We consider multi-agent transport task problems where, e.g. in a factory setting, items have to be delivered from a given start to a goal pose while the delivering robots need to avoid collisions with each other on the floor. We introduce a Task Conflict-Based Search (TCBS) Algorithm to solve the combined delivery task allocation and multi-agent path planning problem optimally. The problem is known to be NP-hard and the optimal solver cannot scale. However, we introduce it as a baseline to evaluate the sub-optimality of other approaches. We show experimental results that compare our solver with different sub-optimal ones in terms of regret.
Existing approaches to multirobot coordination separate scheduling and task allocation, but finding the optimal schedule with joint tasks and spatial constraints requires robots to simultaneously solve the scheduling, task allocation, and path planning problems. We present a formal description of the multirobot joint task allocation problem with heterogeneous capabilities and spatial constraints and an instantiation of the problem for the search and rescue domain. We introduce a novel declarative framework for modeling the problem as a mixed integer linear programming (MILP) problem and present a centralized anytime algorithm with error bounds. We demonstrate that our algorithm can outperform standard MILP solving techniques, greedy heuristics, and a market based approach which separates scheduling and task allocation.