Multi-board FPGA Implementation to Solve the Satisfiability Problem for Multi-Agent Path Finding in Smart Factory

Many smart city applications such as optimal path planning for multiple transportation robots in factories and warehouses are formulated as highly complex combinatorial optimization problems. Since these problem-solving processes require time-critical control and low energy consumption when executed at the edge of computer networks, a promising approach is to implement high speed solvers on Field Programmable Gate Array (FPGA) by exploiting its parallelism and energy efficiency. Here we focus on a variant of the Multi-Agent Path Finding (MAPF) problem, which is a problem of finding optimal discrete space-time trajectories of the robots that are required to complete transportation requests in a semiconductor fabrication factory as early as possible without colliding with each other. According to our future aim to find a feasible solution to a large-sized problem instance in a distributed manner, the present paper proposes a multi-FPGA implementation of a variant of 'AmoebaSATslim,' which is a bio-inspired parallel search algorithm to search for a solution to the Boolean satisfiability problem (SAT). We design an FPGA cluster that links two FPGA boards to tackle a minimal-sized instance for two robots to transport two packages, where each of the boards is responsible for finding the trajectory of each of the robots. The proposed dual-FPGA implementation handles 22,544 variables and achieves up to approximately 17-fold faster execution speed than its software implemented on an x86-based personal computer.