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Emperical Interference

Haptic Intelligence

Modern Magnetic Systems

Perceiving Systems

Physical Intelligence

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Bioinspired Autonomous Miniature Robots

Dynamic Locomotion

Embodied Vision

Human Aspects of Machine Learning

Intelligent Control Systems

Learning and Dynamical Systems

Locomotion in Biorobotic and Somatic Systems

Micro, Nano, and Molecular Systems

Movement Generation and Control

Neural Capture and Synthesis

Physics for Inference and Optimization

Organizational Leadership and Diversity

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Robot Learning

Conference Paper

2022

Autonomous Learning

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Autonomous Learning Robotics Article Identifying Terrain Physical Parameters from Vision-Towards Physical-Parameter-Aware Locomotion and Navigation Chen, J., Frey, J., Zhou, R., Miki, T., Martius, G., Hutter, M. IEEE Robotics and Automation Letters, Identifying Terrain Physical Parameters From Vision, 9(11):9279-9286, August 2024 (Published)
Identifying the physical properties of the surrounding environment is essential for robotic locomotion and navigation to deal with non-geometric hazards, such as slippery and deformable terrains. It would be of great benefit for robots to anticipate these extreme physical properties before contact; however, estimating environmental physical parameters from vision is still an open challenge. Animals can achieve this by using their prior experience and knowledge of what they have seen and how it felt. In this work, we propose a cross-modal self-supervised learning framework for vision-based environmental physical parameter estimation, which paves the way for future physical-property-aware locomotion and navigation. We bridge the gap between existing policies trained in simulation and identification of physical terrain parameters from vision. We propose to train a physical decoder in simulation to predict friction and stiffness from multi-modal input. The trained network allows the labeling of real-world images with physical parameters in a self-supervised manner to further train a visual network during deployment, which can densely predict the friction and stiffness from image data. We validate our physical decoder in simulation and the real world using a quadruped ANYmal robot, outperforming an existing baseline method. We show that our visual network can predict the physical properties in indoor and outdoor experiments while allowing fast adaptation to new environments.
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Autonomous Learning Article Sensing multi-directional forces at superresolution using taxel value isoline theory Sun, H., Spiers, A., Lee, H., Fiene, J., Martius, G. Sensing multi-directional forces at superresolution using taxel value isoline theory, August 2024 (Accepted)
Robots can benefit from a good sense of touch to perceive their interaction with the world. However, contacts are complex phenomena that involve tactile sensing devices, contact objects, and the complex directional (normal and shear) force motions in-between. To advance tactile sensor research, we propose a comprehensive theory that unites these components, providing insights for sensor designs, explaining performance drops due to shear forces, and suggesting application scenarios with various contact objects. Our theory, based on sensor isolines, achieves superresolution sensing performance using only a few sensing units, avoiding the need for dense layouts. Through analysis of the sensor perception field and force sensitivity from a structural perspective, along with the influences of contact object sizes, we also explore the effects of different force directions: normal, tangential shear, and radial shear forces. The theoretical model covers all these aspects and predicts a system-level inherent accuracy loss introduced by shear forces compared to pure normal forces. To validate our theory, we developed Barodome, a 3D sensor capable of predicting contact locations and decoupling shear forces from normal forces. The sensor's performance confirms the significant impact of shear forces on performance, alongside normal forces. The observed 0.5 mm drop in the real sensor's performance (normal and shear forces) closely matches the theoretical prediction of 0.33 mm. Overall, our theory offers valuable guidance for future tactile sensor designs, informing various design choices and enhancing the development of advanced robotic touch …
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Autonomous Learning Article PaSTS An Operational Dataset for Domestic Solar Thermal Systems Ebmeier, F., Ludwig, N., Martius, G., Franz, V. H. PaSTS An Operational Dataset for Domestic Solar Thermal Systems, June 2024 (Accepted)
Solar thermal systems play an important role in the decarbonization of the domestic heating sector, yet there exist no publicly available datasets of such systems. Therefore, this paper presents the PaSTS dataset, a unique collection of operational data from domestic Solar Thermal Systems (STS) manufactured by Ritter Energie and marketed under the Paradigma brand. Unlike previous research that primarily relied on simulated or unpublished experimental data, this dataset is derived from the service team at Ritter Energie, offering a realistic reflection of the challenges commonly faced in the field. This paper provides a comprehensive dataset overview, emphasizing its application in anomaly and fault detection tasks within STS and establishes the dataset as the first of its kind. Given the inherent complexities of fault detection in STS, we elaborate on the expert system-based fault detection mechanism currently in …
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Autonomous Learning Article Machine learning of a density functional for anisotropic patchy particles Simon, A., Weimar, J., Martius, G., Oettel, M. Journal of Chemical Theory and Computation, 2024 (Accepted)
Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here we formulate an approach to the Kern-Frenkel model via classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. The density functional is split into a reference part for the orientationally averaged density and an orientational part in mean-field approximation. To bring the orientational part into a kernel form suitable for machine learning techniques, an expansion into orientational invariants and the proper incorporation of single-particle symmetries is formulated. The mean-field kernel is constructed via machine learning on the basis of hard wall simulation data. Results are compared to the well-known random-phase approximation which strongly underestimates the orientational correlations close to the wall. Successes and shortcomings of the mean-field treatment of the orientational part are highlighted and perspectives are given for attaining a full density functional via machine learning.
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Haptic Intelligence Autonomous Learning Empirical Inference Article Minsight: A Fingertip-Sized Vision-Based Tactile Sensor for Robotic Manipulation Andrussow, I., Sun, H., Kuchenbecker, K. J., Martius, G. Advanced Intelligent Systems, 5(8):2300042, August 2023, Inside back cover, DOI: 10.1002/aisy.202370035 (Published)
Intelligent interaction with the physical world requires perceptual abilities beyond vision and hearing; vibrant tactile sensing is essential for autonomous robots to dexterously manipulate unfamiliar objects or safely contact humans. Therefore, robotic manipulators need high-resolution touch sensors that are compact, robust, inexpensive, and efficient. The soft vision-based haptic sensor presented herein is a miniaturized and optimized version of the previously published sensor Insight. Minsight has the size and shape of a human fingertip and uses machine learning methods to output high-resolution maps of 3D contact force vectors at 60 Hz. Experiments confirm its excellent sensing performance, with a mean absolute force error of 0.07 N and contact location error of 0.6 mm across its surface area. Minsight's utility is shown in two robotic tasks on a 3-DoF manipulator. First, closed-loop force control enables the robot to track the movements of a human finger based only on tactile data. Second, the informative value of the sensor output is shown by detecting whether a hard lump is embedded within a soft elastomer with an accuracy of 98\%. These findings indicate that Minsight can give robots the detailed fingertip touch sensing needed for dexterous manipulation and physical human–robot interaction.
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Autonomous Learning Article Offline Diversity Maximization under Imitation Constraints Marin, V., Jin, C., Martius, G., Kolev, P. Reinforcement Learning Journal, Offline Diversity Maximization under Imitation Constraints, 3:1377-1409, July 2023 (Published)
There has been significant recent progress in the area of unsupervised skill discovery, utilizing various information-theoretic objectives as measures of diversity. Despite these advances, challenges remain: current methods require significant online interaction, fail to leverage vast amounts of available task-agnostic data and typically lack a quantitative measure of skill utility. We address these challenges by proposing a principled offline algorithm for unsupervised skill discovery that, in addition to maximizing diversity, ensures that each learned skill imitates state-only expert demonstrations to a certain degree. Our main analytical contribution is to connect Fenchel duality, reinforcement learning, and unsupervised skill discovery to maximize a mutual information objective subject to KL-divergence state occupancy constraints. Furthermore, we demonstrate the effectiveness of our method on the standard offline benchmark D4RL and on a custom offline dataset collected from a 12-DoF quadruped robot for which the policies trained in simulation transfer well to the real robotic system.
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Autonomous Learning Haptic Intelligence Empirical Inference Article Predicting the Force Map of an ERT-Based Tactile Sensor Using Simulation and Deep Networks Lee, H., Sun, H., Park, H., Serhat, G., Javot, B., Martius, G., Kuchenbecker, K. J. IEEE Transactions on Automation Science and Engineering, 20(1):425-439, January 2023 (Published)
Electrical resistance tomography (ERT) can be used to create large-scale soft tactile sensors that are flexible and robust. Good performance requires a fast and accurate mapping from the sensor's sequential voltage measurements to the distribution of force across its surface. However, particularly with multiple contacts, this task is challenging for both previously developed approaches: physics-based modeling and end-to-end data-driven learning. Some promising results were recently achieved using sim-to-real transfer learning, but estimating multiple contact locations and accurate contact forces remains difficult because simulations tend to be less accurate with a high number of contact locations and/or high force. This paper introduces a modular hybrid method that combines simulation data synthesized from an electromechanical finite element model with real measurements collected from a new ERT-based tactile sensor. We use about 290,000 simulated and 90,000 real measurements to train two deep neural networks: the first (Transfer-Net) captures the inevitable gap between simulation and reality, and the second (Recon-Net) reconstructs contact forces from voltage measurements. The number of contacts, contact locations, force magnitudes, and contact diameters are evaluated for a manually collected multi-contact dataset of 150 measurements. Our modular pipeline's results outperform predictions by both a physics-based model and end-to-end learning.
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Autonomous Learning Article Discovering causal relations and equations from data Camps-Valls, G., Gerhardus, A., Ninad, U., Varando, G., Martius, G., Balaguer-Ballester, E., Vinuesa, R., Diaz, E., Zanna, L., Runge, J. Physics Reports, 1044:1-68, 2023
Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws, and principles that are invariant, robust, and causal has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventions on the system under study. With the advent of big data and data-driven methods, the fields of causal and equation discovery have developed and accelerated progress in computer science, physics, statistics, philosophy, and many applied fields. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for data-driven causal and equation discovery, point out connections, and showcase comprehensive case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is revolutionised with the efficient exploitation of observational data and simulations, modern machine learning algorithms and the combination with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.
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Autonomous Learning Article Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition Franca, F. D., Virgolin, M., Kommenda, M., Majumder, M., Cranmer, M., Espada, G., Ingelse, L., Fonseca, A., Landajuela, M., Petersen, B., Glatt, R., Mundhenk, N., Lee, C., Hochhalter, J., Randall, D., Kamienny, P., Zhang, H., Dick, G., Simon, A., Burlacu, B., et al. arXiv, 2023 URL BibTeX

Autonomous Learning Article Guiding the Design of Superresolution Tactile Skins with Taxel Value Isolines Theory Sun, H., Martius, G. Science Robotics, 7(63):eabm0608, February 2022 (Published)
Tactile feedback is essential to make robots more agile and effective in unstructured environments. However, high-resolution tactile skins are not widely available; this is due to the large size of robust sensing units and because many units typically lead to fragility in wiring and to high costs. One route toward high-resolution and robust tactile skins involves the embedding of a few sensor units (taxels) into a flexible surface material and the use of signal processing to achieve sensing with superresolution accuracy. Here, we propose a theory for geometric superresolution to guide the development of tactile sensors of this kind and link it to machine learning techniques for signal processing. This theory is based on sensor isolines and allows us to compute the possible force sensitivity and accuracy in contact position and force magnitude as a spatial quantity before building a sensor. We evaluate the influence of different factors, such as elastic properties of the material, structure design, and transduction methods, using finite element simulations and by implementing real sensors. We empirically determine sensor isolines and validate the theory in two custom-built sensors with 1D and 2D measurement surfaces that use barometric units. Using machine learning methods to infer contact information, our sensors obtain an average superresolution factor of over 100 and 1200, respectively. Our theory can guide future tactile sensor designs and inform various design choices. We propose a theory using taxel value isolines to guide superresolution tactile sensor design and evaluate it empirically.
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Autonomous Learning Haptic Intelligence Article A Soft Thumb-Sized Vision-Based Sensor with Accurate All-Round Force Perception Sun, H., Kuchenbecker, K. J., Martius, G. Nature Machine Intelligence, 4(2):135-145, February 2022 (Published)
Vision-based haptic sensors have emerged as a promising approach to robotic touch due to affordable high-resolution cameras and successful computer-vision techniques. However, their physical design and the information they provide do not yet meet the requirements of real applications. We present a robust, soft, low-cost, vision-based, thumb-sized 3D haptic sensor named Insight: it continually provides a directional force-distribution map over its entire conical sensing surface. Constructed around an internal monocular camera, the sensor has only a single layer of elastomer over-molded on a stiff frame to guarantee sensitivity, robustness, and soft contact. Furthermore, Insight is the first system to combine photometric stereo and structured light using a collimator to detect the 3D deformation of its easily replaceable flexible outer shell. The force information is inferred by a deep neural network that maps images to the spatial distribution of 3D contact force (normal and shear). Insight has an overall spatial resolution of 0.4 mm, force magnitude accuracy around 0.03 N, and force direction accuracy around 5 degrees over a range of 0.03--2 N for numerous distinct contacts with varying contact area. The presented hardware and software design concepts can be transferred to a wide variety of robot parts.
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Autonomous Learning Article Inference of affordances and active motor control in simulated agents Scholz, F., Gumbsch, C., Otte, S., Butz, M. V. Frontiers in Neurobiotics, 16, 2022 (Published) DOI BibTeX

Autonomous Learning Article Inferring Markovian quantum master equations of few-body observables in interacting spin chains Carnazza, F., Carollo, F., Zietlow, D., Andergassen, S., Martius, G., Lesanovsky, I. New Journal of Physics, 24, IOP Publishing, 2022 (Published) DOI BibTeX

Autonomous Learning Article Intelligent problem-solving as integrated hierarchical reinforcement learning Eppe, M., Gumbsch, C., Kerzel, M., Nguyen, P. D. H., Butz, M. V., Wermter, S. Nature Machine Intelligence, 4(1):11-20, 2022 (Published)
According to cognitive psychology and related disciplines, the development of complex problem-solving behaviour in biological agents depends on hierarchical cognitive mechanisms. Hierarchical reinforcement learning is a promising computational approach that may eventually yield comparable problem-solving behaviour in artificial agents and robots. However, so far, the problem-solving abilities of many human and non-human animals are clearly superior to those of artificial systems. Here we propose steps to integrate biologically inspired hierarchical mechanisms to enable advanced problem-solving skills in artificial agents. We first review the literature in cognitive psychology to highlight the importance of compositional abstraction and predictive processing. Then we relate the gained insights with contemporary hierarchical reinforcement learning methods. Interestingly, our results suggest that all identified cognitive mechanisms have been implemented individually in isolated computational architectures, raising the question of why there exists no single unifying architecture that integrates them. As our final contribution, we address this question by providing an integrative perspective on the computational challenges to develop such a unifying architecture. We expect our results to guide the development of more sophisticated cognitively inspired hierarchical machine learning architectures.
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Autonomous Learning Article When to Be Critical? Performance and Evolvability in Different Regimes of Neural Ising Agents Khajehabdollahi, S., Prosi, J., Giannakakis, E., Martius, G., Levina, A. Artificial Life, 28(4):458-478, 2022 (Published) DOI BibTeX

Autonomous Learning Article Falsification of hybrid systems with symbolic reachability analysis and trajectory splicing Bogomolov, B. S., Frehse, G., Gurung, A., Li, D., Martius, G., Ray, R. Nonlinear Analysis: Hybrid Systems, 42:101093, Elsevier, November 2021 (Published) DOI URL BibTeX

Autonomous Motion Autonomous Learning Article How to Train Your Differentiable Filter Kloss, A., Martius, G., Bohg, J. Autonomous Robots, 45(4):561-578, Springer, June 2021 (Published)
In many robotic applications, it is crucial to maintain a belief about the state of a system, which serves as input for planning and decision making and provides feedback during task execution. Bayesian Filtering algorithms address this state estimation problem, but they require models of process dynamics and sensory observations and the respective noise characteristics of these models. Recently, multiple works have demonstrated that these models can be learned by end-to-end training through differentiable versions of recursive filtering algorithms. In this work, we investigate the advantages of differentiable filters (DFs) over both unstructured learning approaches and manually-tuned filtering algorithms, and provide practical guidance to researchers interested in applying such differentiable filters. For this, we implement DFs with four different underlying filtering algorithms and compare them in extensive experiments. Specifically, we (i) evaluate different implementation choices and training approaches, (ii) investigate how well complex models of uncertainty can be learned in DFs, (iii) evaluate the effect of end-to-end training through DFs and (iv) compare the DFs among each other and to unstructured LSTM models.
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Autonomous Learning Article Machine learning time-local generators of open quantum dynamics Mazza, P. P., Zietlow, D., Carollo, F., Andergassen, S., Martius, G., Lesanovsky, I. Physical Review Research, 3(2):023084, April 2021 (Published) pdf DOI BibTeX

Autonomous Learning Article A Reinforcement Learning Approach to View Planning for Automated Inspection Tasks Landgraf, C., Meese, B., Pabst, M., Martius, G., Huber, M. F. Sensors, 21(6):2030, MDPI, 2021 (Published) DOI BibTeX

Autonomous Learning Article Editorial: Complexity and Self-Organization Gershenson, C., Polani, D., Martius, G. Frontiers in Robotics and AI, 8, 2021 DOI URL BibTeX

Autonomous Learning Article Jumping over baselines with new methods to predict activation maps from resting-state fMRI Lacosse, E., Scheffler, K., Lohmann, G., Martius, G. Scientific Reports, 11:3480, Nature Group, 2021 (Published)
Cognitive fMRI research primarily relies on task-averaged responses over many subjects to describe general principles of brain function. Nonetheless, there exists a large variability between subjects that is also reflected in spontaneous brain activity as measured by resting state fMRI (rsfMRI). Leveraging this fact, several recent studies have therefore aimed at predicting task activation from rsfMRI using various machine learning methods within a growing literature on ‘connectome fingerprinting’. In reviewing these results, we found lack of an evaluation against robust baselines that reliably supports a novelty of predictions for this task. On closer examination to reported methods, we found most underperform against trivial baseline model performances based on massive group averaging when whole-cortex prediction is considered. Here we present a modification to published methods that remedies this problem to large extent. Our proposed modification is based on a single-vertex approach that replaces commonly used brain parcellations. We further provide a summary of this model evaluation by characterizing empirical properties of where prediction for this task appears possible, explaining why some predictions largely fail for certain targets. Finally, with these empirical observations we investigate whether individual prediction scores explain individual behavioral differences in a task.
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Autonomous Learning Article Self-tuning serverless task farming using proactive elasticity control Kehrer, S., Zietlow, D., Scheffold, J., Blochinger, W. Cluster Computing, 24(2):799-817, Springer, 2021 (Published) DOI BibTeX

Autonomous Learning Article Autonomous Identification and Goal-Directed Invocation of Event-Predictive Behavioral Primitives Gumbsch, C., Butz, M. V., Martius, G. IEEE Transactions on Cognitive and Developmental Systems, 13(2):298-311, June 2019 (Published)
Voluntary behavior of humans appears to be composed of small, elementary building blocks or behavioral primitives. While this modular organization seems crucial for the learning of complex motor skills and the flexible adaption of behavior to new circumstances, the problem of learning meaningful, compositional abstractions from sensorimotor experiences remains an open challenge. Here, we introduce a computational learning architecture, termed surprise-based behavioral modularization into event-predictive structures (SUBMODES), that explores behavior and identifies the underlying behavioral units completely from scratch. The SUBMODES architecture bootstraps sensorimotor exploration using a self-organizing neural controller. While exploring the behavioral capabilities of its own body, the system learns modular structures that predict the sensorimotor dynamics and generate the associated behavior. In line with recent theories of event perception, the system uses unexpected prediction error signals, i.e., surprise, to detect transitions between successive behavioral primitives. We show that, when applied to two robotic systems with completely different body kinematics, the system manages to learn a variety of complex behavioral primitives. Moreover, after initial self-exploration the system can use its learned predictive models progressively more effectively for invoking model predictive planning and goal-directed control in different tasks and environments.
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Autonomous Learning Article Even Delta-Matroids and the Complexity of Planar Boolean CSPs Kazda, A., Kolmogorov, V., Rolinek, M. ACM Transactions on Algorithms, 15(2):1-33, 2019, Article No. 22 (Published) DOI BibTeX

Autonomous Learning Article Machine Learning for Haptics: Inferring Multi-Contact Stimulation From Sparse Sensor Configuration Sun, H., Martius, G. Frontiers in Neurorobotics, 13:51, 2019
Robust haptic sensation systems are essential for obtaining dexterous robots. Currently, we have solutions for small surface areas such as fingers, but affordable and robust techniques for covering large areas of an arbitrary 3D surface are still missing. Here, we introduce a general machine learning framework to infer multi-contact haptic forces on a 3D robot’s limb surface from internal deformation measured by only a few physical sensors. The general idea of this framework is to predict first the whole surface deformation pattern from the sparsely placed sensors and then to infer number, locations and force magnitudes of unknown contact points. We show how this can be done even if training data can only be obtained for single-contact points using transfer learning at the example of a modified limb of the Poppy robot. With only 10 strain-gauge sensors we obtain a high accuracy also for multiple-contact points. The method can be applied to arbitrarily shaped surfaces and physical sensor types, as long as training data can be obtained.
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Autonomous Learning Article Nonlinear decoding of a complex movie from the mammalian retina Botella-Soler, V., Deny, S., Martius, G., Marre, O., Tkačik, G. PLOS Computational Biology, 14(5):1-27, Public Library of Science, May 2018
Author summary Neurons in the retina transform patterns of incoming light into sequences of neural spikes. We recorded from ∼100 neurons in the rat retina while it was stimulated with a complex movie. Using machine learning regression methods, we fit decoders to reconstruct the movie shown from the retinal output. We demonstrated that retinal code can only be read out with a low error if decoders make use of correlations between successive spikes emitted by individual neurons. These correlations can be used to ignore spontaneous spiking that would, otherwise, cause even the best linear decoders to “hallucinate” nonexistent stimuli. This work represents the first high resolution single-trial full movie reconstruction and suggests a new paradigm for separating spontaneous from stimulus-driven neural activity.
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Autonomous Learning Article Novel plasticity rule can explain the development of sensorimotor intelligence Der, R., Martius, G. Proceedings of the National Academy of Sciences, 112(45):E6224-E6232, 2015
Grounding autonomous behavior in the nervous system is a fundamental challenge for neuroscience. In particular, self-organized behavioral development provides more questions than answers. Are there special functional units for curiosity, motivation, and creativity? This paper argues that these features can be grounded in synaptic plasticity itself, without requiring any higher-level constructs. We propose differential extrinsic plasticity (DEP) as a new synaptic rule for self-learning systems and apply it to a number of complex robotic systems as a test case. Without specifying any purpose or goal, seemingly purposeful and adaptive rhythmic behavior is developed, displaying a certain level of sensorimotor intelligence. These surprising results require no system-specific modifications of the DEP rule. They rather arise from the underlying mechanism of spontaneous symmetry breaking, which is due to the tight brain body environment coupling. The new synaptic rule is biologically plausible and would be an interesting target for neurobiological investigation. We also argue that this neuronal mechanism may have been a catalyst in natural evolution.
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Autonomous Learning Article Information Driven Self-Organization of Complex Robotic Behaviors Martius, G., Der, R., Ay, N. PLoS ONE, 8(5):e63400, Public Library of Science, 2013 DOI URL BibTeX

Autonomous Learning Article Linear combination of one-step predictive information with an external reward in an episodic policy gradient setting: a critical analysis Zahedi, K., Martius, G., Ay, N. Frontiers in Psychology, 4(801), 2013
One of the main challenges in the field of embodied artificial intelligence is the open-ended autonomous learning of complex behaviours. Our approach is to use task-independent, information-driven intrinsic motivation(s) to support task-dependent learning. The work presented here is a preliminary step in which we investigate the predictive information (the mutual information of the past and future of the sensor stream) as an intrinsic drive, ideally supporting any kind of task acquisition. Previous experiments have shown that the predictive information (PI) is a good candidate to support autonomous, open-ended learning of complex behaviours, because a maximisation of the PI corresponds to an exploration of morphology- and environment-dependent behavioural regularities. The idea is that these regularities can then be exploited in order to solve any given task. Three different experiments are presented and their results lead to the conclusion that the linear combination of the one-step PI with an external reward function is not generally recommended in an episodic policy gradient setting. Only for hard tasks a great speed-up can be achieved at the cost of an asymptotic performance lost.
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Autonomous Learning Article Robustness of guided self-organization against sensorimotor disruptions Martius, G. Advances in Complex Systems, 16(02n03):1350001, 2013
Self-organizing processes are crucial for the development of living beings. Practical applications in robots may benefit from the self-organization of behavior, e.g.~to increase fault tolerance and enhance flexibility, provided that external goals can also be achieved. We present results on the guidance of self-organizing control by visual target stimuli and show a remarkable robustness to sensorimotor disruptions. In a proof of concept study an autonomous wheeled robot is learning an object finding and ball-pushing task from scratch within a few minutes in continuous domains. The robustness is demonstrated by the rapid recovery of the performance after severe changes of the sensor configuration.
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Autonomous Learning Article Variants of guided self-organization for robot control Martius, G., Herrmann, J. Theory in Biosci., 131(3):129-137, Springer Berlin / Heidelberg, 2012 DOI URL BibTeX

Autonomous Learning Article A Sensor-Based Learning Algorithm for the Self-Organization of Robot Behavior Hesse, F., Martius, G., Der, R., Herrmann, J. M. Algorithms, 2(1):398-409, 2009
Ideally, sensory information forms the only source of information to a robot. We consider an algorithm for the self-organization of a controller. At short timescales the controller is merely reactive but the parameter dynamics and the acquisition of knowledge by an internal model lead to seemingly purposeful behavior on longer timescales. As a paradigmatic example, we study the simulation of an underactuated snake-like robot. By interacting with the real physical system formed by the robotic hardware and the environment, the controller achieves a sensitive and body-specific actuation of the robot.
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Autonomous Learning Article Rocking Stamper and Jumping Snake from a Dynamical System Approach to Artificial Life Der, R., Hesse, F., Martius, G. Adaptive Behavior, 14(2):105-115, 2006
Dynamical systems offer intriguing possibilities as a substrate for the generation of behavior because of their rich behavioral complexity. However this complexity together with the largely covert relation between the parameters and the behavior of the agent is also the main hindrance in the goal-oriented design of a behavior system. This paper presents a general approach to the self-regulation of dynamical systems so that the design problem is circumvented. We consider the controller (a neural net work) as the mediator for changes in the sensor values over time and define a dynamics for the parameters of the controller by maximizing the dynamical complexity of the sensorimotor loop under the condition that the consequences of the actions taken are still predictable. This very general principle is given a concrete mathematical formulation and is implemented in an extremely robust and versatile algorithm for the parameter dynamics of the controller. We consider two different applications, a mechanical device called the rocking stamper and the ODE simulations of a "snake" with five degrees of freedom. In these and many other examples studied we observed various behavior modes of high dynamical complexity.
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