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.