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Behavior as broken symmetry in embodied self-organizing robots

      by Ralf Der and Georg Martius , see here for the reference
Abstract: Self-organization---ubiquitous in nature---is a major challenge for both artificial life and modern robotics offering intriguing perspectives for practical applications utilized so far only incipiently. There is some progress, though, in formulating general objective functions for driving systems into self-organization (SO). Based on general principles like information maximization, these approaches are domain invariant and free of arbitrariness. However, and this seems to be a major source of concerns, if nothing is specified from outside, will SO simply make the robot an arbitrary subject that is completely unpredictable in its behaviors and thus rather a thread than a hope. The aim of this paper is to show that this attitude is not justified. Instead, we develop an understanding of what happens if the system is self-organizing, what the role of the embodiment is and how we can find clues for predicting and shaping the behavior patterns emerging in a genuine SO scenario. The approach is based on a new unsupervised learning rule staging two antagonistic activities---driving systems towards instability while preserving the physical symmetries of the system as much as possible. This leads to spontaneous symmetry breaking, the leading phenomenon of SO known from nature that has been overlooked by the robotics community so far. It is shown by a number of examples that the unsupervised learning rule induces an amazing variety of behaviors---patterns in space and time that can be interpreted as broken symmetries.

Video S1: The two-wheeled robot as a 3D physical object. The ground is elastic so that the wheels are sinking in depending on their load. Left, wheelsize = 1: with the given elasticity, the robot is lying more or less flat on the ground when driving straight. There is a strong slip effect when accelerating. Moreover, when moving in a curve, there is an inclination due to the physical forces making the effective radius of the wheels different, see the video vehicskipandfriction. This is even more pronounced with larger wheel sizes (middle and left, size = 1.2). These 3D effects make both odometry and the execution of motion plans very difficult as they involve the full physics of the robot.

Video S2: Emerging geometric pattern. Entering a limit cycle pattern with enabled learning.

Video S3: Emerging behavior by symmetry breaking I. Initially, after about 20 min the robot develops a swaying motion pattern, as if it is very actively trying to move the legs in a coherent way while keeping ground contact.

Video S4: Emerging behavior by symmetry breaking II. 30 min later...

Video S5: Emerging behavior by symmetry breaking III. 20 min later (75 min after start) a raising behavior develops where the trunk is repeatedly being lifted from the ground (standing up).

Video S5: Emerging behavior by symmetry breaking IV. an hour laterr a totter behavior emerges with slow locomotion.

Video S7: External sensors leed to new behavior I. Seesaw motion pattern with forward/backward speed sensor.

Video S8: External sensors leed to new behavior II. Jumping motion pattern emerging with vertical speed sensor.

This document was translated from LATEX by HEVEA.