用网络流优化机器人任务与运动规划，提升效率与规模适应性。
Optimization-based Task and Motion Planning under Signal Temporal Logic Specifications using Logic Network Flow
- 将时序逻辑转为网络边上的多面体约束，实现更紧的松弛解。
- 在多机器人场景中，计算时间更短，分支定界时探索节点更少。
- 适合大规模复杂任务规划，尤其对实时性要求高的系统
本文提出一种基于优化的任务与运动规划框架——逻辑网络流（Logic Network Flow），将信号时序逻辑（STL）规范融入高效的混合整数线性规划。该方法将时序谓词编码为网络流边上的多面体约束，而非传统逻辑树中节点间的约束。结合动态网络流，逻辑网络流相比传统逻辑树能提供更紧的凸松弛。在多个多机器人运动规划案例中进行评估，结果表明：在多种规划问题中，本方法计算时间更短；随着问题规模扩大，虽每个节点计算负载增加，但分支定界过程探索的节点数更少，仍能获得更好的上下界。
原文摘要 · Abstract (English)
This paper proposes an optimization-based task and motion planning framework, named "Logic Network Flow", to integrate signal temporal logic (STL) specifications into efficient mixed-binary linear programmings. In this framework, temporal predicates are encoded as polyhedron constraints on each edge of the network flow, instead of as constraints between the nodes as in the traditional Logic Tree formulation. Synthesized with Dynamic Network Flows, Logic Network Flows render a tighter convex relaxation compared to Logic Trees derived from these STL specifications. Our formulation is evaluated on several multi-robot motion planning case studies. Empirical results demonstrate that our formulation outperforms Logic Tree formulation in terms of computation time for several planning problems. As the problem size scales up, our method still discovers better lower and upper bounds by exploring fewer number of nodes during the branch-and-bound process, although this comes at the cost of increased computational load for each node when exploring branches.
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