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2006


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Learning operational space control

Peters, J., Schaal, S.

In Robotics: Science and Systems II (RSS 2006), pages: 255-262, (Editors: Gaurav S. Sukhatme and Stefan Schaal and Wolfram Burgard and Dieter Fox), Cambridge, MA: MIT Press, RSS , 2006, clmc (inproceedings)

Abstract
While operational space control 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 complex robots, e.g., humanoid robots. In such cases, learning control methods can offer an interesting alternative to analytical control algorithms. However, the resulting learning problem is ill-defined as it requires to learn an inverse mapping of a usually redundant system, which is well known to suffer from the property of non-covexity of the solution space, i.e., the learning system could generate motor commands that try to steer the robot into physically impossible configurations. A first important insight for this paper is that, nevertheless, a physically correct solution to the inverse problem does exits when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on a recent insight that many operational space controllers can be understood in terms of a constraint optimal control problem. The cost function associated with this optimal control problem allows us to formulate a learning algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the view of machine learning, the learning problem corresponds to a reinforcement learning problem that maximizes an immediate reward and that employs an expectation-maximization policy search algorithm. Evaluations on a three degrees of freedom robot arm illustrate the feasability of our suggested approach.

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link (url) [BibTex]

2006


link (url) [BibTex]


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Reinforcement Learning for Parameterized Motor Primitives

Peters, J., Schaal, S.

In Proceedings of the 2006 International Joint Conference on Neural Networks, pages: 73-80, IJCNN, 2006, clmc (inproceedings)

Abstract
One of the major challenges in both action generation for robotics and in the understanding of human motor control is to learn the "building blocks of movement generation", called motor primitives. Motor primitives, as used in this paper, are parameterized control policies such as splines or nonlinear differential equations with desired attractor properties. While a lot of progress has been made in teaching parameterized motor primitives using supervised or imitation learning, the self-improvement by interaction of the system with the environment remains a challenging problem. In this paper, we evaluate different reinforcement learning approaches for improving the performance of parameterized motor primitives. 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.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Statistical Learning of LQG controllers

Theodorou, E.

Technical Report-2006-1, Computational Action and Vision Lab University of Minnesota, 2006, clmc (techreport)

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PDF [BibTex]

PDF [BibTex]


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Dynamic Hebbian learning in adaptive frequency oscillators

Righetti, L., Buchli, J., Ijspeert, A.

Physica D: Nonlinear Phenomena, 216(2):269-281, 2006 (article)

Abstract
Nonlinear oscillators are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for oscillators which adapts their frequency to the frequency of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of oscillators, from phase oscillators to relaxation oscillators and strange attractors with a generic learning rule. One major feature of our learning rule is that the oscillators constructed can adapt their frequency without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive oscillator. The convergence of the learning is proved for the Hopf oscillator, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic oscillators like relaxation oscillators and strange attractors.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Approximate nearest neighbor regression in very high dimensions

Vijayakumar, S., DSouza, A., Schaal, S.

In Nearest-Neighbor Methods in Learning and Vision, pages: 103-142, (Editors: Shakhnarovich, G.;Darrell, T.;Indyk, P.), Cambridge, MA: MIT Press, 2006, clmc (inbook)

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link (url) [BibTex]

link (url) [BibTex]


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Movement generation using dynamical systems : a humanoid robot performing a drumming task

Degallier, S., Santos, C. P., Righetti, L., Ijspeert, A.

In 2006 6th IEEE-RAS International Conference on Humanoid Robots, pages: 512-517, IEEE, Genova, Italy, 2006 (inproceedings)

Abstract
The online generation of trajectories in humanoid robots remains a difficult problem. In this contribution, we present a system that allows the superposition, and the switch between, discrete and rhythmic movements. Our approach uses nonlinear dynamical systems for generating trajectories online and in real time. Our goal is to make use of attractor properties of dynamical systems in order to provide robustness against small perturbations and to enable online modulation of the trajectories. The system is demonstrated on a humanoid robot performing a drumming task.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Engineering Entrainment and Adaptation in Limit Cycle Systems – From biological inspiration to applications in robotics

Buchli, J., Righetti, L., Ijspeert, A.

Biological Cybernetics, 95(6):645-664, December 2006 (article)

Abstract
Periodic behavior is key to life and is observed in multiple instances and at multiple time scales in our metabolism, our natural environment, and our engineered environment. A natural way of modeling or generating periodic behavior is done by using oscillators, i.e., dynamical systems that exhibit limit cycle behavior. While there is extensive literature on methods to analyze such dynamical systems, much less work has been done on methods to synthesize an oscillator to exhibit some specific desired characteristics. The goal of this article is twofold: (1) to provide a framework for characterizing and designing oscillators and (2) to review how classes of well-known oscillators can be understood and related to this framework. The basis of the framework is to characterize oscillators in terms of their fundamental temporal and spatial behavior and in terms of properties that these two behaviors can be designed to exhibit. This focus on fundamental properties is important because it allows us to systematically compare a large variety of oscillators that might at first sight appear very different from each other. We identify several specifications that are useful for design, such as frequency-locking behavior, phase-locking behavior, and specific output signal shape. We also identify two classes of design methods by which these specifications can be met, namely offline methods and online methods. By relating these specifications to our framework and by presenting several examples of how oscillators have been designed in the literature, this article provides a useful methodology and toolbox for designing oscillators for a wide range of purposes. In particular, the focus on synthesis of limit cycle dynamical systems should be useful both for engineering and for computational modeling of physical or biological phenomena.

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link (url) DOI [BibTex]


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Design methodologies for central pattern generators: an application to crawling humanoids

Righetti, L., Ijspeert, A.

In Proceedings of Robotics: Science and Systems, Philadelphia, USA, August 2006 (inproceedings)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Programmable central pattern generators: an application to biped locomotion control

Righetti, L., Ijspeert, A.

In Proceedings of the IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., pages: 1585-1590, IEEE, 2006 (inproceedings)

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[BibTex]

[BibTex]