  Multi-agent systems (MASs) can autonomously learn to solve previously unknown
tasks by means of each agent's individual intelligence as well as by
collaborating and exploiting collective intelligence. This article considers a
group of autonomous agents learning to track the same given reference
trajectory in a possibly small number of trials. We propose a novel collective
learning control method that combines iterative learning control (ILC) with a
collective update strategy. We derive conditions for desirable convergence
properties of such systems. We show that the proposed method allows the
collective to combine the advantages of the agents' individual learning
strategies and thereby overcomes trade-offs and limitations of single-agent
ILC. This benefit is achieved by designing a heterogeneous collective, i.e., a
different learning law is assigned to each agent. All theoretical results are
confirmed in simulations and experiments with two-wheeled-inverted-pendulum
robots (TWIPRs) that jointly learn to perform the desired maneuver.
