# Information-driven self-organization: the dynamical system approach to autonomous robot behavior

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## Abstract

In recent years, information theory has come into the focus of researchers interested in the sensorimotor dynamics of both robots and living beings. One root for these approaches is the idea that living beings are information processing systems and that the optimization of these processes should be an evolutionary advantage. Apart from these more fundamental questions, there is much interest recently in the question how a robot can be equipped with an internal drive for innovation or curiosity that may serve as a drive for an open-ended, self-determined development of the robot. The success of these approaches depends essentially on the choice of a convenient measure for the information. This article studies in some detail the use of the predictive information (PI), also called excess entropy or effective measure complexity, of the sensorimotor process. The PI of a process quantifies the total information of past experience that can be used for predicting future events. However, the application of information theoretic measures in robotics mostly is restricted to the case of a finite, discrete state-action space. This article aims at applying the PI in the dynamical systems approach to robot control. We study linear systems as a first step and derive exact results for the PI together with explicit learning rules for the parameters of the controller. Interestingly, these learning rules are of Hebbian nature and local in the sense that the synaptic update is given by the product of activities available directly at the pertinent synaptic ports. The general findings are exemplified by a number of case studies. In particular, in a two-dimensional system, designed at mimicking embodied systems with latent oscillatory locomotion patterns, it is shown that maximizing the PI means to recognize and amplify the latent modes of the robotic system. This and many other examples show that the learning rules derived from the maximum PI principle are a versatile tool for the self-organization of behavior in complex robotic systems.

## Keywords

Autonomous systems Predictive information Self-organization Sensorimotor loop Embodiment Hebbian learning Intrinsic motivation## Notes

### Acknowledgments

Part of this work was completed during a stay of Nihat Ay and Ralf Der at the CSIRO in Sydney, Australia. Hospitality and financial support are gratefully acknowledged. Nihat Ay also acknowledges support by the Santa Fe Institute at the early stage of the paper. Mikhail Prokopenko thanks the Max Planck Institute of Mathematics in the Sciences in Leipzig, Germany, for support and hospitality at the Institute. The authors thank the anonymous reviewer for many important comments that helped to improve the paper substantially.

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