DD-GBP: Anytime Multi-Arm Planning and Continuous Execution via Distributed Dynamic Gaussian Belief Propagation
Safely executing long-horizon multi-arm tasks online in complex dynamic environments remains challenging. We propose a new distributed dynamic Gaussian belief propagation (DD-GBP) method that directly plans joint-space trajectories through parallel local inference. A unified Gaussian-process (GP) parameterization connects adaptive planning horizons, interpolation-time factors, and continuous execution. Each robot maintains a local tree-structured factor graph and exchanges messages asynchronously over active inter-arm links. Dynamic subnet reconstruction and event-triggered updates reduce communication and inference costs while responding to moving obstacles. We also provide theoretical analyses of local inference accuracy, anytime early stopping, triggered-replanning consistency, and GP-consistent execution. In 50 long-horizon, multi-target four-arm scenes with moving obstacles, DD-GBP achieves $92.5\%$ collision-free all-target completion and the highest success rate among six representative baselines. Scenario ablations demonstrate long-horizon safety and robustness to communication impairment and extreme conditions; success remains $86.0\%$ under $90\%$ packet loss. Execution results further show substantially suppressed extreme velocity and acceleration peaks relative to Syn-GBP. On one workstation, obstacle-free tests with 30 coexisting arms retain $99.87\%$ success and a $15.80$ ms mean warm solve, exceeding 60 Hz and outperforming the compared methods in scalability. Dual-arm transport experiments under dynamic interference demonstrate online response and practical deployability. To the best of our knowledge, these results establish a new state of the art for online long-horizon multi-arm planning in dynamic scenes.