ADMM Optimization for Multi-agent Path Planning with Spatio-Temporal Constraints
As part of Thrust 2 of our project, we study novel algorithms for multi-agent path planning for continuous environments with sound but incomplete detection guarantees but that can also pursue secondary optimization objectives.
We created a path planning method based on the continuous optimization Alternating Direction Method of Multipliers (ADMM) While ADMM is a well-studied algorithm from the optimization and machine learning literature). The resulting algorithm is very flexible, and can handle many different types of objectives and non-convex temporal-spatial constraints while allowing infeasible initializations. Although this approach can only ensure local convergence, when combined with a proper initialization, the algorithm empirically shows robust convergence.