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LTLDiff: Finite Linear Temporal Logic-Guided Data Generation and Diffusion Policies for Multi-agent Robotic Manipulation
Chuhan Meng, Haiyan Yin
TL;DR
Multi-agent manipulation requires coordination that diffusion policies can fail to maintain under temporal and ordering constraints. LTLDiff learns LTLf specifications from natural-language objectives, uses them for demonstration generation and diffusion-policy conditioning, and outperforms diffusion policies on most evaluated multi-agent tasks, while remaining limited on long-horizon tasks.
Problem
Existing multi-agent manipulation approaches struggle to satisfy coordination, temporal, and safety requirements together, particularly when learning-based policies lack explicit temporal structure.
Source: §1 · pp. 1–2Method
LTLDiff learns task-specific LTLf formulas from natural-language objectives, uses them to guide demonstrations, and conditions multi-agent diffusion-policy training and planning.
Source: §1 · p. 2, §3.5 · pp. 7–8Results
Constraint-aware diffusion policies outperformed diffusion policies on most RoboFactory multi-agent manipulation tasks with a high level of coordination.
Source: §5 · p. 11Takeaways & Limitations
The experiments support using LTLf across demonstration generation and diffusion-policy learning for coordinated multi-agent manipulation.
Source: §1 · p. 2, §5 · p. 11LTLDiff performs poorly on long-horizon tasks, motivating closed-loop feedback and continual replanning.
Source: §5 · p. 11
Abstract
from arXiv · showhide
Multi-agent robotic manipulation tasks require coordination among agents to satisfy task-level temporal, logical, and safety constraints. Recently, diffusion policies have been used to perform the task. However, they still suffer from desynchronization, incorrect action ordering, and coordination failures in tasks that require simultaneous or sequential multi-agent interaction. Therefore, LTLDiff is proposed as a framework that combines Finite Linear Temporal Logic (LTLf) specification learning for both the generation of demonstrations and learning via diffusion policies. Each task has a specific LTLf formula that is learned from a set of natural language instructions using a large-scale language model. To enable a fixed-dimensional vector embedding of the learned specification from the language model, LTLf uses an abstract syntax tree representation scheme. This embedding of logic serves as a condition for (i) logic-guided data collection and (ii) diffusion-based policy training, encouraging trajectories that are consistent with the desired ordering and coordination requirements. Experiments on multi-agent LTLDiff manipulation tasks demonstrate improved task success rates compared to the baseline. Together, these contributions demonstrate the effectiveness of LTLDiff for coordinated multi-agent manipulation.
1 Introduction
LTLDiff combines adaptable diffusion policies with LTLf specifications to address coordination, ordering, and temporal constraints in multi-agent manipulation. It learns task-specific logic from natural-language objectives, guides demonstration generation, and conditions policy training, with higher success rates across most evaluated tasks.
1 Introduction
- LTLDiff combines diffusion-policy adaptation with LTLf conditioning to address complementary limitations of rule-based and learning-based multi-agent control.The framework applies LTLf specifications as structured inputs rather than enforcing them solely as hard runtime rules.Source: §1 · p. 2
- An LTLf generator pairs task formulas with natural-language objectives and uses them to guide multi-agent demonstration generation.A large language model supports the formula-generation process.Source: §1 · p. 2
- LTLMAG integrates LTLf constraints into multi-agent diffusion-policy planning for coordinated task execution.The contribution extends LTLf-guided diffusion policies to multi-agent settings.Source: §1 · p. 2
- LTLDiff achieves higher task success rates across most evaluated RoboFactory manipulation tasks than the baseline method and LTLDOG-R.The reported comparison is presented as evidence for the framework’s effectiveness.Source: §1 · p. 2
2 Related Work
Related work contrasts rule-based methods that provide safety and feasibility guarantees with learning-based methods that offer flexibility. LTLf provides a temporal formalism, while LTLDiff combines logic-guided offline demonstrations with diffusion-policy conditioning.
2 Related Work
- Rule-based planning can generate collision-free trajectories with strong safety and feasibility guarantees but remains restrictive for complex manipulation tasks.Examples include A* and LTL-based planning when geometric and kinematic constraints are known.Source: §2.2 · p. 3
- Learning-based approaches use demonstrations or offline data to improve flexibility, but their effectiveness depends on the quality of available trajectories.Behavioral cloning and offline reinforcement learning are identified as representative approaches.Source: §2.2 · p. 3
- LTLf expresses high-level task constraints in temporal form and has been applied to robotic planning and reinforcement learning.Prior LTLf solutions often rely on physical trial-and-error interaction and are rarely compatible with offline policy learning.Source: §2.3 · p. 3
- LTLDiff reduces reliance on trial-and-error by using LTLf to guide offline demonstration generation and condition diffusion-based policy learning.The same logic is used across both stages of the offline learning pipeline.Source: §2.3 · p. 3
3 LTLDiff
LTLDiff learns task-level LTLf specifications from natural-language descriptions, uses them to guide offline demonstration generation, and conditions multi-agent diffusion policies for coordinated trajectory generation.
3 LTLDiff
- LTLDiff learns policies for physically valid multi-agent trajectories guided by LTLf specifications encoding task ordering and coordination requirements.Source: §3.1 · p. 3, LTLf Task Specification · p. 4
- The encoded logic and compositional constraints guide offline data generation, whose demonstrations pair trajectories with task-specific LTLf specifications.Source: Figure 1 · p. 4, LTLf Task Specification · p. 4, §3.4 · p. 6
- Natural-language task descriptions are converted into LTLf formulas by Qwen, which generates multiple candidates and selects the most appropriate formula.Source: §3.2 · p. 5
- Each LTLf formula is tokenized, parsed into an abstract syntax tree, and recursively encoded into a fixed-dimensional vector for neural-network inputs.Source: §3.3 · p. 5, Tokenization and Parsing · p. 5, AST-based Encoding · p. 6
- LTLMAG conditions diffusion policies on observations and LTLf embeddings while a learned regressor supplies satisfaction guidance during reverse denoising.Source: §3.5 · pp. 7–8
- Per-agent trajectories are locally updated and concatenated into joint trajectories, while time-varying guidance weights trade off symbolic satisfaction against the learned diffusion prior.Source: §3.5 · p. 8
4 Experiment
LTLDiff is evaluated against the baseline and LTLDOG-R across single-, two-, three-, and four-agent tasks, with ablations isolating LTLf in data generation and diffusion training. It achieves stronger task success overall, while long-horizon four-agent coordination remains challenging.
Comparative Evaluation
- Single-agent task success improves over the baseline and LTLDOG-R, with stronger performance as the number of demonstrations increases.Source: Single-agent Tasks · p. 9, Table 1 · p. 9
- Across all two-agent tasks, LTLDiff achieves the highest success rate, with especially marked improvements on Lift Barrier and Two Robots Stack Cube using 150 demonstrations.Source: Table 1 · p. 9, Two-agent Tasks · p. 10
- Three-agent success rates increase by 25%, 32%, and 16% over the baseline with 50, 100, and 150 demonstrations, respectively.Source: Table 1 · p. 9, Three-agent Tasks · p. 10
- Four-agent success is higher than both comparators but remains low because long-horizon coordination and temporal dependencies are difficult to maintain.Source: Table 1 · p. 9, Four-agent Tasks · p. 10
Ablation Study
- The conclusion attributes a more significant contribution to LTLf conditioning than to the regressor neural network alone.Source: Four-agent Tasks · p. 10
- The ablation study evaluates LTLf constraints separately in data generation and diffusion-policy training using task success rates reported in Table 2.Source: Table 2 · p. 10, §4.2 · p. 11
- LTLf-guided data generation captures task-level temporal logic that demonstrations alone may not reveal, reducing asynchronous actions and incorrect action ordering in coordination tasks.Source: Table 2 · p. 10, Importance of LTLf in Data Generation · p. 11
- LTLf conditioning biases trajectory sampling toward temporal consistency and coordinated behavior, while removing it causes significant success-rate decreases especially in three- and four-agent tasks.Source: Table 2 · p. 10, Importance of LTLf in Diffusion Policy · p. 11
5 Conclusion
The study concludes that constraint-aware demonstrations enable diffusion policies to learn task-level temporal properties for coordinated multi-agent manipulation. However, LTLDiff performs poorly on long-horizon tasks, motivating closed-loop replanning.
5 Conclusion
- Constraint-aware demonstrations yielded diffusion policies that outperformed unconstrained policies on most high-coordination RoboFactory manipulation tasks.The demonstrations were generated with motion planners and LTLf formulas, then used to train diffusion policies without hard execution-time constraints.Source: §5 · p. 11
- LTLDiff performs poorly on long-horizon tasks, motivating future integration of closed-loop feedback such as receding horizon control.The proposed feedback would continually replan from real-time observations to correct execution errors and compensate for unrepresented state distributions.Source: §5 · p. 11
A LTLf Formulae
The appendix lists LTLf formulas for robotic manipulation tasks and associates atomic propositions with task events, object states, and coordination conditions.
A LTLf Formulae
- Table 3 presents LTLf formulas for each robotic manipulation task.Source: Table 3 · p. 13
- The listed formulas use atomic propositions to encode task events and states such as object placement, stacking, camera alignment, and shoe transfer.Source: A LTLf Formulae · p. 14
B Task Descriptions
The task descriptions specify multi-agent manipulation setups and target conditions for object placement, camera alignment, photography, shoe transfer, food placement, and stacking.
B Task Descriptions
- Some tasks require ordered multi-agent interactions, such as passing a shoe through successive arms before final placement.Source: B Task Descriptions · pp. 14–15
- Table 4 organizes task descriptions alongside target conditions for multi-agent manipulation tasks.Source: Table 4 · p. 14
- Target conditions define geometric or spatial requirements, including threshold distances, specified heights, alignment, stable stacking, and final target locations.Source: B Task Descriptions · pp. 15–16
- The tasks include coordinated object placement and stacking, camera alignment and shutter clicking, shoe handoffs, food placement in a pot, and cube stacking.Source: B Task Descriptions · pp. 15–16
C Prompt Template For LTLf
The prompt template instructs a language model to convert task descriptions into JSON containing a task name, atomic propositions, and a structured LTL formula.
C Prompt Template For LTLf
- The template frames the model as an expert in robotics and formal methods and provides a task-specific description and target condition as input.Source: C Prompt Template For LTLf · p. 17
- The template requires JSON output with a task name, a proposition list, and a detailed LTL formula using those propositions.Source: C Prompt Template For LTLf · p. 17
- The generated formula must encode ordering with temporal operators such as U or G and explicitly include all propositions.Source: C Prompt Template For LTLf · p. 17
- The prompt requires negation with ! and prohibits explanations or text outside the JSON object.Source: C Prompt Template For LTLf · p. 17