DD-GBP: Anytime Multi-Arm Planning and Continuous Execution via Distributed Dynamic Gaussian Belief Propagation
Authors: Zhao Jin, Fengyi Dai, Yuetong Yin, Yunan Wang, Wenjie Chen, Chuxiong Hu
Organizations: State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China · Beijing Key Laboratory of Transformative High-end Manufacturing Equipment and Technology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China · State Key Laboratory of High-end Heavy-load Robots, Midea Group, Foshan 528300, China
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.
Figures & tables
Fig. 1: Factor tree for f(x1,x2,x3)∝f0(x1)f1(x1,x2)f2(x2,x3) . Circles denote variable nodes and squares denote factor nodes. Messages pass in both directions along each edge.
Fig. 2: DD-GBP planning and execution, with an illustrative four-arm scene at the upper right. Each local Gaussian update uses one backward–forward sweep with fixed linearizations and received messages. Robot-wise iterations stop at a local criterion or budget. Blue dashed links exchange messages; gray dashed feedback triggers reconstruction. GP interpolation provides continuous references.
Fig. 3: Illustration of the proposed multi-arm DD-GBP factor graph network. Solid circles denote each robot’s own variable nodes, while dashed circles represent locally stored remote variable nodes from other robots; hexagons and parallelograms denote different types of factor nodes corresponding to motion and interaction constraints. Dashed arrows indicate inter-arm communication links for distributed inference. For clarity, the schematic omits the interpolated obstacle factors connecting adjacent support states.
Fig. 4: (a) Robots are encapsulated by bounding spheres, with robot-obstacle and inter-robot distances defined by the minimum separation between their boundaries. (b) Triggered robots and their local interaction neighborhoods. (c) Illustrative multi-arm simulation scenes; scalability tests omit the external obstacles shown here.
Fig. 5: Backward–forward message passing for each arm’s local tree-structured graph. The process consists of a peripheral initialization step (black arrows), followed by a backward pass from the goal to the start (blue arrows), and a forward pass from the start to the goal (green arrows), and state exchanges at the beginning and end (dashed arrows).
Fig. 6: (a) Per-arm execution peaks in Tab. I order: circles show medians, diamonds show maxima. Gray lines mark DD-GBP’s mean peaks. (b) Scaling: dashed/ solid curves show Tc / Tw , alongside Succ. (c) Scenario sensitivity: boxes show per-scene Succ.; blue/ orange curves show mean Succ./ Tw (right axis); diamonds mark the reference.
(a) Method
Succ. ↑
dˉs↑
Tc↓
Tw↓
Cg↑
Lg↓
Tg↓
eq↓
vpk↓
apk↓
(%)
(mm)
(ms)
(ms)
(rad)
(s)
(mrad)
(rad/s)
(rad/s 2 )
DD-GBP
92.5
73.5
25.8
16.3
3.00
4.14
5.88
2.41
0.77
15.6
Syn-GBP
53.5
58.0
15.5
7.5
2.99
4.04
5.77
5.26
1.0
48.3
GPMP2
23.0
29.9
22.6
15.1
2.93
4.10
7.13
15.81
1.4
109.8
Gafur
19.5
48.9
111.0
88.0
2.05
11.78
27.51
7.59
2.2
357.5
MR-STORM
9.5
25.4
24.3
24.1
2.95
5.32
13.14
6.86
0.81
59.4
TABLE I: 50-scene methods (a) and ablations (b). w/ and w/o: with and without. Bold: group best.
Fig. 7: Intersecting transport (A1–A5, B1–B5) and multi-obstacle interference ((a)–(j)). Robot arrows indicate approximate future motion; yellow circles/ arrows mark detected obstacles/ disturbance directions; insets show the planning scene. Full executions appear in the supplementary videos.
Fig. 8: Execution under interference: (a) sphere-surface clearances and replanning triggers (shading); (b,c) joint velocities/ accelerations, normalized by per-joint velocity limits/ acceleration references (coefficients 0.2 / 0.3 ); dotted lines mark ±1 . Joint colors are shared by both arms.
Component
Setting
Time grid
Joint support-count/ interval adaptation; Nmin=3 , Nmax=14 , Δt∈[0.01,0.6] s
Three internal points per interval; first three obstacle intervals and first two inter-arm intervals
TABLE S1: DD-GBP reference settings.
Fig. S1: Single-parameter sensitivity: boxes summarize per-scene Succ.; blue/ orange curves show mean Succ./ warm solve time; diamonds mark the shared DD-GBP reference. λc changes obstacle and inter-arm precisions together; ∞ removes the interaction-range restriction.
Parameter
Value
Succ. ↑ (%)
Tc↓ (ms)
Tw↓ (ms)
DD-GBP (ref.)
Default
92.5
25.753
16.346
Range rc (m)
0.1
75.0
11.962
12.698
Range rc (m)
0.2
90.5
15.078
14.572
Range rc (m)
0.3
90.0
24.065
15.750
Range rc (m)
0.6
86.0
33.444
21.128
Range rc (m)
0.8
85.5
35.430
22.675
TABLE S2: Current one-parameter studies: 50 scenes and 200 arms per setting; one shared reference.
K
Succ. ↑
dˉs↑
Tc↓
Tw↓
Cg↑
Lg↓
Tg↓
(%)
(mm)
(ms)
(ms)
(rad)
(s)
DD-GBP
1
100.0
100.0
6.7
4.6
3.00
3.79
4.39
2
100.0
100.0
10.4
9.2
3.00
3.80
4.54
4
100.0
92.7
10.0
11.3
3.00
3.77
4.73
8
99.8
94.8
10.6
11.2
3.00
3.76
4.83
TABLE S3: Detailed scalability results for Fig. 6 (b).
Configuration
eq (aligned)
eqraw
vRMS
max∣q˙∣
aRMS
max∣q¨∣
(mrad)
(mrad)
(rad/s)
(rad/s)
(rad/s 2 )
(rad/s 2 )
DD-GBP
2.41±1.14
29.04±2.77
0.286±0.0264
0.900
1.82±0.440
53.2
Syn-GBP
5.26±13.50
31.72±8.04
0.296±0.0320
7.40
2.33±1.94
760.7
GPMP2
15.81±23.00
36.13±15.43
0.280±0.0422
6.10
4.14±3.29
659.9
Gafur (NMPC)
7.59±6.78
7.54±6.75
0.303±0.150
4.99
14.5±16.6
880.9
MR-STORM
6.86±1.08
9.65±1.32
0.185±0.0236
4.06
2.34±1.08
527.9
TABLE S5: Recorded execution diagnostics: 50 scenes and 200 arms per configuration.
We propose DistGP: a multi-robot learning method for collaborative learning of a global function using only local experience and computation. We utilise a sparse Gaussian process (GP) model with a factorisation that mirrors the multi-robot structure of the task, and admits distributed training via Gaussian belief propagation (GBP). Our loopy model outperforms Tree-Structured GPs \cite{bui2014tree} and can be trained online and in settings with dynamic connectivity. We show that such distributed, asynchronous training can reach the same performance as a centralised, batch-trained model, albeit with slower convergence. Last, we compare to DiNNO \cite{yu2022dinno}, a distributed neural network (NN) optimiser, and find DistGP achieves superior accuracy, is more robust to sparse communication and is better able to learn continually.
Seth Nabarro, Mark van der Wilk, Andrew J. Davison
Dyson Robotics Lab, Imperial College London · Department of Computer Science, University of Oxford
Multi-agent Next-Best-View (NBV) selection for safe path planning in uncertain and unknown environments requires informative, safety-aware, and efficient coordination. Centralized approaches rely on sharing raw sensor data or significant communication overhead, resulting in limited scalability. We propose a distributed, risk-aware multi-agent NBV framework in which each robot maintains a private local 3D Gaussian Splatting map and the team jointly maximizes expected information gain (EIG) restricted to masked zones along planned trajectories. The resulting distributed objective is solved by Consensus ADMM (C-ADMM) over a communication graph, with each robot exchanging only candidate viewpoints, planned trajectory descriptors, and scalar EIG contributions. Collision risk along each trajectory is modeled via Average Value-at-Risk (AV@R) over the local 3DGS map and used both to shape the masking radius and to score planned paths. Experiments in Gibson environments at multiple team sizes show that the distributed formulation approaches the centralized baseline in mapping quality and trajectory safety while reducing communication by orders of magnitude.
Amirhossein Mollaei Khass, Vivek Pandey, Guangyi Liu +3
Department of Mechanical Engineering and Mechanics, Lehigh University · Amazon Robotics
Multi-robot trajectory planning is a fundamental problem in multi-robot coordination but remains computationally challenging due to its nonconvex, multimodal, and high-dimensional nature. This work builds upon D4orm, a dynamics-aware diffusion-denoising framework, and develops a family of planning architectures for diverse operational requirements. Unlike conventional numerical optimization methods, D4orm employs sampling-based optimization to generate solution trajectories through massively parallel sampling, leveraging modern computing architectures such as GPUs. Its diffusion-denoising structure iteratively optimizes deformations to candidate control trajectories, providing an efficient and versatile paradigm for generating kinodynamically feasible and conflict-free trajectories. Using D4orm as the building block for advanced planners, we present a decoupled planner for improved scalability, an online receding-horizon planner with feedback control, and a distributed planner for resource-constrained settings. Evaluations with differential-drive and holonomic robots in 2D and 3D environments demonstrate that D4orm-based approaches find high-quality solutions faster and more reliably than other sampling-based optimization methods, such as MPPI, as well as a learned diffusion-model-based method. We further demonstrate zero-shot deployment on ten real quadrotors with obstacles, large-scale deconfliction with 100 simulated robots, and fully onboard distributed `lifelong' operation with six ground robots. Overall, these results establish diffusion denoising as a scalable and reliable framework for multi-robot coordination. Code and video: https://github.com/proroklab/d4orm
Yuhao Zhang, Keisuke Okumura, Ajay Shankar +1
Department of Computer Science and Technology, University of Cambridge, U.K. · National Institute of Advanced Industrial Science and Technology (AIST), Japan