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Cumulatively developing robots offer a unique opportunity to reenact the constant interplay between neural mechanisms related to learning, memory, prospection, and abstraction from the perspective of an integrated system that acts, learns, remembers, reasons, andmakes mistakes. Situated within such interplay lie some of the computationally elusive and fundamental aspects of cognitive behavior: the ability to recall and flexibly exploit diverse experiences of one's past in the context of the present to realize goals, simulate the future, and keep learning further. This article is an adventurous exploration in this direction using a simple engaging scenario of how the humanoid iCub learns to construct the tallest possible stack given an arbitrary set of objects to play with. The learning takes place cumulatively, with the robot interacting with different objects (some previously experienced, some novel) in an openended fashion. Since the solution itself depends on what objects are available in the "now," multiple episodes of past experiences have to be remembered and creatively integrated in the context of the present to be successful. Starting from zero, where the robot knows nothing, we explore the computational basis of organization episodic memory in a cumulatively learning humanoid and address (1) how relevant past experiences can be reconstructed based on the present context, (2) how multiple stored episodic memories compete to survive in the neural space and not be forgotten, (3) how remembered past experiences can be combined with explorative actions to learn something new, and (4) how multiple remembered experiences can be recombined to generate novel behaviors (without exploration). Through the resulting behaviors of the robot as it builds, breaks, learns, and remembers, we emphasize that mechanisms of episodic memory are fundamental design features necessary to enable the survival of autonomous robots in a real world where neither everything can be known nor can everything be experienced. [ABSTRACT FROM AUTHOR]