  Swarms of aerial drones have recently been considered for last-mile
deliveries in urban logistics or automated construction. At the same time,
collaborative transportation of payloads by multiple drones is another
important area of recent research. However, efficient coordination algorithms
for collaborative transportation of many payloads by many drones remain to be
considered. In this work, we formulate the collaborative transportation of
payloads by a swarm of drones as a novel, under-capacitated generalization of
vehicle routing problems (VRP), which may also be of separate interest. In
contrast to standard VRP and capacitated VRP, we must additionally consider
waiting times for payloads lifted cooperatively by multiple drones, and the
corresponding coordination. Algorithmically, we provide a solution encoding
that avoids deadlocks and formulate an appropriate alternating minimization
scheme to solve the problem. On the hardware side, we integrate our algorithms
with collision avoidance and drone controllers. The approach and the impact of
the system integration are successfully verified empirically, both on a swarm
of real nano-quadcopters and for large swarms in simulation. Overall, we
provide a framework for collaborative transportation with aerial drone swarms,
that uses only as many drones as necessary for the transportation of any single
payload.
