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.

翻译：信号时序逻辑（STL）下的多智能体规划常因协作任务导致问题固有的高维性而面临计算挑战，难以在保证可满足性的前提下实现可扩展的综合。为此，我们将STL规划建模为受多智能体STL约束的优化问题，并提出一种基于罚函数的无约束松弛方法，通过块坐标梯度下降（BCGD）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。利用平滑STL语义定义的二次罚函数，我们证明在标准正则性假设下，BCGD迭代收敛于罚问题的平稳点。为强制约束可行性，BCGD求解器嵌入双层优化框架：内层对固定罚参数执行BCGD更新，外层循环则逐步增大罚参数以持续提升多智能体STL鲁棒性。所提框架支持可扩展计算，并通过多种复杂多机器人规划场景验证其有效性。