera. Then, when two robots are within communication range, they initiate a distributed place recognition and robust pose graph optimization protocol with a novel incremental maximum clique outlier rejection; the protocol allows the robots to improve their local trajectory estimates by leveraging inter-robot loop closures. Finally, each robot uses its improved trajectory estimate to correct the local mesh using mesh deformation techniques. We demonstrate Kimera-Multi in photo-realistic simulations and real data. Kimera-Multi (i) is able to build accurate 3D metric-semantic meshes, (ii) is robust to incorrect loop closures while requiring less computation than state-of-the-art distributed SLAM back-ends, and (iii) is efficient, both in terms of computation at each robot as well as communication bandwidth.

This article presents the firstcertifiably correctalgorithm fordistributedpose-graph optimization (PGO), the backbone of modern collaborative simultaneous localization and mapping (CSLAM) and camera network localization (CNL) systems. Our method is based upon a sparse semidefinite relaxation that we prove provides globally optimal PGO solutions under moderate measurement noise (matching the guarantees enjoyed by the state-of-the-art centralized methods), but is amenable to distributed optimization using the low-rank Riemannian Staircase framework. To implement the Riemannian Staircase in the distributed setting, we developRiemannian block coordinate descent(RBCD), a novel method for (locally) minimizing a function over a product of Riemannian manifolds. We also propose the first distributed solution verification and saddle escape methods to certify the global optimality of critical points recovered via RBCD, and to descend from suboptimal critical points (if necessary). All components of our approach are inherently decentralized: they require only local communication, provide privacy protection, and are easily parallelizable. Extensive evaluations on synthetic and real-world datasets demonstrate that the proposed method correctly recovers globally optimal solutions under moderate noise, and outperforms alternative distributed techniques in terms of solution precision and convergence speed.

Many robotics applications require alignment and fusion of observations obtained at multiple views to form a global model of the environment. Multiway data association methods provide a mechanism to improve alignment accuracy of pairwise associations and ensure their consistency. However, existing methods that solve this computationally challenging problem are often too slow for real-time applications. Furthermore, some of the existing techniques can violate the cycle consistency principle, thus drastically reducing the fusion accuracy. This article presents the consistent lifting, embedding, and alignment rectification (CLEAR) algorithm to address these issues. By leveraging insights from the multiway matching and spectral graph clustering literature, CLEAR provides cycle-consistent and accurate solutions in a computationally efficient manner. Numerical experiments on both synthetic and real datasets are carried out to demonstrate the scalability and superior performance of our algorithm in real-world problems. This algorithmic framework can provide significant improvement in the accuracy and efficiency of existing discrete assignment problems, which traditionally use pairwise (but potentially inconsistent) correspondences. An implementation of CLEAR is made publicly available online.