  In this paper, we consider a large-scale instance of the classical
Pickup-and-Delivery Vehicle Routing Problem (PDVRP) that must be solved by a
network of mobile cooperating robots. Robots must self-coordinate and
self-allocate a set of pickup/delivery tasks while minimizing a given cost
figure. This results in a large, challenging Mixed-Integer Linear Problem that
must be cooperatively solved without a central coordinator. We propose a
distributed algorithm based on a primal decomposition approach that provides a
feasible solution to the problem in finite time. An interesting feature of the
proposed scheme is that each robot computes only its portion of solution,
thereby preserving privacy of sensible information. The algorithm also exhibits
attractive scalability properties that guarantee solvability of the problem
even in large networks. To the best of our knowledge, this is the first attempt
to provide a scalable distributed solution to the problem. The algorithm is
first tested through Gazebo simulations on a ROS 2 platform, highlighting the
effectiveness of the proposed solution. Finally, experiments on a real testbed
with a team of ground and aerial robots are provided.
