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2014


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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]

2014


PDF link (url) [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]

2013


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3-D Object Reconstruction of Symmetric Objects by Fusing Visual and Tactile Sensing

Illonen, J., Bohg, J., Kyrki, V.

The International Journal of Robotics Research, 33(2):321-341, Sage, October 2013 (article)

Abstract
In this work, we propose to reconstruct a complete 3-D model of an unknown object by fusion of visual and tactile information while the object is grasped. Assuming the object is symmetric, a first hypothesis of its complete 3-D shape is generated. A grasp is executed on the object with a robotic manipulator equipped with tactile sensors. Given the detected contacts between the fingers and the object, the initial full object model including the symmetry parameters can be refined. This refined model will then allow the planning of more complex manipulation tasks. The main contribution of this work is an optimal estimation approach for the fusion of visual and tactile data applying the constraint of object symmetry. The fusion is formulated as a state estimation problem and solved with an iterative extended Kalman filter. The approach is validated experimentally using both artificial and real data from two different robotic platforms.

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Web DOI Project Page [BibTex]

2013


Web DOI Project Page [BibTex]


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Quasi-Newton Methods: A New Direction

Hennig, P., Kiefel, M.

Journal of Machine Learning Research, 14(1):843-865, March 2013 (article)

Abstract
Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newton methods can be interpreted as approximations of Bayesian linear regression under varying prior assumptions. This new notion elucidates some shortcomings of classical algorithms, and lights the way to a novel nonparametric quasi-Newton method, which is able to make more efficient use of available information at computational cost similar to its predecessors.

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website+code pdf link (url) [BibTex]

website+code pdf link (url) [BibTex]


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Analytical probabilistic modeling for radiation therapy treatment planning

Bangert, M., Hennig, P., Oelfke, U.

Physics in Medicine and Biology, 58(16):5401-5419, 2013 (article)

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PDF DOI [BibTex]

PDF DOI [BibTex]


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Optimal control of reaching includes kinematic constraints

Mistry, M., Theodorou, E., Schaal, S., Kawato, M.

Journal of Neurophysiology, 2013, clmc (article)

Abstract
We investigate adaptation under a reaching task with an acceleration-based force field perturbation designed to alter the nominal straight hand trajectory in a potentially benign manner:pushing the hand of course in one direction before subsequently restoring towards the target. In this particular task, an explicit strategy to reduce motor effort requires a distinct deviation from the nominal rectilinear hand trajectory. Rather, our results display a clear directional preference during learning, as subjects adapted perturbed curved trajectories towards their initial baselines. We model this behavior using the framework of stochastic optimal control theory and an objective function that trades-of the discordant requirements of 1) target accuracy, 2) motor effort, and 3) desired trajectory. Our work addresses the underlying objective of a reaching movement, and we suggest that robustness, particularly against internal model uncertainly, is as essential to the reaching task as terminal accuracy and energy effciency.

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PDF [BibTex]

PDF [BibTex]


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Dynamical Movement Primitives: Learning Attractor Models for Motor Behaviors

Ijspeert, A., Nakanishi, J., Pastor, P., Hoffmann, H., Schaal, S.

Neural Computation, (25):328-373, 2013, clmc (article)

Abstract
Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by meansof a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.

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link (url) [BibTex]

link (url) [BibTex]


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Optimal distribution of contact forces with inverse-dynamics control

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S.

The International Journal of Robotics Research, 32(3):280-298, March 2013 (article)

Abstract
The development of legged robots for complex environments requires controllers that guarantee both high tracking performance and compliance with the environment. More specifically the control of the contact interaction with the environment is of crucial importance to ensure stable, robust and safe motions. In this contribution we develop an inverse-dynamics controller for floating-base robots under contact constraints that can minimize any combination of linear and quadratic costs in the contact constraints and the commands. Our main result is the exact analytical derivation of the controller. Such a result is particularly relevant for legged robots as it allows us to use torque redundancy to directly optimize contact interactions. For example, given a desired locomotion behavior, we can guarantee the minimization of contact forces to reduce slipping on difficult terrains while ensuring high tracking performance of the desired motion. The main advantages of the controller are its simplicity, computational efficiency and robustness to model inaccuracies. We present detailed experimental results on simulated humanoid and quadruped robots as well as a real quadruped robot. The experiments demonstrate that the controller can greatly improve the robustness of locomotion of the robots.1

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2012


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Entropy Search for Information-Efficient Global Optimization

Hennig, P., Schuler, C.

Journal of Machine Learning Research, 13, pages: 1809-1837, -, June 2012 (article)

Abstract
Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum. The reason for the absence of probabilistic global optimizers is that the corresponding inference problem is intractable in several ways. This paper develops desiderata for probabilistic optimization algorithms, then presents a concrete algorithm which addresses each of the computational intractabilities with a sequence of approximations and explicitly adresses the decision problem of maximizing information gain from each evaluation.

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PDF Web Project Page [BibTex]

2012


PDF Web Project Page [BibTex]


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From Dynamic Movement Primitives to Associative Skill Memories

Pastor, P., Kalakrishnan, M., Meier, F., Stulp, F., Buchli, J., Theodorou, E., Schaal, S.

Robotics and Autonomous Systems, 2012 (article)

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Project Page [BibTex]

Project Page [BibTex]


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Model-free reinforcement learning of impedance control in stochastic environments

Stulp, Freek, Buchli, Jonas, Ellmer, Alice, Mistry, Michael, Theodorou, Evangelos A., Schaal, S.

Autonomous Mental Development, IEEE Transactions on, 4(4):330-341, 2012 (article)

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[BibTex]

[BibTex]


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Reinforcement Learning with Sequences of Motion Primitives for Robust Manipulation

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

IEEE Transactions on Robotics, 2012 (article)

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[BibTex]

[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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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]

2010


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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]

2009


Valero-Cuevas, F., Hoffmann, H., Kurse, M. U., Kutch, J. J., Theodorou, E. A.

IEEE Reviews in Biomedical Engineering – (All authors have equally contributed), (2):110?135, 2009, clmc (article)

Abstract
Computational models of the neuromuscular system hold the potential to allow us to reach a deeper understanding of neuromuscular function and clinical rehabilitation by complementing experimentation. By serving as a means to distill and explore specific hypotheses, computational models emerge from prior experimental data and motivate future experimental work. Here we review computational tools used to understand neuromuscular function including musculoskeletal modeling, machine learning, control theory, and statistical model analysis. We conclude that these tools, when used in combination, have the potential to further our understanding of neuromuscular function by serving as a rigorous means to test scientific hypotheses in ways that complement and leverage experimental data.

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link (url) [BibTex]

2009


link (url) [BibTex]


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On-line learning and modulation of periodic movements with nonlinear dynamical systems

Gams, A., Ijspeert, A., Schaal, S., Lenarčič, J.

Autonomous Robots, 27(1):3-23, 2009, clmc (article)

Abstract
Abstract  The paper presents a two-layered system for (1) learning and encoding a periodic signal without any knowledge on its frequency and waveform, and (2) modulating the learned periodic trajectory in response to external events. The system is used to learn periodic tasks on a humanoid HOAP-2 robot. The first layer of the system is a dynamical system responsible for extracting the fundamental frequency of the input signal, based on adaptive frequency oscillators. The second layer is a dynamical system responsible for learning of the waveform based on a built-in learning algorithm. By combining the two dynamical systems into one system we can rapidly teach new trajectories to robots without any knowledge of the frequency of the demonstration signal. The system extracts and learns only one period of the demonstration signal. Furthermore, the trajectories are robust to perturbations and can be modulated to cope with a dynamic environment. The system is computationally inexpensive, works on-line for any periodic signal, requires no additional signal processing to determine the frequency of the input signal and can be applied in parallel to multiple dimensions. Additionally, it can adapt to changes in frequency and shape, e.g. to non-stationary signals, such as hand-generated signals and human demonstrations.

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link (url) [BibTex]

link (url) [BibTex]


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Local dimensionality reduction for non-parametric regression

Hoffman, H., Schaal, S., Vijayakumar, S.

Neural Processing Letters, 2009, clmc (article)

Abstract
Locally-weighted regression is a computationally-efficient technique for non-linear regression. However, for high-dimensional data, this technique becomes numerically brittle and computationally too expensive if many local models need to be maintained simultaneously. Thus, local linear dimensionality reduction combined with locally-weighted regression seems to be a promising solution. In this context, we review linear dimensionality-reduction methods, compare their performance on nonparametric locally-linear regression, and discuss their ability to extend to incremental learning. The considered methods belong to the following three groups: (1) reducing dimensionality only on the input data, (2) modeling the joint input-output data distribution, and (3) optimizing the correlation between projection directions and output data. Group 1 contains principal component regression (PCR); group 2 contains principal component analysis (PCA) in joint input and output space, factor analysis, and probabilistic PCA; and group 3 contains reduced rank regression (RRR) and partial least squares (PLS) regression. Among the tested methods, only group 3 managed to achieve robust performance even for a non-optimal number of components (factors or projection directions). In contrast, group 1 and 2 failed for fewer components since these methods rely on the correct estimate of the true intrinsic dimensionality. In group 3, PLS is the only method for which a computationally-efficient incremental implementation exists. Thus, PLS appears to be ideally suited as a building block for a locally-weighted regressor in which projection directions are incrementally added on the fly.

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link (url) [BibTex]

link (url) [BibTex]


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Incorporating Muscle Activation-Contraction dynamics to an optimal control framework for finger movements

Theodorou, Evangelos A., Valero-Cuevas, Francisco J.

Abstracts of Neural Control of Movement Conference (NCM 2009), 2009, clmc (article)

Abstract
Recent experimental and theoretical work [1] investigated the neural control of contact transition between motion and force during tapping with the index finger as a nonlinear optimization problem. Such transitions from motion to well-directed contact force are a fundamental part of dexterous manipulation. There are 3 alternative hypotheses of how this transition could be accomplished by the nervous system as a function of changes in direction and magnitude of the torque vector controlling the finger. These hypotheses are 1) an initial change in direction with a subsequent change in magnitude of the torque vector; 2) an initial change in magnitude with a subsequent directional change of the torque vector; and 3) a simultaneous and proportionally equal change of both direction and magnitude of the torque vector. Experimental work in [2] shows that the nervous system selects the first strategy, and in [1] we suggest that this may in fact be the optimal strategy. In [4] the framework of Iterative Linear Quadratic Optimal Regulator (ILQR) was extended to incorporate motion and force control. However, our prior simulation work assumed direct and instantaneous control of joint torques, which ignores the known delays and filtering properties of skeletal muscle. In this study, we implement an ILQR controller for a more biologically plausible biomechanical model of the index finger than [4], and add activation-contraction dynamics to the system to simulate muscle function. The planar biomechanical model includes the kinematics of the 3 joints while the applied torques are driven by activation?contraction dynamics with biologically plausible time constants [3]. In agreement with our experimental work [2], the task is to, within 500 ms, move the finger from a given resting configuration to target configuration with a desired terminal velocity. ILQR does not only stabilize the finger dynamics according to the objective function, but it also generates smooth joint space trajectories with minimal tuning and without an a-priori initial control policy (which is difficult to find for highly dimensional biomechanical systems). Furthemore, the use of this optimal control framework and the addition of activation-contraction dynamics considers the full nonlinear dynamics of the index finger and produces a sequence of postures which are compatible with experimental motion data [2]. These simulations combined with prior experimental results suggest that optimal control is a strong candidate for the generation of finger movements prior to abrupt motion-to-force transitions. This work is funded in part by grants NIH R01 0505520 and NSF EFRI-0836042 to Dr. Francisco J. Valero- Cuevas 1 Venkadesan M, Valero-Cuevas FJ. 
Effects of neuromuscular lags on controlling contact transitions. 
Philosophical Transactions of the Royal Society A: 2008. 2 Venkadesan M, Valero-Cuevas FJ. 
Neural Control of Motion-to-Force Transitions with the Fingertip. 
J. Neurosci., Feb 2008; 28: 1366 - 1373; 3 Zajac. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng, 17 4. Weiwei Li., Francisco Valero Cuevas: ?Linear Quadratic Optimal Control of Contact Transition with Fingertip ? ACC 2009

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PDF [BibTex]

PDF [BibTex]


no image
On-line learning and modulation of periodic movements with nonlinear dynamical systems

Gams, A., Ijspeert, A., Schaal, S., Lenarčič, J.

Autonomous Robots, 27(1):3-23, 2009, clmc (article)

Abstract
Abstract  The paper presents a two-layered system for (1) learning and encoding a periodic signal without any knowledge on its frequency and waveform, and (2) modulating the learned periodic trajectory in response to external events. The system is used to learn periodic tasks on a humanoid HOAP-2 robot. The first layer of the system is a dynamical system responsible for extracting the fundamental frequency of the input signal, based on adaptive frequency oscillators. The second layer is a dynamical system responsible for learning of the waveform based on a built-in learning algorithm. By combining the two dynamical systems into one system we can rapidly teach new trajectories to robots without any knowledge of the frequency of the demonstration signal. The system extracts and learns only one period of the demonstration signal. Furthermore, the trajectories are robust to perturbations and can be modulated to cope with a dynamic environment. The system is computationally inexpensive, works on-line for any periodic signal, requires no additional signal processing to determine the frequency of the input signal and can be applied in parallel to multiple dimensions. Additionally, it can adapt to changes in frequency and shape, e.g. to non-stationary signals, such as hand-generated signals and human demonstrations.

am

link (url) [BibTex]

link (url) [BibTex]

2008


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Learning to control in operational space

Peters, J., Schaal, S.

International Journal of Robotics Research, 27, pages: 197-212, 2008, clmc (article)

Abstract
One of the most general frameworks for phrasing control problems for complex, redundant robots is operational space control. However, while this framework is of essential importance for robotics and well-understood from an analytical point of view, it can be prohibitively hard to achieve accurate control in face of modeling errors, which are inevitable in com- plex robots, e.g., humanoid robots. In this paper, we suggest a learning approach for opertional space control as a direct inverse model learning problem. A first important insight for this paper is that a physically cor- rect solution to the inverse problem with redundant degrees-of-freedom does exist when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on the insight that many operational space controllers can be understood in terms of a constrained optimal control problem. The cost function as- sociated with this optimal control problem allows us to formulate a learn- ing algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the machine learning point of view, this learning problem corre- sponds to a reinforcement learning problem that maximizes an immediate reward. We employ an expectation-maximization policy search algorithm in order to solve this problem. Evaluations on a three degrees of freedom robot arm are used to illustrate the suggested approach. The applica- tion to a physically realistic simulator of the anthropomorphic SARCOS Master arm demonstrates feasibility for complex high degree-of-freedom robots. We also show that the proposed method works in the setting of learning resolved motion rate control on real, physical Mitsubishi PA-10 medical robotics arm.

am ei

link (url) DOI [BibTex]

2008


link (url) DOI [BibTex]


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Adaptation to a sub-optimal desired trajectory

M. Mistry, E. A. G. L. T. Y. S. S. M. K.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

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PDF [BibTex]

PDF [BibTex]


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Operational space control: A theoretical and emprical comparison

Nakanishi, J., Cory, R., Mistry, M., Peters, J., Schaal, S.

International Journal of Robotics Research, 27(6):737-757, 2008, clmc (article)

Abstract
Dexterous manipulation with a highly redundant movement system is one of the hallmarks of hu- man motor skills. From numerous behavioral studies, there is strong evidence that humans employ compliant task space control, i.e., they focus control only on task variables while keeping redundant degrees-of-freedom as compliant as possible. This strategy is robust towards unknown disturbances and simultaneously safe for the operator and the environment. The theory of operational space con- trol in robotics aims to achieve similar performance properties. However, despite various compelling theoretical lines of research, advanced operational space control is hardly found in actual robotics imple- mentations, in particular new kinds of robots like humanoids and service robots, which would strongly profit from compliant dexterous manipulation. To analyze the pros and cons of different approaches to operational space control, this paper focuses on a theoretical and empirical evaluation of different methods that have been suggested in the literature, but also some new variants of operational space controllers. We address formulations at the velocity, acceleration and force levels. First, we formulate all controllers in a common notational framework, including quaternion-based orientation control, and discuss some of their theoretical properties. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm with several benchmark tasks. As an aside, we also introduce a novel parameter estimation algorithm for rigid body dynamics, which ensures physical consistency, as this issue was crucial for our successful robot implementations. Our extensive empirical results demonstrate that one of the simplified acceleration-based approaches can be advantageous in terms of task performance, ease of parameter tuning, and general robustness and compliance in face of inevitable modeling errors.

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link (url) [BibTex]

link (url) [BibTex]


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A library for locally weighted projection regression

Klanke, S., Vijayakumar, S., Schaal, S.

Journal of Machine Learning Research, 9, pages: 623-626, 2008, clmc (article)

Abstract
In this paper we introduce an improved implementation of locally weighted projection regression (LWPR), a supervised learning algorithm that is capable of handling high-dimensional input data. As the key features, our code supports multi-threading, is available for multiple platforms, and provides wrappers for several programming languages.

am

link (url) [BibTex]

link (url) [BibTex]


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Optimization strategies in human reinforcement learning

Hoffmann, H., Theodorou, E., Schaal, S.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

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PDF [BibTex]

PDF [BibTex]

2007


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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]

2007


link (url) [BibTex]

2005


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Composite adaptive control with locally weighted statistical learning

Nakanishi, J., Farrell, J. A., Schaal, S.

Neural Networks, 18(1):71-90, January 2005, clmc (article)

Abstract
This paper introduces a provably stable learning adaptive control framework with statistical learning. The proposed algorithm employs nonlinear function approximation with automatic growth of the learning network according to the nonlinearities and the working domain of the control system. The unknown function in the dynamical system is approximated by piecewise linear models using a nonparametric regression technique. Local models are allocated as necessary and their parameters are optimized on-line. Inspired by composite adaptive control methods, the proposed learning adaptive control algorithm uses both the tracking error and the estimation error to update the parameters. We first discuss statistical learning of nonlinear functions, and motivate our choice of the locally weighted learning framework. Second, we begin with a class of first order SISO systems for theoretical development of our learning adaptive control framework, and present a stability proof including a parameter projection method that is needed to avoid potential singularities during adaptation. Then, we generalize our adaptive controller to higher order SISO systems, and discuss further extension to MIMO problems. Finally, we evaluate our theoretical control framework in numerical simulations to illustrate the effectiveness of the proposed learning adaptive controller for rapid convergence and high accuracy of control.

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link (url) [BibTex]

2005


link (url) [BibTex]


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A model of smooth pursuit based on learning of the target dynamics using only retinal signals

Shibata, T., Tabata, H., Schaal, S., Kawato, M.

Neural Networks, 18, pages: 213-225, 2005, clmc (article)

Abstract
While the predictive nature of the primate smooth pursuit system has been evident through several behavioural and neurophysiological experiments, few models have attempted to explain these results comprehensively. The model we propose in this paper in line with previous models employing optimal control theory; however, we hypothesize two new issues: (1) the medical superior temporal (MST) area in the cerebral cortex implements a recurrent neural network (RNN) in order to predict the current or future target velocity, and (2) a forward model of the target motion is acquired by on-line learning. We use stimulation studies to demonstrate how our new model supports these hypotheses.

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link (url) [BibTex]

link (url) [BibTex]


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Parametric and Non-Parametric approaches for nonlinear tracking of moving objects

Hidaka, Y, Theodorou, E.

Technical Report-2005-1, 2005, clmc (article)

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PDF [BibTex]

PDF [BibTex]

2004


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Discovering optimal imitation strategies

Billard, A., Epars, Y., Calinon, S., Cheng, G., Schaal, S.

Robotics and Autonomous Systems, 47(2-3):68-77, 2004, clmc (article)

Abstract
This paper develops a general policy for learning relevant features of an imitation task. We restrict our study to imitation of manipulative tasks or of gestures. The imitation process is modeled as a hierarchical optimization system, which minimizes the discrepancy between two multi-dimensional datasets. To classify across manipulation strategies, we apply a probabilistic analysis to data in Cartesian and joint spaces. We determine a general metric that optimizes the policy of task reproduction, following strategy determination. The model successfully discovers strategies in six different imitative tasks and controls task reproduction by a full body humanoid robot.

am

[BibTex]

2004


[BibTex]


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Rhythmic movement is not discrete

Schaal, S., Sternad, D., Osu, R., Kawato, M.

Nature Neuroscience, 7(10):1137-1144, 2004, clmc (article)

Abstract
Rhythmic movements, like walking, chewing, or scratching, are phylogenetically old mo-tor behaviors found in many organisms, ranging from insects to primates. In contrast, discrete movements, like reaching, grasping, or kicking, are behaviors that have reached sophistication primarily in younger species, particularly in primates. Neurophysiological and computational research on arm motor control has focused almost exclusively on dis-crete movements, essentially assuming similar neural circuitry for rhythmic tasks. In con-trast, many behavioral studies focused on rhythmic models, subsuming discrete move-ment as a special case. Here, using a human functional neuroimaging experiment, we show that in addition to areas activated in rhythmic movement, discrete movement in-volves several higher cortical planning areas, despite both movement conditions were confined to the same single wrist joint. These results provide the first neuroscientific evi-dence that rhythmic arm movement cannot be part of a more general discrete movement system, and may require separate neurophysiological and theoretical treatment.

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link (url) [BibTex]

link (url) [BibTex]


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Learning from demonstration and adaptation of biped locomotion

Nakanishi, J., Morimoto, J., Endo, G., Cheng, G., Schaal, S., Kawato, M.

Robotics and Autonomous Systems, 47(2-3):79-91, 2004, clmc (article)

Abstract
In this paper, we introduce a framework for learning biped locomotion using dynamical movement primitives based on non-linear oscillators. Our ultimate goal is to establish a design principle of a controller in order to achieve natural human-like locomotion. We suggest dynamical movement primitives as a central pattern generator (CPG) of a biped robot, an approach we have previously proposed for learning and encoding complex human movements. Demonstrated trajectories are learned through movement primitives by locally weighted regression, and the frequency of the learned trajectories is adjusted automatically by a novel frequency adaptation algorithmbased on phase resetting and entrainment of coupled oscillators. Numerical simulations and experimental implementation on a physical robot demonstrate the effectiveness of the proposed locomotioncontroller.

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link (url) [BibTex]

link (url) [BibTex]


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Feedback error learning and nonlinear adaptive control

Nakanishi, J., Schaal, S.

Neural Networks, 17(10):1453-1465, 2004, clmc (article)

Abstract
In this paper, we present our theoretical investigations of the technique of feedback error learning (FEL) from the viewpoint of adaptive control. We first discuss the relationship between FEL and nonlinear adaptive control with adaptive feedback linearization, and show that FEL can be interpreted as a form of nonlinear adaptive control. Second, we present a Lyapunov analysis suggesting that the condition of strictly positive realness (SPR) associated with the tracking error dynamics is a sufficient condition for asymptotic stability of the closed-loop dynamics. Specifically, for a class of second order SISO systems, we show that this condition reduces to KD^2 > KP; where KP and KD are positive position and velocity feedback gains, respectively. Moreover, we provide a ÔpassivityÕ-based stability analysis which suggests that SPR of the tracking error dynamics is a necessary and sufficient condition for asymptotic hyperstability. Thus, the condition KD^2>KP mentioned above is not only a sufficient but also necessary condition to guarantee asymptotic hyperstability of FEL, i.e. the tracking error is bounded and asymptotically converges to zero. As a further point, we explore the adaptive control and FEL framework for feedforward control formulations, and derive an additional sufficient condition for asymptotic stability in the sense of Lyapunov. Finally, we present numerical simulations to illustrate the stability properties of FEL obtained from our mathematical analysis.

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link (url) [BibTex]

link (url) [BibTex]

2003


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Computational approaches to motor learning by imitation

Schaal, S., Ijspeert, A., Billard, A.

Philosophical Transaction of the Royal Society of London: Series B, Biological Sciences, 358(1431):537-547, 2003, clmc (article)

Abstract
Movement imitation requires a complex set of mechanisms that map an observed movement of a teacher onto one's own movement apparatus. Relevant problems include movement recognition, pose estimation, pose tracking, body correspondence, coordinate transformation from external to egocentric space, matching of observed against previously learned movement, resolution of redundant degrees-of-freedom that are unconstrained by the observation, suitable movement representations for imitation, modularization of motor control, etc. All of these topics by themselves are active research problems in computational and neurobiological sciences, such that their combination into a complete imitation system remains a daunting undertaking - indeed, one could argue that we need to understand the complete perception-action loop. As a strategy to untangle the complexity of imitation, this paper will examine imitation purely from a computational point of view, i.e. we will review statistical and mathematical approaches that have been suggested for tackling parts of the imitation problem, and discuss their merits, disadvantages and underlying principles. Given the focus on action recognition of other contributions in this special issue, this paper will primarily emphasize the motor side of imitation, assuming that a perceptual system has already identified important features of a demonstrated movement and created their corresponding spatial information. Based on the formalization of motor control in terms of control policies and their associated performance criteria, useful taxonomies of imitation learning can be generated that clarify different approaches and future research directions.

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link (url) [BibTex]

2003


link (url) [BibTex]

2002


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Forward models in visuomotor control

Mehta, B., Schaal, S.

J Neurophysiol, 88(2):942-53, August 2002, clmc (article)

Abstract
In recent years, an increasing number of research projects investigated whether the central nervous system employs internal models in motor control. While inverse models in the control loop can be identified more readily in both motor behavior and the firing of single neurons, providing direct evidence for the existence of forward models is more complicated. In this paper, we will discuss such an identification of forward models in the context of the visuomotor control of an unstable dynamic system, the balancing of a pole on a finger. Pole balancing imposes stringent constraints on the biological controller, as it needs to cope with the large delays of visual information processing while keeping the pole at an unstable equilibrium. We hypothesize various model-based and non-model-based control schemes of how visuomotor control can be accomplished in this task, including Smith Predictors, predictors with Kalman filters, tapped-delay line control, and delay-uncompensated control. Behavioral experiments with human participants allow exclusion of most of the hypothesized control schemes. In the end, our data support the existence of a forward model in the sensory preprocessing loop of control. As an important part of our research, we will provide a discussion of when and how forward models can be identified and also the possible pitfalls in the search for forward models in control.

am

link (url) [BibTex]

2002


link (url) [BibTex]


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Scalable techniques from nonparameteric statistics for real-time robot learning

Schaal, S., Atkeson, C. G., Vijayakumar, S.

Applied Intelligence, 17(1):49-60, 2002, clmc (article)

Abstract
Locally weighted learning (LWL) is a class of techniques from nonparametric statistics that provides useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of robotic systems. This paper introduces several LWL algorithms that have been tested successfully in real-time learning of complex robot tasks. We discuss two major classes of LWL, memory-based LWL and purely incremental LWL that does not need to remember any data explicitly. In contrast to the traditional belief that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested on up to 90 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing by a humanoid robot arm, and inverse-dynamics learning for a seven and a 30 degree-of-freedom robot. In all these examples, the application of our statistical neural networks techniques allowed either faster or more accurate acquisition of motor control than classical control engineering.

am

link (url) [BibTex]

link (url) [BibTex]

2001


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Synchronized robot drumming by neural oscillator

Kotosaka, S., Schaal, S.

Journal of the Robotics Society of Japan, 19(1):116-123, 2001, clmc (article)

Abstract
Sensory-motor integration is one of the key issues in robotics. In this paper, we propose an approach to rhythmic arm movement control that is synchronized with an external signal based on exploiting a simple neural oscillator network. Trajectory generation by the neural oscillator is a biologically inspired method that can allow us to generate a smooth and continuous trajectory. The parameter tuning of the oscillators is used to generate a synchronized movement with wide intervals. We adopted the method for the drumming task as an example task. By using this method, the robot can realize synchronized drumming with wide drumming intervals in real time. The paper also shows the experimental results of drumming by a humanoid robot.

am

[BibTex]

2001


[BibTex]


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Origins and violations of the 2/3 power law in rhythmic 3D movements

Schaal, S., Sternad, D.

Experimental Brain Research, 136, pages: 60-72, 2001, clmc (article)

Abstract
The 2/3 power law, the nonlinear relationship between tangential velocity and radius of curvature of the endeffector trajectory, has been suggested as a fundamental constraint of the central nervous system in the formation of rhythmic endpoint trajectories. However, studies on the 2/3 power law have largely been confined to planar drawing patterns of relatively small size. With the hypothesis that this strategy overlooks nonlinear effects that are constitutive in movement generation, the present experiments tested the validity of the power law in elliptical patterns which were not confined to a planar surface and which were performed by the unconstrained 7-DOF arm with significant variations in pattern size and workspace orientation. Data were recorded from five human subjects where the seven joint angles and the endpoint trajectories were analyzed. Additionally, an anthropomorphic 7-DOF robot arm served as a "control subject" whose endpoint trajectories were generated on the basis of the human joint angle data, modeled as simple harmonic oscillations. Analyses of the endpoint trajectories demonstrate that the power law is systematically violated with increasing pattern size, in both exponent and the goodness of fit. The origins of these violations can be explained analytically based on smooth rhythmic trajectory formation and the kinematic structure of the human arm. We conclude that in unconstrained rhythmic movements, the power law seems to be a by-product of a movement system that favors smooth trajectories, and that it is unlikely to serve as a primary movement generating principle. Our data rather suggests that subjects employed smooth oscillatory pattern generators in joint space to realize the required movement patterns.

am

link (url) [BibTex]

link (url) [BibTex]


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Graph-matching vs. entropy-based methods for object detection
Neural Networks, 14(3):345-354, 2001, clmc (article)

Abstract
Labeled Graph Matching (LGM) has been shown successful in numerous ob-ject vision tasks. This method is the basis for arguably the best face recognition system in the world. We present an algorithm for visual pattern recognition that is an extension of LGM ("LGM+"). We compare the performance of LGM and LGM+ algorithms with a state of the art statistical method based on Mutual Information Maximization (MIM). We present an adaptation of the MIM method for multi-dimensional Gabor wavelet features. The three pattern recognition methods were evaluated on an object detection task, using a set of stimuli on which none of the methods had been tested previously. The results indicate that while the performance of the MIM method operating upon Gabor wavelets is superior to the same method operating on pixels and to LGM, it is surpassed by LGM+. LGM+ offers a significant improvement in performance over LGM without losing LGMâ??s virtues of simplicity, biological plausibility, and a computational cost that is 2-3 orders of magnitude lower than that of the MIM algorithm. 

am

link (url) [BibTex]

link (url) [BibTex]


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Biomimetic gaze stabilization based on feedback-error learning with nonparametric regression networks

Shibata, T., Schaal, S.

Neural Networks, 14(2):201-216, 2001, clmc (article)

Abstract
Oculomotor control in a humanoid robot faces similar problems as biological oculomotor systems, i.e. the stabilization of gaze in face of unknown perturbations of the body, selective attention, stereo vision, and dealing with large information processing delays. Given the nonlinearities of the geometry of binocular vision as well as the possible nonlinearities of the oculomotor plant, it is desirable to accomplish accurate control of these behaviors through learning approaches. This paper develops a learning control system for the phylogenetically oldest behaviors of oculomotor control, the stabilization reflexes of gaze. In a step-wise procedure, we demonstrate how control theoretic reasonable choices of control components result in an oculomotor control system that resembles the known functional anatomy of the primate oculomotor system. The core of the learning system is derived from the biologically inspired principle of feedback-error learning combined with a state-of-the-art non-parametric statistical learning network. With this circuitry, we demonstrate that our humanoid robot is able to acquire high performance visual stabilization reflexes after about 40 s of learning despite significant nonlinearities and processing delays in the system.

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link (url) [BibTex]


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Fast learning of biomimetic oculomotor control with nonparametric regression networks (in Japanese)

Shibata, T., Schaal, S.

Journal of the Robotics Society of Japan, 19(4):468-479, 2001, clmc (article)

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[BibTex]

[BibTex]