Multi-Agent Temporal Logic Planning via Penalty Functions and Block-Coordinate Optimization
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arXiv
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| Format: | Preprint |
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2026
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| author | Vlahakis, Eleftherios E. Kordabad, Arash Bahari Lindemann, Lars Sopasakis, Pantelis Soudjani, Sadegh Dimarogonas, Dimos V. |
| author_facet | Vlahakis, Eleftherios E. Kordabad, Arash Bahari Lindemann, Lars Sopasakis, Pantelis Soudjani, Sadegh Dimarogonas, Dimos V. |
| contents | 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 arbitrary multi-agent 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17434 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-Agent Temporal Logic Planning via Penalty Functions and Block-Coordinate Optimization Vlahakis, Eleftherios E. Kordabad, Arash Bahari Lindemann, Lars Sopasakis, Pantelis Soudjani, Sadegh Dimarogonas, Dimos V. Systems and Control Multiagent Systems 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 arbitrary multi-agent 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. |
| title | Multi-Agent Temporal Logic Planning via Penalty Functions and Block-Coordinate Optimization |
| topic | Systems and Control Multiagent Systems |
| url | https://arxiv.org/abs/2602.17434 |