Learning physics: extrapolation and learning equations

Learning physics: extrapolation and learning equations

In this project, we develop specific machine learning methods for identifying an underlying functional form that gave rise to data.

In particular for mechanical systems which are governed by the laws of physics, if we can learn the actual equations then accurate predictions outside of the domain of the available data can be made, i.e. we are able to extrapolate. Our current approach uses a modified feed-forward network with sine, cosine, identity and multiplicative units (with two terms) and a particular regularization and model selection scheme.


Preprint paper: G. Martius and C. H. Lampert. Extrapolation and learning equations. arXiv 1610.02995. [  arXiv ]
Self-exploration for tendon-driven robots

Self-exploration for tendon-driven robots

In order to test our self-organizing control framework on real and challenging systems, we apply our neural plasticity rule to tendon driven musculosceletal robots such as the Myorobotics arm-shoulder system.

 Check out the videos and the papers below.

Papers: G. Martius, R. Hostettler, A. Knoll, and R. Der. Compliant control for soft robots: emergent behavior of a tendon
G. Martius, R. Hostettler, A. Knoll, and R. Der. Compliant control for soft robots: emergent behavior of a tendon driven anthropomorphic arm. In Proc. IEEE Int. Conf. on Intelligent Robots and Systems (IROS), 2016. in press. [ bib | Supplementary page (videos) | pdf ]

 

Biologically Plausible Synaptic Plasticity

Biologically Plausible Synaptic Plasticity

To find how autonomous behavior and its development can be realized by a brain or an artificial neural network is a fundamental challenge for neuroscience and robotics. Commonly, the self-organized unfolding of behavior is explained by postulating special concepts like internal drives, curiosity, specific reward systems, or selective pressures. We propose a simple, local, and biologically plausible synaptic mechanism that enables an embodied agent to self-organize its individual sensorimotor development without recourse to such higher-level constructs. When applied to robotic systems, a rich spectrum of rhythmic behaviors emerges, ranging from locomotion patterns to spontaneous cooperation between partners. A possible utilization of our novel mechanism in nature would lead to a new understanding of the early stages of sensorimotor development and of leaps in evolution.

Paper: R. Der and G. Martius. Novel plasticity rule can explain the development of sensorimotor intelligence. Proceedings of the National Academy of Sciences, 2015.  . [ bib | DOI | http | arXiv ]
See also the Supplementary page.

 

Quantifying autonomous behavior

Quantifying autonomous behavior

In recent years research in autonomous robots has been more and more successful in developing algorithms for generating behavior from a generic task-independent objective. However, without a specific task it is difficult to evaluate the behavior. The same difficulty is also faced in characterizing the behavior of freely moving animals. Together with Eckehard Olbrich, I investigate methods based on information theoretic quantities that are able to deal with high-dimensional systems. An important feature of our method is to provide a length-scale-dependent quantity. This  allows to isolate the complexity of behavior on the coarse level,  on finer levels and on the noise level. We apply this method to toy examples and data from high-dimensional robotic systems.

Paper: G. Martius and E. Olbrich. Quantifying emergent behavior of autonomous robots. Entropy, 17(10):7266, 2015. [ bib | DOI | http ]
See also the Supplementary page.
Predictive Information Maximization

Predictive Information Maximization

Information theory is a powerful tool to express principles to drive autonomous systems because it is domain invariant and allows for an intuitive interpretation. This paper studies the use of the predictive information (PI), also called excess entropy or effective measure complexity, of the sensorimotor process as a driving force to generate behavior. We study nonlinear and nonstationary systems and introduce the time-local predicting information (TiPI) which allows us to derive exact results together with explicit update rules for the parameters of the controller in the dynamical systems framework. In this way the information principle, formulated at the level of behavior, is translated to the dynamics of the synapses. We underpin our results with a number of case studies with high-dimensional robotic systems. We show the spontaneous cooperativity in a complex physical system with decentralized control. Moreover, a jointly controlled humanoid robot develops a high behavioral variety depending on its physics and the environment it is dynamically embedded into. The behavior can be decomposed into a succession of low-dimensional modes that
increasingly explore the behavior space. This is a promising way to avoid the curse of dimensionality which hinders learning systems to scale well.

Paper: G. Martius, R. Der, and N. Ay. Information driven self-organization of complex robotic behaviors. PLoS ONE, 8(5):e63400, 2013.

Supplementary with videos etc

The Playful Machine

The Playful Machine

Autonomous robots may become our closest companions in the near future. While the technology for physically building such machines is already available today, a problem lies in the generation of the behavior for such complex machines. Nature proposes a solution: young children and higher animals learn to master their complex brain-body systems by playing. Can this be an option for robots? How can a machine be playful? Our work provides answers by developing a general principle—homeokinesis, the dynamical symbiosis between brain, body, and environment—that is shown to drive robots to self- determined, individual development in a playful and obviously embodiment- related way: a dog-like robot starts playing with a barrier, eventually jumping or climbing over it; a snakebot develops coiling and jumping modes; humanoids develop climbing behaviors when fallen into a pit, or engage in wrestling-like scenarios when encountering an opponent.

theplayfulmachine_coverRalf and me wrote a book called “The Playful Machine – Theoretical Foundations and Practical Realization of Self-Organizing Robots” about our research.  The book also contains chapters on guided self-organization, a new method that helps to make the playful machines fit for fulfilling tasks in the real world. The book provides two levels of presentation. Students and scientific researchers interested in the field of robotics, self-organization and dynamical systems theory may be satisfied by the in-depth mathematical analysis of the principle, the bootstrapping scenarios, and the emerging behaviors. But the book additionally comes with a robotics simulator inviting also the non- scientific reader to simply enjoy the fabulous world of playful machines by performing the numerous experiments.

Visit the home page of the book or our group homepage for many videos, publications etc.