Asynchronous Distributed Trajectory Estimation of Multi-Robot Systems

Jul 16, 2026

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Distributed trajectory estimation in robotics is commonly implemented under synchronous agent communications and computations, which limits performance under real-world delays. An asynchronous block coordinate descent algorithm is proposed for distributed trajectory estimation, where agents estimate multi-robot states over a sliding time window by solving a derived MAP formulation. The approximation induces negligible errors while removing up to 96.9% of inter-agent communications. Exponential convergence to the optimal state estimate is proven under partial asynchrony. Simulations show up to 64% lower error than a comparable state-of-the-art method, and experiments demonstrate robustness to computation/communication delays spanning three orders of magnitude.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

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Technical Report: Asynchronous Distributed Trajectory Estimation of Multi-Robot Systems Adam Pooley, Matthew Hale arXiv :2607 .0 1 106v 1 [ cs .RO] 1 Jul 2026 Abstract—Distributed trajectory estimation arises in many applications across robotics, but existing implementations typically do not consider asynchrony in agents’ communications and computations. Therefore, we propose an asynchronous block coordinate descent algorithm for distributed trajectory estimation. We consider a team of agents that observes a team of robots and estimates their states over a sliding window. The agents solve an approximation of the maximum a posteriori estimation problem, which we derive. We show this approximation introduces negligible errors and eliminates up to 96.9% of communications among agents. Next, we prove that agents’iterates converge exponentially fast to the optimal estimate of the robots’ states. Simulations show that this approach has up to 64% less error than a comparable state-of-the-art algorithm. Experiments on mobile robots show the robustness of this approach to delays whose lengths span three orders of magnitude. I. INTRODUCTION State estimation is a fundamental problem in autonomy, with applications ranging from mobile robotics and transportation to co-robots working alongside humans [1]–[3] . State estimates can be computed with data from multiple sensors, and decentralized sensing offers several benefits, including robustness to individual sensor failures and the ability to use different sensing modalities. When sensors are embedded in systems that can compute and communicate, distributed state estimation (DSE) allows for collaborative estimation of the state of a system. In this paper, we refer to the computing entities as “agents” and the observed robots as the “targets”, because estimation may be done by external processors rather than the robots themselves. Existing works in the DSE literature [2], [4]–[9] often assume that agents compute and communicate synchronously. However, real-world systems often face computation and communication delays, e.g., due to physical barriers [10], adversarial jamming [11], and saturated bandwidth [12] . Computation speeds can vary between agents due to heterogeneous hardware among them [13], [14] . Attempts to synchronize agents’ operations can induce the “straggler effect” [15], which causes agents to only compute and communicate at the rate of the slowest among them. In such scenarios, synchronizing agents can significantly slow the convergence of multi-agent systems [16] . Therefore, in this paper we propose a decentralized state estimation algorithm that is designed to operate with asynchronous computations and communications. We assume only that delays in agents’ computations and communications are bounded (though the bound can be arbitrary), which is called “partial asynchrony” [17] . We consider state estimation for multi-robot systems, and agents solve a maximum a posteriori (MAP) optimization problem whose solution is the optimal state estimate of the target system. Our problem formulation estimates states over a sliding window of time, which enables new measurements of the target system’s outputs to be used to improve estimates of past states. Our algorithm uses block coordinate descent (BCD) to jointly compute state estimates. Each agent stores estimated values of all states of the target system onboard, but each agent computes estimates for only a subset of these states. Agents communicate with each other to share updated values of state estimates over time. We emphasize that we do not simply apply BCD to a state estimation problem. Instead, we show in a precise way how using BCD to solve the MAP problem requires certain pairs of agents to communicate. Then, we derive an approximation of the MAP problem that substantially reduces required communications while inducing only negligible errors. A. Summary of Contributions The contributions of this work are

FAQs

What problem does the technical report address in distributed multi-robot estimation?

It targets distributed trajectory/state estimation when agents’ communications and computations are not synchronous, as is often the case under realistic delays.

How does the proposed method estimate robot states?

Agents estimate states over a sliding time window by solving an approximation of a maximum a posteriori (MAP) optimization problem using an asynchronous block coordinate descent approach.

What are the main performance and convergence results?

The approximation significantly reduces communications (up to 96.9% fewer) with negligible error, and the algorithm’s iterates are proven to converge exponentially fast to the optimal estimate under partial asynchrony.

Jul 16, 2026

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