  This paper presents a non-iterative approach for finding the assignment of
heterogeneous robots to efficiently execute online Pickup and Just-In-Time
Delivery (PJITD) tasks with optimal resource utilization. The PJITD assignments
problem is formulated as a spatio-temporal multi-task assignment (STMTA)
problem. The physical constraints on the map and vehicle dynamics are
incorporated in the cost formulation. The linear sum assignment problem is
formulated for the heterogeneous STMTA problem. The recently proposed Dynamic
Resource Allocation with Multi-task assignments (DREAM) approach has been
modified to solve the heterogeneous PJITD problem. At the start, it computes
the minimum number of robots required (with their types) to execute given
heterogeneous PJITD tasks. These required robots are added to the team to
guarantee the feasibility of all PJITD tasks. Then robots in an updated team
are assigned to execute the PJITD tasks while minimizing the total cost for the
team to execute all PJITD tasks. The performance of the proposed non-iterative
approach has been validated using high-fidelity software-in-loop simulations
and hardware experiments. The simulations and experimental results clearly
indicate that the proposed approach is scalable and provides optimal resource
utilization.
