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2014


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Pole Balancing with Apollo

Holger Kaden

Eberhard Karls Universität Tübingen, December 2014 (mastersthesis)

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[BibTex]

2014


[BibTex]


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Haptic Robotization of Human Body via Data-Driven Vibrotactile Feedback

Kurihara, Y., Takei, S., Nakai, Y., Hachisu, T., Kuchenbecker, K. J., Kajimoto, H.

Entertainment Computing, 5(4):485-494, December 2014 (article)

hi

[BibTex]

[BibTex]


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Wenn es was zu sagen gibt

(Klaus Tschira Award 2014 in Computer Science)

Trimpe, S.

Bild der Wissenschaft, pages: 20-23, November 2014, (popular science article in German) (article)

am ics

PDF Project Page [BibTex]

PDF Project Page [BibTex]


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Robotics and Neuroscience

Floreano, Dario, Ijspeert, Auke Jan, Schaal, S.

Current Biology, 24(18):R910-R920, sep 2014 (article)

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[BibTex]

[BibTex]


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Learning Coupling Terms for Obstacle Avoidance

Rai, A.

École polytechnique fédérale de Lausanne, August 2014 (mastersthesis)

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Project Page [BibTex]

Project Page [BibTex]


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Object Tracking in Depth Images Using Sigma Point Kalman Filters

Issac, J.

Karlsruhe Institute of Technology, July 2014 (mastersthesis)

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Project Page [BibTex]

Project Page [BibTex]


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Modeling and Rendering Realistic Textures from Unconstrained Tool-Surface Interactions

Culbertson, H., Unwin, J., Kuchenbecker, K. J.

IEEE Transactions on Haptics, 7(3):381-292, July 2014 (article)

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[BibTex]

[BibTex]


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Nonmyopic View Planning for Active Object Classification and Pose Estimation

Atanasov, N., Sankaran, B., Le Ny, J., Pappas, G., Daniilidis, K.

IEEE Transactions on Robotics, May 2014, clmc (article)

Abstract
One of the central problems in computer vision is the detection of semantically important objects and the estimation of their pose. Most of the work in object detection has been based on single image processing and its performance is limited by occlusions and ambiguity in appearance and geometry. This paper proposes an active approach to object detection by controlling the point of view of a mobile depth camera. When an initial static detection phase identifies an object of interest, several hypotheses are made about its class and orientation. The sensor then plans a sequence of viewpoints, which balances the amount of energy used to move with the chance of identifying the correct hypothesis. We formulate an active M-ary hypothesis testing problem, which includes sensor mobility, and solve it using a point-based approximate POMDP algorithm. The validity of our approach is verified through simulation and real-world experiments with the PR2 robot. The results suggest a significant improvement over static object detection

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Web pdf link (url) [BibTex]

Web pdf link (url) [BibTex]


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Data-Driven Grasp Synthesis - A Survey

Bohg, J., Morales, A., Asfour, T., Kragic, D.

IEEE Transactions on Robotics, 30, pages: 289 - 309, IEEE, April 2014 (article)

Abstract
We review the work on data-driven grasp synthesis and the methodologies for sampling and ranking candidate grasps. We divide the approaches into three groups based on whether they synthesize grasps for known, familiar or unknown objects. This structure allows us to identify common object representations and perceptual processes that facilitate the employed data-driven grasp synthesis technique. In the case of known objects, we concentrate on the approaches that are based on object recognition and pose estimation. In the case of familiar objects, the techniques use some form of a similarity matching to a set of previously encountered objects. Finally for the approaches dealing with unknown objects, the core part is the extraction of specific features that are indicative of good grasps. Our survey provides an overview of the different methodologies and discusses open problems in the area of robot grasping. We also draw a parallel to the classical approaches that rely on analytic formulations.

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PDF link (url) DOI Project Page [BibTex]

PDF link (url) DOI Project Page [BibTex]


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Targets-Drives-Means: A declarative approach to dynamic behavior specification with higher usability

Berenz, V., Suzuki, K.

Robotics and Autonomous Systems, 62(4):545-555, 2014 (article)

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link (url) DOI [BibTex]


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Learning objective functions for autonomous motion generation

Kalakrishnan, M.

University of Southern California, University of Southern California, Los Angeles, CA, 2014 (phdthesis)

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Project Page Project Page [BibTex]

Project Page Project Page [BibTex]


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A Limiting Property of the Matrix Exponential

Trimpe, S., D’Andrea, R.

IEEE Transactions on Automatic Control, 59(4):1105-1110, 2014 (article)

am ics

PDF DOI [BibTex]

PDF DOI [BibTex]


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Event-Based State Estimation With Variance-Based Triggering

Trimpe, S., D’Andrea, R.

IEEE Transactions on Automatic Control, 59(12):3266-3281, 2014 (article)

am ics

PDF Supplementary material DOI Project Page [BibTex]

PDF Supplementary material DOI Project Page [BibTex]


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Perspective: Intelligent Systems: Bits and Bots

Spatz, J. P., Schaal, S.

Nature, (509), 2014, clmc (article)

Abstract
What is intelligence, and can we create it? Animals can perceive, reason, react and learn, but they are just one example of an intelligent system. Intelligent systems could be robots as large as humans, helping with search-and- rescue operations in dangerous places, or smart devices as tiny as a cell, delivering drugs to a target within the body. Even computing systems can be intelligent, by perceiving the world, crawling the web and processing â??big dataâ?? to extract and learn from complex information.Understanding not only how intelligence can be reproduced, but also how to build systems that put these ideas into practice, will be a challenge. Small intelligent systems will require new materials and fabrication methods, as well as com- pact information processors and power sources. And for nano-sized systems, the rules change altogether. The laws of physics operate very differently at tiny scales: for a nanorobot, swimming through water is like struggling through treacle.Researchers at the Max Planck Institute for Intelligent Systems have begun to solve these problems by developing new computational methods, experiment- ing with unique robotic systems and fabricating tiny, artificial propellers, like bacterial flagella, to propel nanocreations through their environment.

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PDF link (url) [BibTex]

PDF link (url) [BibTex]


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Data-driven autonomous manipulation

Pastor, P.

University of Southern California, University of Southern California, Los Angeles, CA, 2014 (phdthesis)

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Project Page Project Page [BibTex]

Project Page Project Page [BibTex]


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An autonomous manipulation system based on force control and optimization

Righetti, L., Kalakrishnan, M., Pastor, P., Binney, J., Kelly, J., Voorhies, R. C., Sukhatme, G. S., Schaal, S.

Autonomous Robots, 36(1-2):11-30, January 2014 (article)

Abstract
In this paper we present an architecture for autonomous manipulation. Our approach is based on the belief that contact interactions during manipulation should be exploited to improve dexterity and that optimizing motion plans is useful to create more robust and repeatable manipulation behaviors. We therefore propose an architecture where state of the art force/torque control and optimization-based motion planning are the core components of the system. We give a detailed description of the modules that constitute the complete system and discuss the challenges inherent to creating such a system. We present experimental results for several grasping and manipulation tasks to demonstrate the performance and robustness of our approach.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning of grasp selection based on shape-templates

Herzog, A., Pastor, P., Kalakrishnan, M., Righetti, L., Bohg, J., Asfour, T., Schaal, S.

Autonomous Robots, 36(1-2):51-65, January 2014 (article)

Abstract
The ability to grasp unknown objects still remains an unsolved problem in the robotics community. One of the challenges is to choose an appropriate grasp configuration, i.e., the 6D pose of the hand relative to the object and its finger configuration. In this paper, we introduce an algorithm that is based on the assumption that similarly shaped objects can be grasped in a similar way. It is able to synthesize good grasp poses for unknown objects by finding the best matching object shape templates associated with previously demonstrated grasps. The grasp selection algorithm is able to improve over time by using the information of previous grasp attempts to adapt the ranking of the templates to new situations. We tested our approach on two different platforms, the Willow Garage PR2 and the Barrett WAM robot, which have very different hand kinematics. Furthermore, we compared our algorithm with other grasp planners and demonstrated its superior performance. The results presented in this paper show that the algorithm is able to find good grasp configurations for a large set of unknown objects from a relatively small set of demonstrations, and does improve its performance over time.

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link (url) DOI [BibTex]

2010


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Lack of Discriminatory Function for Endoscopy Skills on a Computer-based Simulator

Kim, S., Spencer, G., Makar, G., Ahmad, N., Jaffe, D., Ginsberg, G., Kuchenbecker, K. J., Kochman, M.

Surgical Endoscopy, 24(12):3008-3015, December 2010 (article)

hi

[BibTex]

2010


[BibTex]


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Identifying the Role of Proprioception in Upper-Limb Prosthesis Control: Studies on Targeted Motion

Blank, A., Okamura, A. M., Kuchenbecker, K. J.

ACM Transactions on Applied Perception, 7(3):1-23, June 2010 (article)

hi

[BibTex]

[BibTex]


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Learning Grasping Points with Shape Context

Bohg, J., Kragic, D.

Robotics and Autonomous Systems, 58(4):362-377, North-Holland Publishing Co., Amsterdam, The Netherlands, The Netherlands, April 2010 (article)

Abstract
This paper presents work on vision based robotic grasping. The proposed method adopts a learning framework where prototypical grasping points are learnt from several examples and then used on novel objects. For representation purposes, we apply the concept of shape context and for learning we use a supervised learning approach in which the classifier is trained with labelled synthetic images. We evaluate and compare the performance of linear and non-linear classifiers. Our results show that a combination of a descriptor based on shape context with a non-linear classification algorithm leads to a stable detection of grasping points for a variety of objects.

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pdf link (url) DOI [BibTex]

pdf link (url) DOI [BibTex]


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Policy learning algorithmis for motor learning (Algorithmen zum automatischen Erlernen von Motorfähigkigkeiten)

Peters, J., Kober, J., Schaal, S.

Automatisierungstechnik, 58(12):688-694, 2010, clmc (article)

Abstract
Robot learning methods which allow au- tonomous robots to adapt to novel situations have been a long standing vision of robotics, artificial intelligence, and cognitive sciences. However, to date, learning techniques have yet to ful- fill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics. If possible, scaling was usually only achieved in precisely pre-structured domains. In this paper, we investigate the ingredients for a general ap- proach policy learning with the goal of an application to motor skill refinement in order to get one step closer towards human- like performance. For doing so, we study two major components for such an approach, i. e., firstly, we study policy learning algo- rithms which can be applied in the general setting of motor skill learning, and, secondly, we study a theoretically well-founded general approach to representing the required control structu- res for task representation and execution.

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link (url) [BibTex]


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A Bayesian approach to nonlinear parameter identification for rigid-body dynamics

Ting, J., DSouza, A., Schaal, S.

Neural Networks, 2010, 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]


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A first optimal control solution for a complex, nonlinear, tendon driven neuromuscular finger model

Theodorou, E. A., Todorov, E., Valero-Cuevas, F.

Proceedings of the ASME 2010 Summer Bioengineering Conference August 30-September 2, 2010, Naples, Florida, USA, 2010, clmc (article)

Abstract
In this work we present the first constrained stochastic op- timal feedback controller applied to a fully nonlinear, tendon driven index finger model. Our model also takes into account an extensor mechanism, and muscle force-length and force-velocity properties. We show this feedback controller is robust to noise and perturbations to the dynamics, while successfully handling the nonlinearities and high dimensionality of the system. By ex- tending prior methods, we are able to approximate physiological realism by ensuring positivity of neural commands and tendon tensions at all timesthus can, for the first time, use the optimal control framework to predict biologically plausible tendon tensions for a nonlinear neuromuscular finger model. METHODS 1 Muscle Model The rigid-body triple pendulum finger model with slightly viscous joints is actuated by Hill-type muscle models. Joint torques are generated by the seven muscles of the index fin-

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PDF [BibTex]

PDF [BibTex]


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Efficient learning and feature detection in high dimensional regression

Ting, J., D’Souza, A., Vijayakumar, S., Schaal, S.

Neural Computation, 22, pages: 831-886, 2010, clmc (article)

Abstract
We present a novel algorithm for efficient learning and feature selection in high- dimensional regression problems. We arrive at this model through a modification of the standard regression model, enabling us to derive a probabilistic version of the well-known statistical regression technique of backfitting. Using the Expectation- Maximization algorithm, along with variational approximation methods to overcome intractability, we extend our algorithm to include automatic relevance detection of the input features. This Variational Bayesian Least Squares (VBLS) approach retains its simplicity as a linear model, but offers a novel statistically robust â??black- boxâ? approach to generalized linear regression with high-dimensional inputs. It can be easily extended to nonlinear regression and classification problems. In particular, we derive the framework of sparse Bayesian learning, e.g., the Relevance Vector Machine, with VBLS at its core, offering significant computational and robustness advantages for this class of methods. We evaluate our algorithm on synthetic and neurophysiological data sets, as well as on standard regression and classification benchmark data sets, comparing it with other competitive statistical approaches and demonstrating its suitability as a drop-in replacement for other generalized linear regression techniques.

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link (url) [BibTex]

link (url) [BibTex]


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Stochastic Differential Dynamic Programming

Theodorou, E., Tassa, Y., Todorov, E.

In the proceedings of American Control Conference (ACC 2010) , 2010, clmc (article)

Abstract
We present a generalization of the classic Differential Dynamic Programming algorithm. We assume the existence of state- and control-dependent process noise, and proceed to derive the second-order expansion of the cost-to-go. Despite having quartic and cubic terms in the initial expression, we show that these vanish, leaving us with the same quadratic structure as standard DDP.

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PDF [BibTex]

PDF [BibTex]


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Learning control in robotics – trajectory-based opitimal control techniques

Schaal, S., Atkeson, C. G.

Robotics and Automation Magazine, 17(2):20-29, 2010, clmc (article)

Abstract
In a not too distant future, robots will be a natural part of daily life in human society, providing assistance in many areas ranging from clinical applications, education and care giving, to normal household environments [1]. It is hard to imagine that all possible tasks can be preprogrammed in such robots. Robots need to be able to learn, either by themselves or with the help of human supervision. Additionally, wear and tear on robots in daily use needs to be automatically compensated for, which requires a form of continuous self-calibration, another form of learning. Finally, robots need to react to stochastic and dynamic environments, i.e., they need to learn how to optimally adapt to uncertainty and unforeseen changes. Robot learning is going to be a key ingredient for the future of autonomous robots. While robot learning covers a rather large field, from learning to perceive, to plan, to make decisions, etc., we will focus this review on topics of learning control, in particular, as it is concerned with learning control in simulated or actual physical robots. In general, learning control refers to the process of acquiring a control strategy for a particular control system and a particular task by trial and error. Learning control is usually distinguished from adaptive control [2] in that the learning system can have rather general optimization objectivesâ??not just, e.g., minimal tracking errorâ??and is permitted to fail during the process of learning, while adaptive control emphasizes fast convergence without failure. Thus, learning control resembles the way that humans and animals acquire new movement strategies, while adaptive control is a special case of learning control that fulfills stringent performance constraints, e.g., as needed in life-critical systems like airplanes. Learning control has been an active topic of research for at least three decades. However, given the lack of working robots that actually use learning components, more work needs to be done before robot learning will make it beyond the laboratory environment. This article will survey some ongoing and past activities in robot learning to assess where the field stands and where it is going. We will largely focus on nonwheeled robots and less on topics of state estimation, as typically explored in wheeled robots [3]â??6], and we emphasize learning in continuous state-action spaces rather than discrete state-action spaces [7], [8]. We will illustrate the different topics of robot learning with examples from our own research with anthropomorphic and humanoid robots.

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link (url) [BibTex]

link (url) [BibTex]


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

Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., Schaal, S.

International Journal of Robotics Research, 30(2):236-258, 2010, clmc (article)

Abstract
We present a control architecture for fast quadruped locomotion over rough terrain. We approach the problem by decomposing it into many sub-systems, in which we apply state-of-the-art learning, planning, optimization, and control techniques to achieve robust, fast locomotion. Unique features of our control strategy include: (1) a system that learns optimal foothold choices from expert demonstration using terrain templates, (2) a body trajectory optimizer based on the Zero- Moment Point (ZMP) stability criterion, and (3) a floating-base inverse dynamics controller that, in conjunction with force control, allows for robust, compliant locomotion over unperceived obstacles. We evaluate the performance of our controller by testing it on the LittleDog quadruped robot, over a wide variety of rough terrains of varying difficulty levels. The terrain that the robot was tested on includes rocks, logs, steps, barriers, and gaps, with obstacle sizes up to the leg length of the robot. We demonstrate the generalization ability of this controller by presenting results from testing performed by an independent external test team on terrain that has never been shown to us.

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]

2007


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Machine Learning of Motor Skills for Robotics

Peters, J.

University of Southern California, Los Angeles, CA, USA, University of Southern California, Los Angeles, CA, USA, 2007, clmc (phdthesis)

Abstract
Autonomous robots that can assist humans in situations of daily life have been a long standing vision of robotics, artificial intelligence, and cognitive sciences. A first step towards this goal is to create robots that can accomplish a multitude of different tasks, triggered by environmental context or higher level instruction. Early approaches to this goal during the heydays of artificial intelligence research in the late 1980s, however, made it clear that an approach purely based on reasoning and human insights would not be able to model all the perceptuomotor tasks that a robot should fulfill. Instead, new hope was put in the growing wake of machine learning that promised fully adaptive control algorithms which learn both by observation and trial-and-error. However, to date, learning techniques have yet to fulfill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics, and usually scaling was only achieved in precisely pre-structured domains. In this thesis, we investigate the ingredients for a general approach to motor skill learning in order to get one step closer towards human-like performance. For doing so, we study two major components for such an approach, i.e., firstly, a theoretically well-founded general approach to representing the required control structures for task representation and execution and, secondly, appropriate learning algorithms which can be applied in this setting. As a theoretical foundation, we first study a general framework to generate control laws for real robots with a particular focus on skills represented as dynamical systems in differential constraint form. We present a point-wise optimal control framework resulting from a generalization of Gauss' principle and show how various well-known robot control laws can be derived by modifying the metric of the employed cost function. The framework has been successfully applied to task space tracking control for holonomic systems for several different metrics on the anthropomorphic SARCOS Master Arm. In order to overcome the limiting requirement of accurate robot models, we first employ learning methods to find learning controllers for task space control. However, when learning to execute a redundant control problem, we face the general problem of the non-convexity of the solution space which can force the robot to steer into physically impossible configurations if supervised learning methods are employed without further consideration. This problem can be resolved using two major insights, i.e., the learning problem can be treated as locally convex and the cost function of the analytical framework can be used to ensure global consistency. Thus, we derive an immediate reinforcement learning algorithm from the expectation-maximization point of view which leads to a reward-weighted regression technique. This method can be used both for operational space control as well as general immediate reward reinforcement learning problems. We demonstrate the feasibility of the resulting framework on the problem of redundant end-effector tracking for both a simulated 3 degrees of freedom robot arm as well as for a simulated anthropomorphic SARCOS Master Arm. While learning to execute tasks in task space is an essential component to a general framework to motor skill learning, learning the actual task is of even higher importance, particularly as this issue is more frequently beyond the abilities of analytical approaches than execution. We focus on the learning of elemental tasks which can serve as the "building blocks of movement generation", called motor primitives. Motor primitives are parameterized task representations based on splines or nonlinear differential equations with desired attractor properties. While imitation learning of parameterized motor primitives is a relatively well-understood problem, the self-improvement by interaction of the system with the environment remains a challenging problem, tackled in the fourth chapter of this thesis. For pursuing this goal, we highlight the difficulties with current reinforcement learning methods, and outline both established and novel algorithms for the gradient-based improvement of parameterized policies. We compare these algorithms in the context of motor primitive learning, and show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm. In conclusion, in this thesis, we have contributed a general framework for analytically computing robot control laws which can be used for deriving various previous control approaches and serves as foundation as well as inspiration for our learning algorithms. We have introduced two classes of novel reinforcement learning methods, i.e., the Natural Actor-Critic and the Reward-Weighted Regression algorithm. These algorithms have been used in order to replace the analytical components of the theoretical framework by learned representations. Evaluations have been performed on both simulated and real robot arms.

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[BibTex]

2007


[BibTex]


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The new robotics - towards human-centered machines

Schaal, S.

HFSP Journal Frontiers of Interdisciplinary Research in the Life Sciences, 1(2):115-126, 2007, clmc (article)

Abstract
Research in robotics has moved away from its primary focus on industrial applications. The New Robotics is a vision that has been developed in past years by our own university and many other national and international research instiutions and addresses how increasingly more human-like robots can live among us and take over tasks where our current society has shortcomings. Elder care, physical therapy, child education, search and rescue, and general assistance in daily life situations are some of the examples that will benefit from the New Robotics in the near future. With these goals in mind, research for the New Robotics has to embrace a broad interdisciplinary approach, ranging from traditional mathematical issues of robotics to novel issues in psychology, neuroscience, and ethics. This paper outlines some of the important research problems that will need to be resolved to make the New Robotics a reality.

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link (url) [BibTex]

link (url) [BibTex]

2006


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Induced Master Motion in Force-Reflecting Teleoperation

Kuchenbecker, K. J., Niemeyer, G.

ASME Journal of Dynamic Systems, Measurement, and Control, 128(4):800-810, December 2006 (article)

hi

[BibTex]

2006


[BibTex]


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Improving Contact Realism Through Event-Based Haptic Feedback

Kuchenbecker, K. J., Fiene, J. P., Niemeyer, G.

IEEE Transactions on Visualization and Computer Graphics, 12(2):219-230, March 2006 (article)

hi

[BibTex]

[BibTex]

1998


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Constructive incremental learning from only local information

Schaal, S., Atkeson, C. G.

Neural Computation, 10(8):2047-2084, 1998, clmc (article)

Abstract
We introduce a constructive, incremental learning system for regression problems that models data by means of spatially localized linear models. In contrast to other approaches, the size and shape of the receptive field of each locally linear model as well as the parameters of the locally linear model itself are learned independently, i.e., without the need for competition or any other kind of communication. Independent learning is accomplished by incrementally minimizing a weighted local cross validation error. As a result, we obtain a learning system that can allocate resources as needed while dealing with the bias-variance dilemma in a principled way. The spatial localization of the linear models increases robustness towards negative interference. Our learning system can be interpreted as a nonparametric adaptive bandwidth smoother, as a mixture of experts where the experts are trained in isolation, and as a learning system which profits from combining independent expert knowledge on the same problem. This paper illustrates the potential learning capabilities of purely local learning and offers an interesting and powerful approach to learning with receptive fields. 

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link (url) [BibTex]

1998


link (url) [BibTex]


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Local adaptive subspace regression

Vijayakumar, S., Schaal, S.

Neural Processing Letters, 7(3):139-149, 1998, clmc (article)

Abstract
Incremental learning of sensorimotor transformations in high dimensional spaces is one of the basic prerequisites for the success of autonomous robot devices as well as biological movement systems. So far, due to sparsity of data in high dimensional spaces, learning in such settings requires a significant amount of prior knowledge about the learning task, usually provided by a human expert. In this paper we suggest a partial revision of the view. Based on empirical studies, we observed that, despite being globally high dimensional and sparse, data distributions from physical movement systems are locally low dimensional and dense. Under this assumption, we derive a learning algorithm, Locally Adaptive Subspace Regression, that exploits this property by combining a dynamically growing local dimensionality reduction technique  as a preprocessing step with a nonparametric learning technique, locally weighted regression, that also learns the region of validity of the regression. The usefulness of the algorithm and the validity of its assumptions are illustrated for a synthetic data set, and for data of the inverse dynamics of human arm movements and an actual 7 degree-of-freedom anthropomorphic robot arm. 

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link (url) [BibTex]

link (url) [BibTex]