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2015


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Distributed Event-based State Estimation

Trimpe, S.

Max Planck Institute for Intelligent Systems, November 2015 (techreport)

Abstract
An event-based state estimation approach for reducing communication in a networked control system is proposed. Multiple distributed sensor-actuator-agents observe a dynamic process and sporadically exchange their measurements and inputs over a bus network. Based on these data, each agent estimates the full state of the dynamic system, which may exhibit arbitrary inter-agent couplings. Local event-based protocols ensure that data is transmitted only when necessary to meet a desired estimation accuracy. This event-based scheme is shown to mimic a centralized Luenberger observer design up to guaranteed bounds, and stability is proven in the sense of bounded estimation errors for bounded disturbances. The stability result extends to the distributed control system that results when the local state estimates are used for distributed feedback control. Simulation results highlight the benefit of the event-based approach over classical periodic ones in reducing communication requirements.

arXiv [BibTex]

2015

arXiv [BibTex]


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Lernende Roboter

Trimpe, S.

In Jahrbuch der Max-Planck-Gesellschaft, Max Planck Society, May 2015, (popular science article in German) (inbook)

link (url) [BibTex]

link (url) [BibTex]


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Autonomous Robots

Schaal, S.

In Jahrbuch der Max-Planck-Gesellschaft, May 2015 (incollection)

[BibTex]

[BibTex]


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Robot Learning

Peters, J., Lee, D., Kober, J., Nguyen-Tuong, D., Bagnell, J. A., Schaal, S.

In Springer Handbook of Robotics 2nd Edition, pages: 1371-1394, Springer Berlin Heidelberg, Berlin, Heidelberg, 2015 (incollection)

[BibTex]

[BibTex]

2013


Learning and Optimization with Submodular Functions
Learning and Optimization with Submodular Functions

Sankaran, B., Ghazvininejad, M., He, X., Kale, D., Cohen, L.

ArXiv, May 2013 (techreport)

Abstract
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast under the umbrella of convexity or submodularity. In this report we will study design and optimization over a common class of functions called submodular functions. Set functions, and specifically submodular set functions, characterize a wide variety of naturally occurring optimization problems, and the property of submodularity of set functions has deep theoretical consequences with wide ranging applications. Informally, the property of submodularity of set functions concerns the intuitive principle of diminishing returns. This property states that adding an element to a smaller set has more value than adding it to a larger set. Common examples of submodular monotone functions are entropies, concave functions of cardinality, and matroid rank functions; non-monotone examples include graph cuts, network flows, and mutual information. In this paper we will review the formal definition of submodularity; the optimization of submodular functions, both maximization and minimization; and finally discuss some applications in relation to learning and reasoning using submodular functions.

arxiv link (url) [BibTex]

2013

arxiv link (url) [BibTex]


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Using Torque Redundancy to Optimize Contact Forces in Legged Robots

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

In Redundancy in Robot Manipulators and Multi-Robot Systems, 57, pages: 35-51, Lecture Notes in Electrical Engineering, Springer Berlin Heidelberg, 2013 (incollection)

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 contact interaction with the environment is of crucial importance to ensure stable, robust and safe motions. In the following, we present an inverse dynamics controller that exploits torque redundancy to directly and explicitly minimize any combination of linear and quadratic costs in the contact constraints and in the commands. Such a result is particularly relevant for legged robots as it allows to use torque redundancy to directly optimize contact interactions. For example, given a desired locomotion behavior, it can guarantee the minimization of contact forces to reduce slipping on difficult terrains while ensuring high tracking performance of the desired motion. The proposed controller is very simple and computationally efficient, and most importantly it can greatly improve the performance of legged locomotion on difficult terrains as can be seen in the experimental results.

link (url) [BibTex]

link (url) [BibTex]

2010


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Locally weighted regression for control

Ting, J., Vijayakumar, S., Schaal, S.

In Encyclopedia of Machine Learning, pages: 613-624, (Editors: Sammut, C.;Webb, G. I.), Springer, 2010, clmc (inbook)

Abstract
This is article addresses two topics: learning control and locally weighted regression.

link (url) [BibTex]

2010

link (url) [BibTex]

2009


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The SL simulation and real-time control software package

Schaal, S.

University of Southern California, Los Angeles, CA, 2009, clmc (techreport)

Abstract
SL was originally developed as a Simulation Laboratory software package to allow creating complex rigid-body dynamics simulations with minimal development times. It was meant to complement a real-time robotics setup such that robot programs could first be debugged in simulation before trying them on the actual robot. For this purpose, the motor control setup of SL was copied from our experience with real-time robot setups with vxWorks (Windriver Systems, Inc.)Ñindeed, more than 90% of the code is identical to the actual robot software, as will be explained later in detail. As a result, SL is divided into three software components: 1) the generic code that is shared by the actual robot and the simulation, 2) the robot specific code, and 3) the simulation specific code. The robot specific code is tailored to the robotic environments that we have experienced over the years, in particular towards VME-based multi-processor real-time operating systems. The simulation specific code has all the components for OpenGL graphics simulations and mimics the robot multi-processor environment in simple C-code. Importantly, SL can be used stand-alone for creating graphics an-imationsÑthe heritage from real-time robotics does not restrict the complexity of possible simulations. This technical report describes SL in detail and can serve as a manual for new users of SL.

link (url) [BibTex]

2009

link (url) [BibTex]


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The SL simulation and real-time control software package

Schaal, S.

University of Southern California, Los Angeles, CA, 2009, clmc (techreport)

Abstract
SL was originally developed as a Simulation Laboratory software package to allow creating complex rigid-body dynamics simulations with minimal development times. It was meant to complement a real-time robotics setup such that robot programs could first be debugged in simulation before trying them on the actual robot. For this purpose, the motor control setup of SL was copied from our experience with real-time robot setups with vxWorks (Windriver Systems, Inc.)â??indeed, more than 90% of the code is identical to the actual robot software, as will be explained later in detail. As a result, SL is divided into three software components: 1) the generic code that is shared by the actual robot and the simulation, 2) the robot specific code, and 3) the simulation specific code. The robot specific code is tailored to the robotic environments that we have experienced over the years, in particular towards VME-based multi-processor real-time operating systems. The simulation specific code has all the components for OpenGL graphics simulations and mimics the robot multi-processor environment in simple C-code. Importantly, SL can be used stand-alone for creating graphics an-imationsâ??the heritage from real-time robotics does not restrict the complexity of possible simulations. This technical report describes SL in detail and can serve as a manual for new users of SL.

link (url) [BibTex]

link (url) [BibTex]

2007


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Relative Entropy Policy Search

Peters, J.

CLMC Technical Report: TR-CLMC-2007-2, Computational Learning and Motor Control Lab, Los Angeles, CA, 2007, clmc (techreport)

Abstract
This technical report describes a cute idea of how to create new policy search approaches. It directly relates to the Natural Actor-Critic methods but allows the derivation of one shot solutions. Future work may include the application to interesting problems.

PDF link (url) [BibTex]

2007

PDF link (url) [BibTex]


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Dynamics systems vs. optimal control ? a unifying view

Schaal, S, Mohajerian, P., Ijspeert, A.

In Progress in Brain Research, (165):425-445, 2007, clmc (inbook)

Abstract
In the past, computational motor control has been approached from at least two major frameworks: the dynamic systems approach and the viewpoint of optimal control. The dynamic system approach emphasizes motor control as a process of self-organization between an animal and its environment. Nonlinear differential equations that can model entrainment and synchronization behavior are among the most favorable tools of dynamic systems modelers. In contrast, optimal control approaches view motor control as the evolutionary or development result of a nervous system that tries to optimize rather general organizational principles, e.g., energy consumption or accurate task achievement. Optimal control theory is usually employed to develop appropriate theories. Interestingly, there is rather little interaction between dynamic systems and optimal control modelers as the two approaches follow rather different philosophies and are often viewed as diametrically opposing. In this paper, we develop a computational approach to motor control that offers a unifying modeling framework for both dynamic systems and optimal control approaches. In discussions of several behavioral experiments and some theoretical and robotics studies, we demonstrate how our computational ideas allow both the representation of self-organizing processes and the optimization of movement based on reward criteria. Our modeling framework is rather simple and general, and opens opportunities to revisit many previous modeling results from this novel unifying view.

link (url) [BibTex]

link (url) [BibTex]


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Learning an Outlier-Robust Kalman Filter

Ting, J., Theodorou, E., Schaal, S.

CLMC Technical Report: TR-CLMC-2007-1, Los Angeles, CA, 2007, clmc (techreport)

Abstract
We introduce a modified Kalman filter that performs robust, real-time outlier detection, without the need for manual parameter tuning by the user. Systems that rely on high quality sensory data (for instance, robotic systems) can be sensitive to data containing outliers. The standard Kalman filter is not robust to outliers, and other variations of the Kalman filter have been proposed to overcome this issue. However, these methods may require manual parameter tuning, use of heuristics or complicated parameter estimation procedures. Our Kalman filter uses a weighted least squares-like approach by introducing weights for each data sample. A data sample with a smaller weight has a weaker contribution when estimating the current time step?s state. Using an incremental variational Expectation-Maximization framework, we learn the weights and system dynamics. We evaluate our Kalman filter algorithm on data from a robotic dog.

PDF [BibTex]

PDF [BibTex]

2006


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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)

PDF [BibTex]

2006

PDF [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)

link (url) [BibTex]

link (url) [BibTex]

2004


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Computational approaches to motor learning by imitation

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

In The Neuroscience of Social Interaction, (1431):199-218, (Editors: Frith, C. D.;Wolpert, D.), Oxford University Press, Oxford, 2004, clmc (inbook)

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.

link (url) [BibTex]

2004

link (url) [BibTex]

1995


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Batting a ball: Dynamics of a rhythmic skill

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

In Studies in Perception and Action, pages: 119-122, (Editors: Bardy, B.;Bostma, R.;Guiard, Y.), Erlbaum, Hillsdayle, NJ, 1995, clmc (inbook)

[BibTex]

1995

[BibTex]

1991


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Ways to smarter CAD-systems

Ehrlenspiel, K., Schaal, S.

In Proceedings of ICED’91Heurista, pages: 10-16, (Editors: Hubka), Edition, Schriftenreihe WDK 21. Zürich, 1991, clmc (inbook)

[BibTex]

1991

[BibTex]