Asynchronous Distributed Multi-Robot Motion Planning Under Imperfect Communication

TL;DR

This work tackles multi-robot motion planning under imperfect communication by introducing Delay-Aware ADMM (DA-ADMM), which tunes penalty parameters based on real-time delay statistics to down-weight stale information in consensus updates. DA-ADMM replaces fixed or residual-based tuning with delay-aware scaling of penalties $\rho$ and $\mu$ and a delay-weighted global update, enabling more robust convergence in both trajectory optimization and MPC across 2D and 3D scenarios (double integrator, Dubins car, and drones). Across extensive simulations, DA-ADMM consistently improves robustness, success rate, and solution quality compared to LB, RB, FP, and FC baselines, especially under varying delay patterns and maximum delays $d_{max}$. The method demonstrates that leveraging stale information with principled weighting can maintain feasibility and performance, suggesting practical resilience for real-world, communication-constrained multi-robot systems. Future directions include integrating reinforcement learning to learn optimal penalty policies from simulation data.

Abstract

This paper addresses the challenge of coordinating multi-robot systems under realistic communication delays using distributed optimization. We focus on consensus ADMM as a scalable framework for generating collision-free, dynamically feasible motion plans in both trajectory optimization and receding-horizon control settings. In practice, however, these algorithms are sensitive to penalty tuning or adaptation schemes (e.g. residual balancing and adaptive parameter heuristics) that do not explicitly consider delays. To address this, we introduce a Delay-Aware ADMM (DA-ADMM) variant that adapts penalty parameters based on real-time delay statistics, allowing agents to down-weight stale information and prioritize recent updates during consensus and dual updates. Through extensive simulations in 2D and 3D environments with double-integrator, Dubins-car, and drone dynamics, we show that DA-ADMM significantly improves robustness, success rate, and solution quality compared to fixed-parameter, residual-balancing, and fixed-constraint baselines. Our results highlight that performance degradation is not solely determined by delay length or frequency, but by the optimizer's ability to contextually reason over delayed information. The proposed DA-ADMM achieves consistently better coordination performance across a wide range of delay conditions, offering a principled and efficient mechanism for resilient multi-robot motion planning under imperfect communication.

Figures (5)

• Figure 1: Comparison between different baselines for the 2D Double Integrator Multi-Agent Trajectory Optimization Experiment. Note that the proposed asynchronous DA-ADMM with delayed communication (b) converges to a similar solution compared to the synchronous ADMM baseline with perfect communication (a). Other fixed parameter ADMM baselines fail to converge under delayed communication (c and d).
• Figure 2: Effect of different delay patterns on distributed optimization baselines. Top and bottom rows correspond to maximum consecutive delay steps of 1 and 2. Each group of box plots represents the comparison between different ADMM variations for a given communication delay probability. The columns correspond to success rate (higher is better), total solution cost (lower is better), final consensus residual (lower is better), and final dual residual (lower is better). The asterisks ($*$) represent statistical significance between the adaptive approach and other baselines with a $p < 0.05$. Note that the DA-ADMM (red) approach provides higher success rate and significantly better solution quality compared to other baselines across a wide range of delay patterns. This improvement is largely due to significantly lower final primal and dual residuals.
• Figure 3: Visual demonstration of the circle formation MPC experiment in PyBullet. Note that DA-ADMM (a) achieves significantly better solution quality relative to FP-ADMM (b) and FC-Opt (c). FP-ADMM suffers from solution drift under delay as shown in the green, blue, and purple agent trajectories in (b).
• Figure 4: DA-ADMM results for the warehouse environment with continuous task assignment.
• Figure 5: Qualitative results for the 3D drone experiment. DA-ADMM is the only baseline that can complete the task with similar performance to the synchronized ADMM with perfect communication. Green denotes successful task completion, and red represents failure within max allowable time.