Abstract: Embodiment and self-organization (SO) form two cornerstones of both modern robotics and the understanding of human and animal intelligence. While the role of the embodiment for the behavior has become of much and increasing interest in recent times, the attitude of the community toward SO is still characterized by some reservations. These concern on the one hand the question how a robotic system can be made to self-organize its behavior in a systematic and transparent manner. There is some progress in that direction by several objective functions for SO and learning rules derived thereof. Based on general principles, these approaches are domain invariant and free of arbitrariness. However, and this seems to be the main argument, 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 threat than a hope. The aim of this paper is to show that this attitude is not justified. Instead, we (i) show how a system can be made to self-organize its behavior, we (ii) develop an understanding of what happens if the system is self-organizing, highlight (iii) what the role of the embodiment is and give (iv) clues for predicting and shaping the behavior patterns emerging in an SO scenario. The approach is based on a new unsupervised learning rule staging two antagonistic activities---driving systems towards instability while conserving the geometric and physical symmetries of the system as much as possible. This leads to a spontaneous symmetry breaking scenario, the guiding phenomenon of SO known from nature. 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 Braitenberg man. Running motion patttern emerging with minimalistic control: Each joint is controlled individually by a feed back loop with strong negative feedback realized by a single nonlinear "wire". Despite this minimalistic and decentralized control, a stable whole-body motion pattern is emerging by the physical "cross-talk" between the body parts.
Video S2: The two-wheeled robot as a 3D physical object. The ground is elastic so that the wheels are sinking in, depending on their load. 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. These physical effects make both odometry and the execution of motion plans very difficult as they involve the full physics of the robot.
Video S3: Spontaneous symmetry breaking and emerging geometric pattern. One of the patterns emerging by the interplay of the embodiment with the learning dynamics. The pattern is the overlay of the trajectories of several laps. This demonstrates the amazing accuracy in drawing the pattern.
Video S4: Emerging behavior by symmetry breaking. Emerging motion pattern in the bungee scenario if only proprioceptive sensors are used (joint angles). The pattern is an example of minimal symmetry breaking. Synchronization is by the physical cross talk due to the inertia effects. Note that in the first part, speed is 25 times real time.
Video S5: Exterioception helps self-organization. With an additional sensor measuring the rotation velocity of the trunk around its yaw axis, the robot synchronizes its internal motions with the trunk rotation. After a while, the robot learns rotating its entire body around the trunk axis, eventually executing a loop. Note that collisions with the bungee rope are ignored.
Video S6: The whole body nature of the running motion pattern. When learning is started in the running motion pattern (RMP), the learning enhances the RMP mode in the course of time more and more by steadily increasing the step length until the whole motion pattern gets unstable after a long time. The first part of the video shows the result in a late phase with a very large step length. The pattern is interrupted by collisions between the legs but is also recovered readily. This video also shows that the RMP is entirely self-generated. When the bungee force is reduced so that the robot reaches ground, the RMP decays but is resumed rapidly if the conditions of its existence (hanging in air) are reestablished.
Video S7: Motion pattern as broken symmetry. Initially, 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 S8: Jump patterns I. After the swaying mode, jumping is the next more active pattern which is still keeping much of the starting symmetries.
Video S9: Jump patterns II. The robot is now provided with a sensor for the vertical velocity of the trunk. As a result, the pattern is now more controlled.
Video S10: Guidance and reinforcement learning I. By using the vertical velocity of the robot as a reward, we can guide the SO process towards jumping very high.
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Video S11: Guidance and reinforcement learning II. Another example of a sensor driven learning to jump into the forward direction.
More videos
Video S12: The crawling snake. Crawling mode of the snakebot. The mode is excited spontaneously by the universal learning algorithm without any external help. In particular, there is no central pattern generator, the only sensor information the robot gets is from its own joint angles.
Video S13: Switching modes by external influences. When applying forces (the red dot) the snake may switch modes. After the first interaction, a kind of sidewinding mode is established, switched into a forward crawling mode that is pretty stable against external pertubations. In the end, the direction of crawling is inverted reflecting the perfect forward-backward symetry of the snakebot. Note the speed up by a factor of 3.
Video S14: The constitutive role of the agent-environment coupling. The physical coupling between agent and environment (here the contact with the ground) is constitutive for the formation and persistence of the modes. In the video, the gravity is switched off (at time 05:45) so that the robot loses contact with the ground, leading to the rapid decay of the crawling mode. After switching on gravity again, a new mode (kind of sidewinding) is emerging showing that the old mode was completely forgotten.
Video S15: Agent-environment coupling: The fighting hexapods. The agent-environment coupling is most intensive if the environment is dominated by other robots in strong physical contact. When getting in contact, the physical reality of each of the robots is strongly determined by the counteractions of its opponent. In the experiments, the only sensor information the robot gets is from its own joint angles.
Video S16: Agent-environment coupling: the fighting humanoids. Both robots have strong magnets as their hands which are temporarily switched on and off (red color when on). The neural controller is driven by a differential Hebbian learning mechanism endorsed with a synaptic scaling procedure (R. Der, in preparation). The only sensor information each robot gets is from its joint angles which are largely influenced by the interactions with both the opponent and the ground. The gray disks are repellers pushing the robots back into the figthing arena.
Video S17: Hexapod with "armband" robot.
Video S18: Walking-like pattern.
Video S19: Predator's jump.
This document was translated from LATEX by HEVEA.