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2019


Thumb xl screenshot 2019 04 08 at 16.22.00
Effect of Remote Masking on Detection of Electrovibration

Jamalzadeh, M., Güçlü, B., Vardar, Y., Basdogan, C.

In Proceedings of the IEEE World Haptics Conference (WHC), pages: 229-234, Tokyo, Japan, July 2019 (inproceedings)

Abstract
Masking has been used to study human perception of tactile stimuli, including those created on haptic touch screens. Earlier studies have investigated the effect of in-site masking on tactile perception of electrovibration. In this study, we investigated whether it is possible to change detection threshold of electrovibration at fingertip of index finger via remote masking, i.e. by applying a (mechanical) vibrotactile stimulus on the proximal phalanx of the same finger. The masking stimuli were generated by a voice coil (Haptuator). For eight participants, we first measured the detection thresholds for electrovibration at the fingertip and for vibrotactile stimuli at the proximal phalanx. Then, the vibrations on the skin were measured at four different locations on the index finger of subjects to investigate how the mechanical masking stimulus propagated as the masking level was varied. Finally, electrovibration thresholds measured in the presence of vibrotactile masking stimuli. Our results show that vibrotactile masking stimuli generated sub-threshold vibrations around fingertip, and hence did not mechanically interfere with the electrovibration stimulus. However, there was a clear psychophysical masking effect due to central neural processes. Electrovibration absolute threshold increased approximately 0.19 dB for each dB increase in the masking level.

hi

DOI [BibTex]

2019


DOI [BibTex]


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Objective and Subjective Assessment of Algorithms for Reducing Three-Axis Vibrations to One-Axis Vibrations

Park, G., Kuchenbecker, K. J.

In Proceedings of the IEEE World Haptics Conference, pages: 467-472, July 2019 (inproceedings)

Abstract
A typical approach to creating realistic vibrotactile feedback is reducing 3D vibrations recorded by an accelerometer to 1D signals that can be played back on a haptic actuator, but some of the information is often lost in this dimensional reduction process. This paper describes seven representative algorithms and proposes four metrics based on the spectral match, the temporal match, and the average value and the variability of them across 3D rotations. These four performance metrics were applied to four texture recordings, and the method utilizing the discrete fourier transform (DFT) was found to be the best regardless of the sensing axis. We also recruited 16 participants to assess the perceptual similarity achieved by each algorithm in real time. We found the four metrics correlated well with the subjectively rated similarities for the six dimensional reduction algorithms, with the exception of taking the 3D vector magnitude, which was perceived to be good despite its low spectral and temporal match metrics.

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DOI [BibTex]

DOI [BibTex]


Thumb xl screenshot 2019 04 08 at 16.08.19
Fingertip Interaction Metrics Correlate with Visual and Haptic Perception of Real Surfaces

Vardar, Y., Wallraven, C., Kuchenbecker, K. J.

In Proceedings of the IEEE World Haptics Conference (WHC), pages: 395-400, Tokyo, Japan, July 2019 (inproceedings)

Abstract
Both vision and touch contribute to the perception of real surfaces. Although there have been many studies on the individual contributions of each sense, it is still unclear how each modality’s information is processed and integrated. To fill this gap, we investigated the similarity of visual and haptic perceptual spaces, as well as how well they each correlate with fingertip interaction metrics. Twenty participants interacted with ten different surfaces from the Penn Haptic Texture Toolkit by either looking at or touching them and judged their similarity in pairs. By analyzing the resulting similarity ratings using multi-dimensional scaling (MDS), we found that surfaces are similarly organized within the three-dimensional perceptual spaces of both modalities. Also, between-participant correlations were significantly higher in the haptic condition. In a separate experiment, we obtained the contact forces and accelerations acting on one finger interacting with each surface in a controlled way. We analyzed the collected fingertip interaction data in both the time and frequency domains. Our results suggest that the three perceptual dimensions for each modality can be represented by roughness/smoothness, hardness/softness, and friction, and that these dimensions can be estimated by surface vibration power, tap spectral centroid, and kinetic friction coefficient, respectively.

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DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Variational Autoencoders Recover PCA Directions (by Accident)

Rolinek, M., Zietlow, D., Martius, G.

In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2019, June 2019 (inproceedings)

Abstract
The Variational Autoencoder (VAE) is a powerful architecture capable of representation learning and generative modeling. When it comes to learning interpretable (disentangled) representations, VAE and its variants show unparalleled performance. However, the reasons for this are unclear, since a very particular alignment of the latent embedding is needed but the design of the VAE does not encourage it in any explicit way. We address this matter and offer the following explanation: the diagonal approximation in the encoder together with the inherent stochasticity force local orthogonality of the decoder. The local behavior of promoting both reconstruction and orthogonality matches closely how the PCA embedding is chosen. Alongside providing an intuitive understanding, we justify the statement with full theoretical analysis as well as with experiments.

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arXiv [BibTex]

arXiv [BibTex]


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Internal Array Electrodes Improve the Spatial Resolution of Soft Tactile Sensors Based on Electrical Resistance Tomography

Lee, H., Park, K., Kim, J., Kuchenbecker, K. J.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 5411-5417, Montreal, Canada, May 2019, Hyosang Lee and Kyungseo Park contributed equally to this publication (inproceedings)

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link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Haptipedia: Accelerating Haptic Device Discovery to Support Interaction & Engineering Design

Seifi, H., Fazlollahi, F., Oppermann, M., Sastrillo, J. A., Ip, J., Agrawal, A., Park, G., Kuchenbecker, K. J., MacLean, K. E.

In Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems (CHI), Glasgow, Scotland, May 2019 (inproceedings)

Abstract
Creating haptic experiences often entails inventing, modifying, or selecting specialized hardware. However, experience designers are rarely engineers, and 30 years of haptic inventions are buried in a fragmented literature that describes devices mechanically rather than by potential purpose. We conceived of Haptipedia to unlock this trove of examples: Haptipedia presents a device corpus for exploration through metadata that matter to both device and experience designers. It is a taxonomy of device attributes that go beyond physical description to capture potential utility, applied to a growing database of 105 grounded force-feedback devices, and accessed through a public visualization that links utility to morphology. Haptipedia's design was driven by both systematic review of the haptic device literature and rich input from diverse haptic designers. We describe Haptipedia's reception (including hopes it will redefine device reporting standards) and our plans for its sustainability through community participation.

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Project Page [BibTex]

Project Page [BibTex]


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Improving Haptic Adjective Recognition with Unsupervised Feature Learning

Richardson, B. A., Kuchenbecker, K. J.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 3804-3810, Montreal, Canada, May 2019 (inproceedings)

Abstract
Humans can form an impression of how a new object feels simply by touching its surfaces with the densely innervated skin of the fingertips. Many haptics researchers have recently been working to endow robots with similar levels of haptic intelligence, but these efforts almost always employ hand-crafted features, which are brittle, and concrete tasks, such as object recognition. We applied unsupervised feature learning methods, specifically K-SVD and Spatio-Temporal Hierarchical Matching Pursuit (ST-HMP), to rich multi-modal haptic data from a diverse dataset. We then tested the learned features on 19 more abstract binary classification tasks that center on haptic adjectives such as smooth and squishy. The learned features proved superior to traditional hand-crafted features by a large margin, almost doubling the average F1 score across all adjectives. Additionally, particular exploratory procedures (EPs) and sensor channels were found to support perception of certain haptic adjectives, underlining the need for diverse interactions and multi-modal haptic data.

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link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


Thumb xl screenshot 2019 02 03 at 19.15.13
A Novel Texture Rendering Approach for Electrostatic Displays

Fiedler, T., Vardar, Y.

In Proceedings of International Workshop on Haptic and Audio Interaction Design (HAID), Lille, France, March 2019 (inproceedings)

Abstract
Generating realistic texture feelings on tactile displays using data-driven methods has attracted a lot of interest in the last decade. However, the need for large data storages and transmission rates complicates the use of these methods for the future commercial displays. In this paper, we propose a new texture rendering approach which can compress the texture data signicantly for electrostatic displays. Using three sample surfaces, we first explain how to record, analyze and compress the texture data, and render them on a touchscreen. Then, through psychophysical experiments conducted with nineteen participants, we show that the textures can be reproduced by a signicantly less number of frequency components than the ones in the original signal without inducing perceptual degradation. Moreover, our results indicate that the possible degree of compression is affected by the surface properties.

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Fiedler19-HAID-Electrostatic [BibTex]

Fiedler19-HAID-Electrostatic [BibTex]

2018


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Deep Reinforcement Learning for Event-Triggered Control

Baumann, D., Zhu, J., Martius, G., Trimpe, S.

In Proceedings of the 57th IEEE International Conference on Decision and Control (CDC), pages: 943-950, 57th IEEE International Conference on Decision and Control (CDC), December 2018 (inproceedings)

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arXiv PDF DOI Project Page Project Page [BibTex]

2018


arXiv PDF DOI Project Page Project Page [BibTex]


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L4: Practical loss-based stepsize adaptation for deep learning

Rolinek, M., Martius, G.

In Advances in Neural Information Processing Systems 31 (NeurIPS 2018), pages: 6434-6444, (Editors: S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett), Curran Associates, Inc., 2018 (inproceedings)

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Github link (url) Project Page [BibTex]

Github link (url) Project Page [BibTex]


Thumb xl publication alife 2018
Systematic self-exploration of behaviors for robots in a dynamical systems framework

Pinneri, C., Martius, G.

In Proc. Artificial Life XI, pages: 319-326, MIT Press, Cambridge, MA, 2018 (inproceedings)

Abstract
One of the challenges of this century is to understand the neural mechanisms behind cognitive control and learning. Recent investigations propose biologically plausible synaptic mechanisms for self-organizing controllers, in the spirit of Hebbian learning. In particular, differential extrinsic plasticity (DEP) [Der and Martius, PNAS 2015], has proven to enable embodied agents to self-organize their individual sensorimotor development, and generate highly coordinated behaviors during their interaction with the environment. These behaviors are attractors of a dynamical system. In this paper, we use the DEP rule to generate attractors and we combine it with a “repelling potential” which allows the system to actively explore all its attractor behaviors in a systematic way. With a view to a self-determined exploration of goal-free behaviors, our framework enables switching between different motion patterns in an autonomous and sequential fashion. Our algorithm is able to recover all the attractor behaviors in a toy system and it is also effective in two simulated environments. A spherical robot discovers all its major rolling modes and a hexapod robot learns to locomote in 50 different ways in 30min.

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link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Learning equations for extrapolation and control

Sahoo, S. S., Lampert, C. H., Martius, G.

In Proc. 35th International Conference on Machine Learning, ICML 2018, Stockholm, Sweden, 2018, 80, pages: 4442-4450, http://proceedings.mlr.press/v80/sahoo18a/sahoo18a.pdf, (Editors: Dy, Jennifer and Krause, Andreas), PMLR, 2018 (inproceedings)

Abstract
We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.

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Code Arxiv Poster Slides link (url) Project Page [BibTex]

Code Arxiv Poster Slides link (url) Project Page [BibTex]


Thumb xl sab
Robust Affordable 3D Haptic Sensation via Learning Deformation Patterns

Sun, H., Martius, G.

Proceedings International Conference on Humanoid Robots, pages: 846-853, IEEE, New York, NY, USA, 2018 IEEE-RAS International Conference on Humanoid Robots, 2018, Oral Presentation (conference)

Abstract
Haptic sensation is an important modality for interacting with the real world. This paper proposes a general framework of inferring haptic forces on the surface of a 3D structure from internal deformations using a small number of physical sensors instead of employing dense sensor arrays. Using machine learning techniques, we optimize the sensor number and their placement and are able to obtain high-precision force inference for a robotic limb using as few as 9 sensors. For the optimal and sparse placement of the measurement units (strain gauges), we employ data-driven methods based on data obtained by finite element simulation. We compare data-driven approaches with model-based methods relying on geometric distance and information criteria such as Entropy and Mutual Information. We validate our approach on a modified limb of the “Poppy” robot [1] and obtain 8 mm localization precision.

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DOI Project Page [BibTex]

DOI Project Page [BibTex]

2017


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Synchronicity Trumps Mischief in Rhythmic Human-Robot Social-Physical Interaction

Fitter, N. T., Kuchenbecker, K. J.

In Proceedings of the International Symposium on Robotics Research (ISRR), Puerto Varas, Chile, December 2017 (inproceedings) In press

Abstract
Hand-clapping games and other forms of rhythmic social-physical interaction might help foster human-robot teamwork, but the design of such interactions has scarcely been explored. We leveraged our prior work to enable the Rethink Robotics Baxter Research Robot to competently play one-handed tempo-matching hand-clapping games with a human user. To understand how such a robot’s capabilities and behaviors affect user perception, we created four versions of this interaction: the hand clapping could be initiated by either the robot or the human, and the non-initiating partner could be either cooperative, yielding synchronous motion, or mischievously uncooperative. Twenty adults tested two clapping tempos in each of these four interaction modes in a random order, rating every trial on standardized scales. The study results showed that having the robot initiate the interaction gave it a more dominant perceived personality. Despite previous results on the intrigue of misbehaving robots, we found that moving synchronously with the robot almost always made the interaction more enjoyable, less mentally taxing, less physically demanding, and lower effort for users than asynchronous interactions caused by robot or human mischief. Taken together, our results indicate that cooperative rhythmic social-physical interaction has the potential to strengthen human-robot partnerships.

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[BibTex]

2017


[BibTex]


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Stiffness Perception during Pinching and Dissection with Teleoperated Haptic Forceps

Ng, C., Zareinia, K., Sun, Q., Kuchenbecker, K. J.

In Proceedings of the International Symposium on Robot and Human Interactive Communication (RO-MAN), pages: 456-463, Lisbon, Portugal, August 2017 (inproceedings)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Design of a Parallel Continuum Manipulator for 6-DOF Fingertip Haptic Display

Young, E. M., Kuchenbecker, K. J.

In Proceedings of the IEEE World Haptics Conference (WHC), pages: 599-604, Munich, Germany, June 2017, Finalist for best poster paper (inproceedings)

Abstract
Despite rapid advancements in the field of fingertip haptics, rendering tactile cues with six degrees of freedom (6 DOF) remains an elusive challenge. In this paper, we investigate the potential of displaying fingertip haptic sensations with a 6-DOF parallel continuum manipulator (PCM) that mounts to the user's index finger and moves a contact platform around the fingertip. Compared to traditional mechanisms composed of rigid links and discrete joints, PCMs have the potential to be strong, dexterous, and compact, but they are also more complicated to design. We define the design space of 6-DOF parallel continuum manipulators and outline a process for refining such a device for fingertip haptic applications. Following extensive simulation, we obtain 12 designs that meet our specifications, construct a manually actuated prototype of one such design, and evaluate the simulation's ability to accurately predict the prototype's motion. Finally, we demonstrate the range of deliverable fingertip tactile cues, including a normal force into the finger and shear forces tangent to the finger at three extreme points on the boundary of the fingertip.

hi

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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High Magnitude Unidirectional Haptic Force Display Using a Motor/Brake Pair and a Cable

Hu, S., Kuchenbecker, K. J.

In Proceedings of the IEEE World Haptics Conference (WHC), pages: 394-399, Munich, Germany, June 2017 (inproceedings)

Abstract
Clever electromechanical design is required to make the force feedback delivered by a kinesthetic haptic interface both strong and safe. This paper explores a onedimensional haptic force display that combines a DC motor and a magnetic particle brake on the same shaft. Rather than a rigid linkage, a spooled cable connects the user to the actuators to enable a large workspace, reduce the moving mass, and eliminate the sticky residual force from the brake. This design combines the high torque/power ratio of the brake and the active output capabilities of the motor to provide a wider range of forces than can be achieved with either actuator alone. A prototype of this device was built, its performance was characterized, and it was used to simulate constant force sources and virtual springs and dampers. Compared to the conventional design of using only a motor, the hybrid device can output higher unidirectional forces at the expense of free space feeling less free.

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DOI Project Page [BibTex]

DOI Project Page [BibTex]


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A Wrist-Squeezing Force-Feedback System for Robotic Surgery Training

Brown, J. D., Fernandez, J. N., Cohen, S. P., Kuchenbecker, K. J.

In Proceedings of the IEEE World Haptics Conference (WHC), pages: 107-112, Munich, Germany, June 2017 (inproceedings)

Abstract
Over time, surgical trainees learn to compensate for the lack of haptic feedback in commercial robotic minimally invasive surgical systems. Incorporating touch cues into robotic surgery training could potentially shorten this learning process if the benefits of haptic feedback were sustained after it is removed. In this paper, we develop a wrist-squeezing haptic feedback system and evaluate whether it holds the potential to train novice da Vinci users to reduce the force they exert on a bimanual inanimate training task. Subjects were randomly divided into two groups according to a multiple baseline experimental design. Each of the ten participants moved a ring along a curved wire nine times while the haptic feedback was conditionally withheld, provided, and withheld again. The realtime tactile feedback of applied force magnitude significantly reduced the integral of the force produced by the da Vinci tools on the task materials, and this result remained even when the haptic feedback was removed. Overall, our findings suggest that wrist-squeezing force feedback can play an essential role in helping novice trainees learn to minimize the force they exert with a surgical robot.

hi

DOI [BibTex]

DOI [BibTex]


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Handling Scan-Time Parameters in Haptic Surface Classification

Burka, A., Kuchenbecker, K. J.

In Proceedings of the IEEE World Haptics Conference (WHC), pages: 424-429, Munich, Germany, June 2017 (inproceedings)

hi

DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Proton 2: Increasing the Sensitivity and Portability of a Visuo-haptic Surface Interaction Recorder

Burka, A., Rajvanshi, A., Allen, S., Kuchenbecker, K. J.

In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pages: 439-445, Singapore, May 2017 (inproceedings)

Abstract
The Portable Robotic Optical/Tactile ObservatioN PACKage (PROTONPACK, or Proton for short) is a new handheld visuo-haptic sensing system that records surface interactions. We previously demonstrated system calibration and a classification task using external motion tracking. This paper details improvements in surface classification performance and removal of the dependence on external motion tracking, necessary before embarking on our goal of gathering a vast surface interaction dataset. Two experiments were performed to refine data collection parameters. After adjusting the placement and filtering of the Proton's high-bandwidth accelerometers, we recorded interactions between two differently-sized steel tooling ball end-effectors (diameter 6.35 and 9.525 mm) and five surfaces. Using features based on normal force, tangential force, end-effector speed, and contact vibration, we trained multi-class SVMs to classify the surfaces using 50 ms chunks of data from each end-effector. Classification accuracies of 84.5% and 91.5% respectively were achieved on unseen test data, an improvement over prior results. In parallel, we pursued on-board motion tracking, using the Proton's camera and fiducial markers. Motion tracks from the external and onboard trackers agree within 2 mm and 0.01 rad RMS, and the accuracy decreases only slightly to 87.7% when using onboard tracking for the 9.525 mm end-effector. These experiments indicate that the Proton 2 is ready for portable data collection.

hi

DOI Project Page [BibTex]

DOI Project Page [BibTex]

2014


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Self-Exploration of the Stumpy Robot with Predictive Information Maximization

Martius, G., Jahn, L., Hauser, H., V. Hafner, V.

In Proc. From Animals to Animats, SAB 2014, 8575, pages: 32-42, LNCS, Springer, 2014 (inproceedings)

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[BibTex]

2014


[BibTex]

2012


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The Playful Machine - Theoretical Foundation and Practical Realization of Self-Organizing Robots

Der, R., Martius, G.

Springer, Berlin Heidelberg, 2012 (book)

Abstract
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? The book 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. The book also develops guided self-organization, a new method that helps to make the playful machines fit for fulfilling tasks in the real world.

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link (url) [BibTex]

2008


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Emergence of Interaction Among Adaptive Agents

Martius, G., Nolfi, S., Herrmann, J. M.

In Proc. From Animals to Animats 10 (SAB 2008), 5040, pages: 457-466, LNCS, Springer, 2008 (inproceedings)

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DOI [BibTex]

2008


DOI [BibTex]


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Structure from Behavior in Autonomous Agents

Martius, G., Fiedler, K., Herrmann, J.

In Proc. IEEE Intl. Conf. Intelligent Robots and Systems (IROS 2008), pages: 858 - 862, 2008 (inproceedings)

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DOI [BibTex]

DOI [BibTex]

2007


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Guided Self-organisation for Autonomous Robot Development

Martius, G., Herrmann, J. M., Der, R.

In Advances in Artificial Life 9th European Conference, ECAL 2007, 4648, pages: 766-775, LNCS, Springer, 2007 (inproceedings)

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[BibTex]

2007


[BibTex]

2006


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Let It Roll – Emerging Sensorimotor Coordination in a Spherical Robot

Der, R., Martius, G., Hesse, F.

In Proc, Artificial Life X, pages: 192-198, Intl. Society for Artificial Life, MIT Press, August 2006 (inproceedings)

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[BibTex]

2006


[BibTex]


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From Motor Babbling to Purposive Actions: Emerging Self-exploration in a Dynamical Systems Approach to Early Robot Development

Der, R., Martius, G.

In Proc. From Animals to Animats 9, SAB 2006, 4095, pages: 406-421, LNCS, Springer, 2006 (inproceedings)

Abstract
Self-organization and the phenomenon of emergence play an essential role in living systems and form a challenge to artificial life systems. This is not only because systems become more lifelike, but also since self-organization may help in reducing the design efforts in creating complex behavior systems. The present paper studies self-exploration based on a general approach to the self-organization of behavior, which has been developed and tested in various examples in recent years. This is a step towards autonomous early robot development. We consider agents under the close sensorimotor coupling paradigm with a certain cognitive ability realized by an internal forward model. Starting from tabula rasa initial conditions we overcome the bootstrapping problem and show emerging self-exploration. Apart from that, we analyze the effect of limited actions, which lead to deprivation of the world model. We show that our paradigm explicitly avoids this by producing purposive actions in a natural way. Examples are given using a simulated simple wheeled robot and a spherical robot driven by shifting internal masses.

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[BibTex]

[BibTex]

2005


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Learning to Feel the Physics of a Body

Der, R., Hesse, F., Martius, G.

In Computational Intelligence for Modelling, Control and Automation, CIMCA 2005 , 2, pages: 252-257, Washington, DC, USA, 2005 (inproceedings)

Abstract
Despite the tremendous progress in robotic hardware and in both sensorial and computing efficiencies the performance of contemporary autonomous robots is still far below that of simple animals. This has triggered an intensive search for alternative approaches to the control of robots. The present paper exemplifies a general approach to the self-organization of behavior which has been developed and tested in various examples in recent years. We apply this approach to an underactuated snake like artifact with a complex physical behavior which is not known to the controller. Due to the weak forces available, the controller so to say has to develop a kind of feeling for the body which is seen to emerge from our approach in a natural way with meandering and rotational collective modes being observed in computer simulation experiments.

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[BibTex]

2005


[BibTex]