Centralized Multi-agent Synthesis with Spatial Constraints via Mixed-Integer Quadratic Programming

Alexandra Forsey-Smerek, Ho Chit Siu, Kevin Leahy

Abstract: We address the challenge of centralized multi-agent motion planning for tasks described in Signal Temporal Logic (STL) which require both adherence to spatial constraints and simultaneous execution of team behaviors. Existing methods to satisfy STL specifications including spatial constraints use decentralized planning approaches. These decentralized methods are unable to enforce temporal constraints jointly across agents and therefore cannot require multiple agents to complete simultaneous team behaviors. We present a mixed-integer quadratic program (MIQP) encoding of the search for multi-agent trajectories to satisfy team STL specifications in a gridworld environment. We experimentally evaluate the solve time of the centralized MIQP encoding against a centralized mixed-integer linear program (MILP) encoding in scenarios with different types of spatial constraints. Numerical results uncover that the solve time for the MIQP encoding is more suitable for problems with inter-agent spatial constraints, such as collision avoidance constraints, while the MILP encoding better suits constraints between agents and static objects in the environment. Our findings provide valuable design recommendations for implementation of either approach according to the type of spatial constraints which must be supported.