Generalizable Multi-Agent Planning from Signal Temporal Logic Specifications via Diffusion

Joe Eappen; Zikang Xiong; Shreyash S. Iyengar; Suresh Jagannathan

cs.MAAug 30, 2026

Generalizable Multi-Agent Planning from Signal Temporal Logic Specifications via Diffusion

Authors: Joe Eappen, Zikang Xiong, Shreyash S. Iyengar, Suresh Jagannathan

Organizations: ECE and CS Departments of Purdue University

Abstract

Multi-agent systems in the real-world (e.g., drone swarms, autonomous cars, warehouse robots) must satisfy rich, temporal tasks while avoiding collisions. Signal Temporal Logic (STL) elegantly encodes such objectives, but current STL planning methods face critical limitations. State-of-the-art optimization-based approaches can handle arbitrary STL specifications but struggle with scalability, becoming computationally impractical as the number of agents grows. Learning-based methods efficiently handle a large number of agents with rapid planning times but fare poorly when deployment-time objectives differ from those used during training, and do not support planning tasks that require different specifications to be ascribed to different agents (i.e., heterogeneity) or team-level specifications requiring coordination of multiple agents. This fundamental trade-off between generalizability and scalability presents a challenge for realizing multi-agent STL planning algorithms in practice. To overcome this challenge, we introduce a new diffusion method for multi-agent planning with STL specifications. Using a differentiable approximation of STL, we integrate the STL gradient in the denoising process, making our approach generalizable to novel formulas whose predicates are placed anywhere within the goal region covered during training, while achieving the same scalability as existing learning-based methods. Our method supports heterogeneous specifications, and by using diffusion models, naturally enhances plan diversity, thereby significantly reducing safety-related violations (e.g., collisions) among agents. A detailed evaluation study justifies the utility of STL-guided diffusion-based multi-agent planners for constructing generalizable, scalable, and diverse plans. Videos and code are available at https://www.jeappen.com/diff-ma-stl/ and https://github.com/jeappen/diff-ma-stl .

Figures & tables

Fig. 1 : Demo on $N=10$ differential drive robots [ 10 ] following a (heterogeneous) seq specification (Sec. V-B ) that requires agents to visit designated locations in a prescribed order (X, Y, Z in the figure for the yellow robot) at specified time intervals. A video is provided on our website: https://www.jeappen.com/diff-ma-stl/

Method	Het. (Specs)	MA Aware	Cmplx. Specs	Scale	Div.	Gen.	Plan. Time
PWL MA-STL [ 2 ]	$\checkmark$	$\checkmark$	$\times$	$\times$	$\times$	$\checkmark$	$>10$ s
STLPY-SA [ 11 ]	$\checkmark$	$\times$	$\checkmark$	$\times$	$\times$	$\checkmark$	$>10$ s
Gradient [ 12 ]	$\checkmark$	$\times$	$\checkmark$	$\times$	$\times$	$\checkmark$	$>10$ s
GNN-ODE [ 9 ]	$\times$	$\checkmark$	$\checkmark$	$\checkmark$	$\times$	$\times$	$<0.1$ s
Diff-SA ( [ 13 ] )	$\checkmark$	$\times$	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\sim 1$ s
Diff-MA (Ours)	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\sim 1$ s

TABLE I: A comparison of MA-STL-A planner choices. Our diffusion-based method excels in Diversity and Generalizability with capabilities beyond other planners. Het. (Specs) : Heterogeneous Specifications i.e., different tasks among agents, MA Aware : Considers Multi-agent interactions while planning, Cmplx. Specs : Can handle complex specifications (with

N>5

agents as studied in prior work [ 9 , Sec. 3] ), Scale : Safely scale to large

N

(at least 32 agents), Plan. Time : Average planning time (s) to generate a single end-to-end plan for novel agent placements, Div. : Exhibits Plan Diversity (as in Sec V-C ), Gen. : Allows Generalizability i.e., handling new specifications at runtime without additional training (in the order of several hours).

Panel of Figure 3 — Fig. 2 : Top: Training overview, Bottom: MA STL-guided inference.

Fig. 3 : Results over different number of agents and specifications. Top: Success Rate (%). Middle: Planning Time (s). Bottom: Time-to-Reach (TtR, steps). Standard deviations are shown around the mean. Our method ( Diff-MA ) on average exceeds STLPY-SA by 20% with a notable relative success rate improvement of 36% for the crowded map (

N=32

), while being 55x faster with zero retraining.

		Agents per Cluster $\downarrow$			Path Overlap (%) $\downarrow$
Spec.	N	D-MA	GO	STLPY	D-MA	GO	STLPY
Branch	16	1.09	3.81	2.35	0.00	0.08	0.00
Cover	16	1.08	6.40	3.02	0.00	0.18	0.00
Loop	16	1.04	4.40	3.40	0.00	8.72	0.27
Seq.	16	1.08	7.74	2.89	0.00	0.25	12.42

TABLE II : Comparison of plan diversity using the average number of agents per cluster and path overlap (%) for different planners (D-MA: Diff-MA , GO: GNN-ODE , STLPY: STLPY-SA ) in the Dubins car environment for Homogeneous specifications (same across agents). The best score (w.r.t. diversity) is highlighted in bold.

Fig. 4 : We evaluate Diff-MA on a larger map with up to

N=128

agents for the Mixed spec. and note degradation in success at high

N

(matching STLPY-SA at

N=128

) with modest increases in planning time.

Fig. 5 : Team-level spec. results on CaTL+ tasks with redundancy (

m>1

) and inter-task avoidance constraints: Choice-Seq (two branches, each a pair of sequential tasks) and Redundant (shared waypoint sequences). Baselines: STLPY-Global (global MILP over all agents, feasible only at

N\!=\!8

) and STLPY-SA with oracle allocation (best of greedy and Hungarian matching by travel distance). Diff-MA requires no task-to-agent allocation and maintains high success at scale (

N\!=\!32

) where STLPY-SA degrades sharply.

Fig. 6 : Per-agent delay (from TtR) with Diff-MA relative to the average time a single agent (

N{=}1

) using STLPY-SA takes to satisfy its specification. Histograms summarize 30 runs of the Mixed task with Baseline Steps = 990.

		Success Rate (%) $\uparrow$		Planning Time (s) $\downarrow$		TtR (steps) $\downarrow$
Spec		D-MA (LA)	$\Delta$ %	D-MA (LA)	$\Delta$ %	D-MA (LA)	$\Delta$ %
Mixed	8	95.00	-4.60%	0.68	-38.75%	1868.17	+0.98%
	16	91.25	-5.81%	0.67	-56.53%	1820.72	+0.46%
	32	90.00	-2.37%	1.20	-61.96%	2038.92	+17.37%

TABLE III : Achievable-loss coefficient ablation. D-MA (LA): low coefficient

\lambda_{\text{ach}}{=}10^{-3}

(vs.

\lambda_{\text{ach}}{=}1

for full Diff-MA ,

\lambda_{\text{STL}}{=}1

throughout).

\Delta\%

gives change relative to full Diff-MA .

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Multi-agent planning under Signal Temporal Logic (STL) is often hindered by collaborative tasks that lead to computational challenges due to the inherent high dimensionality of the problem, preventing scalable synthesis with satisfaction guarantees. To address this, we formulate STL planning as an optimization program under multi-agent STL constraints and introduce a penalty-based unconstrained relaxation that can be efficiently solved via a Block-Coordinate Gradient Descent (BCGD) method, where each block corresponds to a single agent's decision variables, thereby mitigating complexity. By utilizing a quadratic penalty function defined via smooth STL semantics, we show that BCGD iterations converge to a stationary point of the penalized problem under standard regularity assumptions. To enforce feasibility, the BCGD solver is embedded within a two-layer optimization scheme: inner BCGD updates are performed for a fixed penalty parameter, which is then increased in an outer loop to progressively improve multi-agent STL robustness. The proposed framework enables scalable computations and is validated through various complex multi-robot planning scenarios.

Abstract

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