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.

翻译：在信号时序逻辑（STL）下的多智能体规划常因协作任务导致计算挑战，问题固有的高维性阻碍了具有满足保证的可扩展综合。为解决此问题，我们将STL规划表述为任意多智能体约束下的优化程序，并引入一种基于惩罚的无约束松弛方法，该方法可通过块坐标梯度下降（BCGD）算法高效求解——其中每个块对应单个智能体的决策变量，从而降低复杂度。通过利用基于平滑STL语义定义的二次惩罚函数，我们证明在标准正则性假设下，BCGD迭代收敛于惩罚问题的稳定点。为确保可行性，BCGD求解器被嵌入双层优化框架：内层对固定惩罚参数执行BCGD更新，外层循环则逐步增大惩罚参数以持续提升多智能体STL鲁棒性。所提框架实现了可扩展计算，并通过多种复杂多机器人规划场景得到验证。