STL-based multi-agent motion planning for multiple tasks with complex logic

Abstract

A Multi-Agent Multi-Task Signal Temporal Logic (MAMT-STL) framework is proposed for motion planning, addressing limitations in existing STL-based multi-agent multi-task methods that require explicit construction of inter-task constraints for all possible assignments. This process generates redundant variables and invalid constraints, degrading optimization efficiency. To address this problem, Multi-Agent STL (MA-STL) is reformulated into MAMT-STL by decoupling encoding through a binary task assignment matrix and temporal logic matrix. This separation eliminates redundant constraint reconstruction across task assignments while reducing sensitivity to inter-task logic complexity. The framework further enables optional task encoding through modified integer constraints of logical conjunction operators and simplifies task order constraints to substantially improve solving efficiency under complex precedence requirements. The resulting motion planning problem is formulated as a mixed-integer linear program (MILP), with simulations on space robotic and unmanned aerial vehicle (UAV) systems demonstrating effectiveness in complex temporal logic planning and clear computational advantages over existing STL-based methods.