DD-GBP: Anytime Multi-Arm Planning and Continuous Execution via Distributed Dynamic Gaussian Belief Propagation

Zhao Jin; Fengyi Dai; Yuetong Yin; Yunan Wang; Wenjie Chen; Chuxiong Hu

cs.ROOct 14, 2026

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

Abstract

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

Panel of Figure 1 — Fig. 1: Factor tree for $f(\boldsymbol{x}^{1},\boldsymbol{x}^{2},\boldsymbol{x}^{3})\propto f_{0}(\boldsymbol{x}^{1})\,f_{1}(\boldsymbol{x}^{1},\boldsymbol{x}^{2})\,f_{2}(\boldsymbol{x}^{2},\boldsymbol{x}^{3})$ . 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.

Panel of Figure 4 — 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

T_{\mathrm{c}}

T_{\mathrm{w}}

, alongside Succ. (c) Scenario sensitivity: boxes show per-scene Succ.; blue/ orange curves show mean Succ./

T_{\mathrm{w}}

(right axis); diamonds mark the reference.

(a) Method	Succ. $\uparrow$	$\bar{d}_{\mathrm{s}}\uparrow$	$T_{\mathrm{c}}\downarrow$	$T_{\mathrm{w}}\downarrow$	$C_{\mathrm{g}}\uparrow$	$L_{\mathrm{g}}\downarrow$	$T_{\mathrm{g}}\downarrow$	$e_{\mathrm{q}}\downarrow$	$v_{\mathrm{pk}}\downarrow$	$a_{\mathrm{pk}}\downarrow$
	(%)	(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

\pm 1

. Joint colors are shared by both arms.

Component	Setting
Time grid	Joint support-count/ interval adaptation; $N_{\min}=3$ , $N_{\max}=14$ , $\Delta t\in[0.01,0.6]$ s
Inference	Backward–forward scheduling; 20-iteration cap; objective-change tolerance $10^{-3}$
Replanning	Event-triggered; GP-resampled warm starts; linear initialization for a new target
Collision model	Spheres; margin $0.10$ m; obstacle aggregation $\alpha=30$
Collision precision	Obstacle/ inter-arm support-state precision 400; inter-arm interpolation multiplier 10
Interpolation	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.

\lambda_{\mathrm{c}}

changes obstacle and inter-arm precisions together;

\infty

removes the interaction-range restriction.

Parameter	Value	Succ. $\uparrow$ (%)	$T_{\mathrm{c}}$ $\downarrow$ (ms)	$T_{\mathrm{w}}$ $\downarrow$ (ms)
DD-GBP (ref.)	Default	92.5	25.753	16.346
Range $r_{\mathrm{c}}$ (m)	0.1	75.0	11.962	12.698
Range $r_{\mathrm{c}}$ (m)	0.2	90.5	15.078	14.572
Range $r_{\mathrm{c}}$ (m)	0.3	90.0	24.065	15.750
Range $r_{\mathrm{c}}$ (m)	0.6	86.0	33.444	21.128
Range $r_{\mathrm{c}}$ (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.

DD-GBP
$K$	Succ. $\uparrow$	$\bar{d}_{s}\uparrow$	$T_{c}\downarrow$	$T_{w}\downarrow$	$C_{g}\uparrow$	$L_{g}\downarrow$	$T_{g}\downarrow$
	(%)	(mm)	(ms)	(ms)		(rad)	(s)
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	$e_{q}$ (aligned)	$e_{q}^{\rm raw}$	$v_{\rm RMS}$	$\max\|\dot{q}\|$	$a_{\rm RMS}$	$\max\|\ddot{q}\|$
	(mrad)	(mrad)	(rad/s)	(rad/s)	(rad/s 2 )	(rad/s 2 )
DD-GBP	$2.41\pm 1.14$	$29.04\pm 2.77$	$0.286\pm 0.0264$	0.900	$1.82\pm 0.440$	53.2
Syn-GBP	$5.26\pm 13.50$	$31.72\pm 8.04$	$0.296\pm 0.0320$	7.40	$2.33\pm 1.94$	760.7
GPMP2	$15.81\pm 23.00$	$36.13\pm 15.43$	$0.280\pm 0.0422$	6.10	$4.14\pm 3.29$	659.9
Gafur (NMPC)	$7.59\pm 6.78$	$7.54\pm 6.75$	$0.303\pm 0.150$	4.99	$14.5\pm 16.6$	880.9
MR-STORM	$6.86\pm 1.08$	$9.65\pm 1.32$	$0.185\pm 0.0236$	4.06	$2.34\pm 1.08$	527.9

TABLE S5: Recorded execution diagnostics: 50 scenes and 200 arms per configuration.

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Abstract

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