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2020


Combining learned and analytical models for predicting action effects from sensory data
Combining learned and analytical models for predicting action effects from sensory data

Kloss, A., Schaal, S., Bohg, J.

International Journal of Robotics Research, September 2020 (article)

Abstract
One of the most basic skills a robot should possess is predicting the effect of physical interactions with objects in the environment. This enables optimal action selection to reach a certain goal state. Traditionally, dynamics are approximated by physics-based analytical models. These models rely on specific state representations that may be hard to obtain from raw sensory data, especially if no knowledge of the object shape is assumed. More recently, we have seen learning approaches that can predict the effect of complex physical interactions directly from sensory input. It is however an open question how far these models generalize beyond their training data. In this work, we investigate the advantages and limitations of neural network based learning approaches for predicting the effects of actions based on sensory input and show how analytical and learned models can be combined to leverage the best of both worlds. As physical interaction task, we use planar pushing, for which there exists a well-known analytical model and a large real-world dataset. We propose to use a convolutional neural network to convert raw depth images or organized point clouds into a suitable representation for the analytical model and compare this approach to using neural networks for both, perception and prediction. A systematic evaluation of the proposed approach on a very large real-world dataset shows two main advantages of the hybrid architecture. Compared to a pure neural network, it significantly (i) reduces required training data and (ii) improves generalization to novel physical interaction.

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arXiv pdf link (url) DOI [BibTex]


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Automatic Discovery of Interpretable Planning Strategies

Skirzyński, J., Becker, F., Lieder, F.

Machine Learning Journal, May 2020 (article) Submitted

Abstract
When making decisions, people often overlook critical information or are overly swayed by irrelevant information. A common approach to mitigate these biases is to provide decisionmakers, especially professionals such as medical doctors, with decision aids, such as decision trees and flowcharts. Designing effective decision aids is a difficult problem. We propose that recently developed reinforcement learning methods for discovering clever heuristics for good decision-making can be partially leveraged to assist human experts in this design process. One of the biggest remaining obstacles to leveraging the aforementioned methods for improving human decision-making is that the policies they learn are opaque to people. To solve this problem, we introduce AI-Interpret: a general method for transforming idiosyncratic policies into simple and interpretable descriptions. Our algorithm combines recent advances in imitation learning and program induction with a new clustering method for identifying a large subset of demonstrations that can be accurately described by a simple, high-performing decision rule. We evaluate our new AI-Interpret algorithm and employ it to translate information-acquisition policies discovered through metalevel reinforcement learning. The results of three large behavioral experiments showed that the provision of decision rules as flowcharts significantly improved people’s planning strategies and decisions across three different classes of sequential decision problems. Furthermore, a series of ablation studies confirmed that our AI-Interpret algorithm was critical to the discovery of interpretable decision rules and that it is ready to be applied to other reinforcement learning problems. We conclude that the methods and findings presented in this article are an important step towards leveraging automatic strategy discovery to improve human decision-making.

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Automatic Discovery of Interpretable Planning Strategies The code for our algorithm and the experiments is available Project Page [BibTex]


Physical Variables Underlying Tactile Stickiness during Fingerpad Detachment
Physical Variables Underlying Tactile Stickiness during Fingerpad Detachment

Nam, S., Vardar, Y., Gueorguiev, D., Kuchenbecker, K. J.

Frontiers in Neuroscience, 14(235):1-14, April 2020 (article)

Abstract
One may notice a relatively wide range of tactile sensations even when touching the same hard, flat surface in similar ways. Little is known about the reasons for this variability, so we decided to investigate how the perceptual intensity of light stickiness relates to the physical interaction between the skin and the surface. We conducted a psychophysical experiment in which nine participants actively pressed their finger on a flat glass plate with a normal force close to 1.5 N and detached it after a few seconds. A custom-designed apparatus recorded the contact force vector and the finger contact area during each interaction as well as pre- and post-trial finger moisture. After detaching their finger, participants judged the stickiness of the glass using a nine-point scale. We explored how sixteen physical variables derived from the recorded data correlate with each other and with the stickiness judgments of each participant. These analyses indicate that stickiness perception mainly depends on the pre-detachment pressing duration, the time taken for the finger to detach, and the impulse in the normal direction after the normal force changes sign; finger-surface adhesion seems to build with pressing time, causing a larger normal impulse during detachment and thus a more intense stickiness sensation. We additionally found a strong between-subjects correlation between maximum real contact area and peak pull-off force, as well as between finger moisture and impulse.

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link (url) DOI Project Page [BibTex]


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Advancing Rational Analysis to the Algorithmic Level

Lieder, F., Griffiths, T. L.

Behavioral and Brain Sciences, 43, E27, March 2020 (article)

Abstract
The commentaries raised questions about normativity, human rationality, cognitive architectures, cognitive constraints, and the scope or resource rational analysis (RRA). We respond to these questions and clarify that RRA is a methodological advance that extends the scope of rational modeling to understanding cognitive processes, why they differ between people, why they change over time, and how they could be improved.

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Advancing rational analysis to the algorithmic level DOI [BibTex]

Advancing rational analysis to the algorithmic level DOI [BibTex]


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Learning to Overexert Cognitive Control in a Stroop Task

Bustamante, L., Lieder, F., Musslick, S., Shenhav, A., Cohen, J.

Febuary 2020, Laura Bustamante and Falk Lieder contributed equally to this publication. (article) In revision

Abstract
How do people learn when to allocate how much cognitive control to which task? According to the Learned Value of Control (LVOC) model, people learn to predict the value of alternative control allocations from features of a given situation. This suggests that people may generalize the value of control learned in one situation to other situations with shared features, even when the demands for cognitive control are different. This makes the intriguing prediction that what a person learned in one setting could, under some circumstances, cause them to misestimate the need for, and potentially over-exert control in another setting, even if this harms their performance. To test this prediction, we had participants perform a novel variant of the Stroop task in which, on each trial, they could choose to either name the color (more control-demanding) or read the word (more automatic). However only one of these tasks was rewarded, it changed from trial to trial, and could be predicted by one or more of the stimulus features (the color and/or the word). Participants first learned colors that predicted the rewarded task. Then they learned words that predicted the rewarded task. In the third part of the experiment, we tested how these learned feature associations transferred to novel stimuli with some overlapping features. The stimulus-task-reward associations were designed so that for certain combinations of stimuli the transfer of learned feature associations would incorrectly predict that more highly rewarded task would be color naming, which would require the exertion of control, even though the actually rewarded task was word reading and therefore did not require the engagement of control. Our results demonstrated that participants over-exerted control for these stimuli, providing support for the feature-based learning mechanism described by the LVOC model.

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Learning to Overexert Cognitive Control in a Stroop Task DOI [BibTex]

Learning to Overexert Cognitive Control in a Stroop Task DOI [BibTex]


Learning to Predict Perceptual Distributions of Haptic Adjectives
Learning to Predict Perceptual Distributions of Haptic Adjectives

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

Frontiers in Neurorobotics, 13(116):1-16, Febuary 2020 (article)

Abstract
When humans touch an object with their fingertips, they can immediately describe its tactile properties using haptic adjectives, such as hardness and roughness; however, human perception is subjective and noisy, with significant variation across individuals and interactions. Recent research has worked to provide robots with similar haptic intelligence but was focused on identifying binary haptic adjectives, ignoring both attribute intensity and perceptual variability. Combining ordinal haptic adjective labels gathered from human subjects for a set of 60 objects with features automatically extracted from raw multi-modal tactile data collected by a robot repeatedly touching the same objects, we designed a machine-learning method that incorporates partial knowledge of the distribution of object labels into training; then, from a single interaction, it predicts a probability distribution over the set of ordinal labels. In addition to analyzing the collected labels (10 basic haptic adjectives) and demonstrating the quality of our method's predictions, we hold out specific features to determine the influence of individual sensor modalities on the predictive performance for each adjective. Our results demonstrate the feasibility of modeling both the intensity and the variation of haptic perception, two crucial yet previously neglected components of human haptic perception.

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DOI Project Page [BibTex]


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Exercising with Baxter: Preliminary Support for Assistive Social-Physical Human-Robot Interaction

Fitter, N. T., Mohan, M., Kuchenbecker, K. J., Johnson, M. J.

Journal of NeuroEngineering and Rehabilitation, 17(19), Febuary 2020 (article)

Abstract
Background: The worldwide population of older adults will soon exceed the capacity of assisted living facilities. Accordingly, we aim to understand whether appropriately designed robots could help older adults stay active at home. Methods: Building on related literature as well as guidance from experts in game design, rehabilitation, and physical and occupational therapy, we developed eight human-robot exercise games for the Baxter Research Robot, six of which involve physical human-robot contact. After extensive iteration, these games were tested in an exploratory user study including 20 younger adult and 20 older adult users. Results: Only socially and physically interactive games fell in the highest ranges for pleasantness, enjoyment, engagement, cognitive challenge, and energy level. Our games successfully spanned three different physical, cognitive, and temporal challenge levels. User trust and confidence in Baxter increased significantly between pre- and post-study assessments. Older adults experienced higher exercise, energy, and engagement levels than younger adults, and women rated the robot more highly than men on several survey questions. Conclusions: The results indicate that social-physical exercise with a robot is more pleasant, enjoyable, engaging, cognitively challenging, and energetic than similar interactions that lack physical touch. In addition to this main finding, researchers working in similar areas can build on our design practices, our open-source resources, and the age-group and gender differences that we found.

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DOI Project Page [BibTex]

DOI Project Page [BibTex]


Compensating for Fingertip Size to Render Tactile Cues More Accurately
Compensating for Fingertip Size to Render Tactile Cues More Accurately

Young, E. M., Gueorguiev, D., Kuchenbecker, K. J., Pacchierotti, C.

IEEE Transactions on Haptics, 13(1):144-151, January 2020, Katherine J. Kuchenbecker and Claudio Pacchierotti contributed equally to this publication. (article)

Abstract
Fingertip haptic feedback offers advantages in many applications, including robotic teleoperation, gaming, and training. However, fingertip size and shape vary significantly across humans, making it difficult to design fingertip interfaces and rendering techniques suitable for everyone. This article starts with an existing data-driven haptic rendering algorithm that ignores fingertip size, and it then develops two software-based approaches to personalize this algorithm for fingertips of different sizes using either additional data or geometry. We evaluate our algorithms in the rendering of pre-recorded tactile sensations onto rubber casts of six different fingertips as well as onto the real fingertips of 13 human participants. Results on the casts show that both approaches significantly improve performance, reducing force error magnitudes by an average of 78% with respect to the standard non-personalized rendering technique. Congruent results were obtained for real fingertips, with subjects rating each of the two personalized rendering techniques significantly better than the standard non-personalized method.

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DOI [BibTex]

DOI [BibTex]


Toward a Formal Theory of Proactivity
Toward a Formal Theory of Proactivity

Lieder, F., Iwama, G.

January 2020 (article) Submitted

Abstract
Beyond merely reacting to their environment and impulses, people have the remarkable capacity to proactively set and pursue their own goals. But the extent to which they leverage this capacity varies widely across people and situations. The goal of this article is to make the mechanisms and variability of proactivity more amenable to rigorous experiments and computational modeling. We proceed in three steps. First, we develop and validate a mathematically precise behavioral measure of proactivity and reactivity that can be applied across a wide range of experimental paradigms. Second, we propose a formal definition of proactivity and reactivity, and develop a computational model of proactivity in the AX Continuous Performance Task (AX-CPT). Third, we develop and test a computational-level theory of meta-control over proactivity in the AX-CPT that identifies three distinct meta-decision-making problems: intention setting, resolving response conflict between intentions and automaticity, and deciding whether to recall context and intentions into working memory. People's response frequencies in the AX-CPT were remarkably well captured by a mixture between the predictions of our models of proactive and reactive control. Empirical data from an experiment varying the incentives and contextual load of an AX-CPT confirmed the predictions of our meta-control model of individual differences in proactivity. Our results suggest that proactivity can be understood in terms of computational models of meta-control. Our model makes additional empirically testable predictions. Future work will extend our models from proactive control in the AX-CPT to proactive goal creation and goal pursuit in the real world.

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Toward a formal theory of proactivity DOI Project Page [BibTex]


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Semi-Supervised Learning of Multi-Object 3D Scene Representations

Elich, C., Oswald, M. R., Pollefeys, M., Stueckler, J.

CoRR, abs/2010.04030, 2020 (article)

Abstract
Representing scenes at the granularity of objects is a prerequisite for scene understanding and decision making. We propose a novel approach for learning multi-object 3D scene representations from images. A recurrent encoder regresses a latent representation of 3D shapes, poses and texture of each object from an input RGB image. The 3D shapes are represented continuously in function-space as signed distance functions (SDF) which we efficiently pre-train from example shapes in a supervised way. By differentiable rendering we then train our model to decompose scenes self-supervised from RGB-D images. Our approach learns to decompose images into the constituent objects of the scene and to infer their shape, pose and texture from a single view. We evaluate the accuracy of our model in inferring the 3D scene layout and demonstrate its generative capabilities.

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link (url) [BibTex]

link (url) [BibTex]


Resource-Rational Models of Human Goal Pursuit
Resource-Rational Models of Human Goal Pursuit

Prystawski, B., Mohnert, F., Tošić, M., Lieder, F.

2020 (article)

Abstract
Goal-directed behaviour is a deeply important part of human psychology. People constantly set goals for themselves and pursue them in many domains of life. In this paper, we develop computational models that characterize how humans pursue goals in a complex dynamic environment and test how well they describe human behaviour in an experiment. Our models are motivated by the principle of resource rationality and draw upon psychological insights about people's limited attention and planning capacities. We found that human goal pursuit is qualitatively different and substantially less efficient than optimal goal pursuit. Models of goal pursuit based on the principle of resource rationality captured human behavior better than both a model of optimal goal pursuit and heuristics that are not resource-rational. We conclude that human goal pursuit is jointly shaped by its function, the structure of the environment, and cognitive costs and constraints on human planning and attention. Our findings are an important step toward understanding humans goal pursuit, as cognitive limitations play a crucial role in shaping people's goal-directed behaviour.

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Resource-rational models of human goal pursuit DOI [BibTex]


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Analytical classical density functionals from an equation learning network

Lin, S., Martius, G., Oettel, M.

The Journal of Chemical Physics, 152(2):021102, 2020, arXiv preprint \url{https://arxiv.org/abs/1910.12752} (article)

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Preprint_PDF DOI [BibTex]

Preprint_PDF DOI [BibTex]


Wearable and Stretchable Strain Sensors: Materials, Sensing Mechanisms, and Applications
Wearable and Stretchable Strain Sensors: Materials, Sensing Mechanisms, and Applications

Souri, H., Banerjee, H., Jusufi, A., Radacsi, N., Stokes, A. A., Park, I., Sitti, M., Amjadi, M.

Advanced Intelligent Systems, 2020 (article)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


Getting in Touch with Children with Autism: Specialist Guidelines for a Touch-Perceiving Robot
Getting in Touch with Children with Autism: Specialist Guidelines for a Touch-Perceiving Robot

Burns, R. B., Seifi, H., Lee, H., Kuchenbecker, K. J.

Paladyn. Journal of Behavioral Robotics, 2020 (article) Accepted

Abstract
Children with autism need innovative solutions that help them learn to master everyday experiences and cope with stressful situations. We propose that socially assistive robot companions could better understand and react to a child’s needs if they utilized tactile sensing. We examined the existing relevant literature to create an initial set of six tactile-perception requirements, and we then evaluated these requirements through interviews with 11 experienced autism specialists from a variety of backgrounds. Thematic analysis of the comments shared by the specialists revealed three overarching themes: the touch-seeking and touch-avoiding behavior of autistic children, their individual differences and customization needs, and the roles that a touch-perceiving robot could play in such interactions. Using the interview study feedback, we refined our initial list into seven qualitative requirements that describe robustness and maintainability, sensing range, feel, gesture identification, spatial, temporal, and adaptation attributes for the touch-perception system of a robot companion for children with autism. Lastly, by utilizing the literature and current best practices in tactile sensor development and signal processing, we transformed these qualitative requirements into quantitative specifications. We discuss the implications of these requirements for future HRI research in the sensing, computing, and user research communities.

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Project Page [BibTex]


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Fish-like aquatic propulsion studied using a pneumatically-actuated soft-robotic model

Wolf, Z., Jusufi, A., Vogt, D. M., Lauder, G. V.

Bioinspiration & Biomimetics, 15(4):046008, Inst. of Physics, London, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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Visual-Inertial Mapping with Non-Linear Factor Recovery

Usenko, V., Demmel, N., Schubert, D., Stückler, J., Cremers, D.

IEEE Robotics and Automation Letters (RA-L), 5, 2020, accepted for presentation at IEEE International Conference on Robotics and Automation (ICRA) 2020, to appear, arXiv:1904.06504 (article)

Abstract
Cameras and inertial measurement units are complementary sensors for ego-motion estimation and environment mapping. Their combination makes visual-inertial odometry (VIO) systems more accurate and robust. For globally consistent mapping, however, combining visual and inertial information is not straightforward. To estimate the motion and geometry with a set of images large baselines are required. Because of that, most systems operate on keyframes that have large time intervals between each other. Inertial data on the other hand quickly degrades with the duration of the intervals and after several seconds of integration, it typically contains only little useful information. In this paper, we propose to extract relevant information for visual-inertial mapping from visual-inertial odometry using non-linear factor recovery. We reconstruct a set of non-linear factors that make an optimal approximation of the information on the trajectory accumulated by VIO. To obtain a globally consistent map we combine these factors with loop-closing constraints using bundle adjustment. The VIO factors make the roll and pitch angles of the global map observable, and improve the robustness and the accuracy of the mapping. In experiments on a public benchmark, we demonstrate superior performance of our method over the state-of-the-art approaches.

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Code Preprint [BibTex]

Code Preprint [BibTex]


Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control
Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Nubert, J., Koehler, J., Berenz, V., Allgower, F., Trimpe, S.

IEEE Robotics and Automation Letters, 2020 (article) Accepted

Abstract
Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.

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arXiv PDF DOI [BibTex]

arXiv PDF DOI [BibTex]

2011


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Learning, planning, and control for quadruped locomotion over challenging terrain

Kalakrishnan, Mrinal, Buchli, Jonas, Pastor, Peter, Mistry, Michael, Schaal, S.

International Journal of Robotics Research, 30(2):236-258, February 2011 (article)

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[BibTex]

2011


[BibTex]


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Aerial righting reflexes in flightless animals

Jusufi, A., Zeng, Y., Full, R., Dudley, R.

Integ. Comp. Biol. , 2011 (article)

bio

[BibTex]

[BibTex]


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Bayesian robot system identification with input and output noise

Ting, J., D’Souza, A., Schaal, S.

Neural Networks, 24(1):99-108, 2011, clmc (article)

Abstract
For complex robots such as humanoids, model-based control is highly beneficial for accurate tracking while keeping negative feedback gains low for compliance. However, in such multi degree-of-freedom lightweight systems, conventional identification of rigid body dynamics models using CAD data and actuator models is inaccurate due to unknown nonlinear robot dynamic effects. An alternative method is data-driven parameter estimation, but significant noise in measured and inferred variables affects it adversely. Moreover, standard estimation procedures may give physically inconsistent results due to unmodeled nonlinearities or insufficiently rich data. This paper addresses these problems, proposing a Bayesian system identification technique for linear or piecewise linear systems. Inspired by Factor Analysis regression, we develop a computationally efficient variational Bayesian regression algorithm that is robust to ill-conditioned data, automatically detects relevant features, and identifies input and output noise. We evaluate our approach on rigid body parameter estimation for various robotic systems, achieving an error of up to three times lower than other state-of-the-art machine learning methods

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link (url) [BibTex]

link (url) [BibTex]


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Learning variable impedance control

Buchli, J., Stulp, F., Theodorou, E., Schaal, S.

International Journal of Robotics Research, 2011, clmc (article)

Abstract
One of the hallmarks of the performance, versatility, and robustness of biological motor control is the ability to adapt the impedance of the overall biomechanical system to different task requirements and stochastic disturbances. A transfer of this principle to robotics is desirable, for instance to enable robots to work robustly and safely in everyday human environments. It is, however, not trivial to derive variable impedance controllers for practical high degree-of-freedom (DOF) robotic tasks. In this contribution, we accomplish such variable impedance control with the reinforcement learning (RL) algorithm PISq ({f P}olicy {f I}mprovement with {f P}ath {f I}ntegrals). PISq is a model-free, sampling based learning method derived from first principles of stochastic optimal control. The PISq algorithm requires no tuning of algorithmic parameters besides the exploration noise. The designer can thus fully focus on cost function design to specify the task. From the viewpoint of robotics, a particular useful property of PISq is that it can scale to problems of many DOFs, so that reinforcement learning on real robotic systems becomes feasible. We sketch the PISq algorithm and its theoretical properties, and how it is applied to gain scheduling for variable impedance control. We evaluate our approach by presenting results on several simulated and real robots. We consider tasks involving accurate tracking through via-points, and manipulation tasks requiring physical contact with the environment. In these tasks, the optimal strategy requires both tuning of a reference trajectory emph{and} the impedance of the end-effector. The results show that we can use path integral based reinforcement learning not only for planning but also to derive variable gain feedback controllers in realistic scenarios. Thus, the power of variable impedance control is made available to a wide variety of robotic systems and practical applications.

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link (url) [BibTex]

link (url) [BibTex]


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Understanding haptics by evolving mechatronic systems

Loeb, G. E., Tsianos, G.A., Fishel, J.A., Wettels, N., Schaal, S.

Progress in Brain Research, 192, pages: 129, 2011 (article)

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[BibTex]

[BibTex]


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Intelligent Mobility—Autonomous Outdoor Robotics at the DFKI

Joyeux, S., Schwendner, J., Kirchner, F., Babu, A., Grimminger, F., Machowinski, J., Paranhos, P., Gaudig, C.

KI, 25(2):133-139, May 2011 (article)

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DOI [BibTex]

DOI [BibTex]

1996


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A Kendama learning robot based on bi-directional theory

Miyamoto, H., Schaal, S., Gandolfo, F., Koike, Y., Osu, R., Nakano, E., Wada, Y., Kawato, M.

Neural Networks, 9(8):1281-1302, 1996, clmc (article)

Abstract
A general theory of movement-pattern perception based on bi-directional theory for sensory-motor integration can be used for motion capture and learning by watching in robotics. We demonstrate our methods using the game of Kendama, executed by the SARCOS Dextrous Slave Arm, which has a very similar kinematic structure to the human arm. Three ingredients have to be integrated for the successful execution of this task. The ingredients are (1) to extract via-points from a human movement trajectory using a forward-inverse relaxation model, (2) to treat via-points as a control variable while reconstructing the desired trajectory from all the via-points, and (3) to modify the via-points for successful execution. In order to test the validity of the via-point representation, we utilized a numerical model of the SARCOS arm, and examined the behavior of the system under several conditions.

am

link (url) [BibTex]

1996


link (url) [BibTex]


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One-handed juggling: A dynamical approach to a rhythmic movement task

Schaal, S., Sternad, D., Atkeson, C. G.

Journal of Motor Behavior, 28(2):165-183, 1996, clmc (article)

Abstract
The skill of rhythmic juggling a ball on a racket is investigated from the viewpoint of nonlinear dynamics. The difference equations that model the dynamical system are analyzed by means of local and non-local stability analyses. These analyses yield that the task dynamics offer an economical juggling pattern which is stable even for open-loop actuator motion. For this pattern, two types of pre dictions are extracted: (i) Stable periodic bouncing is sufficiently characterized by a negative acceleration of the racket at the moment of impact with the ball; (ii) A nonlinear scaling relation maps different juggling trajectories onto one topologically equivalent dynamical system. The relevance of these results for the human control of action was evaluated in an experiment where subjects performed a comparable task of juggling a ball on a paddle. Task manipulations involved different juggling heights and gravity conditions of the ball. The predictions were confirmed: (i) For stable rhythmic performance the paddle's acceleration at impact is negative and fluctuations of the impact acceleration follow predictions from global stability analysis; (ii) For each subject, the realizations of juggling for the different experimental conditions are related by the scaling relation. These results allow the conclusion that for the given task, humans reliably exploit the stable solutions inherent to the dynamics of the task and do not overrule these dynamics by other control mechanisms. The dynamical scaling serves as an efficient principle to generate different movement realizations from only a few parameter changes and is discussed as a dynamical formalization of the principle of motor equivalence.

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link (url) [BibTex]

link (url) [BibTex]