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2010


Decoding complete reach and grasp actions from local primary motor cortex populations
Decoding complete reach and grasp actions from local primary motor cortex populations

(Featured in Nature’s Research Highlights (Nature, Vol 466, 29 July 2010))

Vargas-Irwin, C. E., Shakhnarovich, G., Yadollahpour, P., Mislow, J., Black, M. J., Donoghue, J. P.

J. of Neuroscience, 39(29):9659-9669, July 2010 (article)

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pdf pdf from publisher Movie 1 Movie 2 Project Page [BibTex]

2010


pdf pdf from publisher Movie 1 Movie 2 Project Page [BibTex]


Learning Grasping Points with Shape Context
Learning Grasping Points with Shape Context

Bohg, J., Kragic, D.

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

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

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pdf link (url) DOI [BibTex]

pdf link (url) DOI [BibTex]


Guest editorial: State of the art in image- and video-based human pose and motion estimation
Guest editorial: State of the art in image- and video-based human pose and motion estimation

Sigal, L., Black, M. J.

International Journal of Computer Vision, 87(1):1-3, March 2010 (article)

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pdf from publisher [BibTex]

pdf from publisher [BibTex]


{HumanEva}: Synchronized video and motion capture dataset and baseline algorithm for evaluation of articulated human motion
HumanEva: Synchronized video and motion capture dataset and baseline algorithm for evaluation of articulated human motion

Sigal, L., Balan, A., Black, M. J.

International Journal of Computer Vision, 87(1):4-27, Springer Netherlands, March 2010 (article)

Abstract
While research on articulated human motion and pose estimation has progressed rapidly in the last few years, there has been no systematic quantitative evaluation of competing methods to establish the current state of the art. We present data obtained using a hardware system that is able to capture synchronized video and ground-truth 3D motion. The resulting HumanEva datasets contain multiple subjects performing a set of predefined actions with a number of repetitions. On the order of 40,000 frames of synchronized motion capture and multi-view video (resulting in over one quarter million image frames in total) were collected at 60 Hz with an additional 37,000 time instants of pure motion capture data. A standard set of error measures is defined for evaluating both 2D and 3D pose estimation and tracking algorithms. We also describe a baseline algorithm for 3D articulated tracking that uses a relatively standard Bayesian framework with optimization in the form of Sequential Importance Resampling and Annealed Particle Filtering. In the context of this baseline algorithm we explore a variety of likelihood functions, prior models of human motion and the effects of algorithm parameters. Our experiments suggest that image observation models and motion priors play important roles in performance, and that in a multi-view laboratory environment, where initialization is available, Bayesian filtering tends to perform well. The datasets and the software are made available to the research community. This infrastructure will support the development of new articulated motion and pose estimation algorithms, will provide a baseline for the evaluation and comparison of new methods, and will help establish the current state of the art in human pose estimation and tracking.

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pdf pdf from publisher [BibTex]

pdf pdf from publisher [BibTex]


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

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

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

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

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link (url) [BibTex]


Roombots: Reconfigurable Robots for Adaptive Furniture
Roombots: Reconfigurable Robots for Adaptive Furniture

Spröwitz, A., Pouya, S., Bonardi, S., van den Kieboom, J., Möckel, R., Billard, A., Dillenbourg, P., Ijspeert, A.

Computational Intelligence Magazine, IEEE, 5(3):20-32, 2010 (article)

Abstract
Imagine a world in which our furniture moves around like legged robots, interacts with us, and changes shape and function during the day according to our needs. This is the long term vision we have in the Roombots project. To work towards this dream, we are developing modular robotic modules that have rotational degrees of freedom for locomotion as well as active connection mechanisms for runtime reconfiguration. A piece of furniture, e.g. a stool, will thus be composed of several modules that activate their rotational joints together to implement locomotor gaits, and will be able to change shape, e.g. transforming into a chair, by sequences of attachments and detachments of modules. In this article, we firstly present the project and the hardware we are currently developing. We explore how reconfiguration from a configuration A to a configuration B can be controlled in a distributed fashion. This is done using metamodules-two Roombots modules connected serially-that use broadcast signals and connections to a structured ground to collectively build desired structures without the need of a centralized planner. We then present how locomotion controllers can be implemented in a distributed system of coupled oscillators-one per degree of freedom-similarly to the concept of central pattern generators (CPGs) found in the spinal cord of vertebrate animals. The CPGs are based on coupled phase oscillators to ensure synchronized behavior and have different output filters to allow switching between oscillations and rotations. A stochastic optimization algorithm is used to explore optimal CPG configurations for different simulated Roombots structures.

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DOI [BibTex]

DOI [BibTex]


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Gait planning based on kinematics for a quadruped gecko model with redundancy

Son, D., Jeon, D., Nam, W. C., Chang, D., Seo, T., Kim, J.

Robotics and Autonomous Systems, 58, 2010 (article)

pi

[BibTex]

[BibTex]


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Flat dry elastomer adhesives as attachment materials for climbing robots

Unver, O., Sitti, M.

IEEE transactions on robotics, 26(1):131-141, IEEE, 2010 (article)

pi

[BibTex]

[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]


 Automated Home-Cage Behavioral Phenotyping of Mice
Automated Home-Cage Behavioral Phenotyping of Mice

Jhuang, H., Garrote, E., Mutch, J., Poggio, T., Steele, A., Serre, T.

Nature Communications, Nature Communications, 2010 (article)

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software, demo pdf [BibTex]

software, demo pdf [BibTex]


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An experimental analysis of elliptical adhesive contact

Sümer, B., Onal, C. D., Aksak, B., Sitti, M.

Journal of Applied Physics, 107(11):113512, AIP, 2010 (article)

pi

Project Page [BibTex]

Project Page [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]


ImageFlow: Streaming Image Search
ImageFlow: Streaming Image Search

Jampani, V., Ramos, G., Drucker, S.

MSR-TR-2010-148, Microsoft Research, Redmond, 2010 (techreport)

Abstract
Traditional grid and list representations of image search results are the dominant interaction paradigms that users face on a daily basis, yet it is unclear that such paradigms are well-suited for experiences where the user‟s task is to browse images for leisure, to discover new information or to seek particular images to represent ideas. We introduce ImageFlow, a novel image search user interface that ex-plores a different alternative to the traditional presentation of image search results. ImageFlow presents image results on a canvas where we map semantic features (e.g., rele-vance, related queries) to the canvas‟ spatial dimensions (e.g., x, y, z) in a way that allows for several levels of en-gagement – from passively viewing a stream of images, to seamlessly navigating through the semantic space and ac-tively collecting images for sharing and reuse. We have implemented our system as a fully functioning prototype, and we report on promising, preliminary usage results.

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url pdf link (url) [BibTex]

url pdf 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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Enhanced wet adhesion and shear of elastomeric micro-fiber arrays with mushroom tip geometry and a photopolymerized p (DMA-co-MEA) tip coating

Glass, P., Chung, H., Washburn, N. R., Sitti, M.

Langmuir, 26(22):17357-17362, American Chemical Society, 2010 (article)

pi

Project Page [BibTex]

Project Page [BibTex]


Visual Object-Action Recognition: Inferring Object Affordances from Human Demonstration
Visual Object-Action Recognition: Inferring Object Affordances from Human Demonstration

Kjellström, H., Romero, J., Kragic, D.

Computer Vision and Image Understanding, pages: 81-90, 2010 (article)

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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]


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Teleoperated 3-D force feedback from the nanoscale with an atomic force microscope

Onal, C. D., Sitti, M.

IEEE Transactions on nanotechnology, 9(1):46-54, IEEE, 2010 (article)

pi

[BibTex]

[BibTex]


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Roll and pitch motion analysis of a biologically inspired quadruped water runner robot

Park, H. S., Floyd, S., Sitti, M.

The International Journal of Robotics Research, 29(10):1281-1297, SAGE Publications Sage UK: London, England, 2010 (article)

pi

[BibTex]

[BibTex]


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Microstructured elastomeric surfaces with reversible adhesion and examples of their use in deterministic assembly by transfer printing

Kim, Seok, Wu, Jian, Carlson, Andrew, Jin, Sung Hun, Kovalsky, Anton, Glass, Paul, Liu, Zhuangjian, Ahmed, Numair, Elgan, Steven L, Chen, Weiqiu, others

Proceedings of the National Academy of Sciences, 107(40):17095-17100, National Acad Sciences, 2010 (article)

pi

Project Page [BibTex]

Project Page [BibTex]


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Tankbot: A palm-size, tank-like climbing robot using soft elastomer adhesive treads

Unver, O., Sitti, M.

The International Journal of Robotics Research, 29(14):1761-1777, SAGE Publications Sage UK: London, England, 2010 (article)

pi

[BibTex]

[BibTex]


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Note: Aligned deposition and modal characterization of micron and submicron poly (methyl methacyrlate) fiber cantilevers

Nain, A. S., Filiz, S., Burak Ozdoganlar, O., Sitti, M., Amon, C.

Review of Scientific Instruments, 81(1):016102, AIP, 2010 (article)

pi

[BibTex]

[BibTex]


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Enhanced adhesion of dopamine methacrylamide elastomers via viscoelasticity tuning

Chung, H., Glass, P., Pothen, J. M., Sitti, M., Washburn, N. R.

Biomacromolecules, 12(2):342-347, American Chemical Society, 2010 (article)

pi

Project Page [BibTex]

Project Page [BibTex]

2004


On the variability of manual spike sorting
On the variability of manual spike sorting

Wood, F., Black, M. J., Vargas-Irwin, C., Fellows, M., Donoghue, J. P.

IEEE Trans. Biomedical Engineering, 51(6):912-918, June 2004 (article)

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pdf pdf from publisher [BibTex]

2004


pdf pdf from publisher [BibTex]


Modeling and decoding motor cortical activity using a switching {Kalman} filter
Modeling and decoding motor cortical activity using a switching Kalman filter

Wu, W., Black, M. J., Mumford, D., Gao, Y., Bienenstock, E., Donoghue, J. P.

IEEE Trans. Biomedical Engineering, 51(6):933-942, June 2004 (article)

Abstract
We present a switching Kalman filter model for the real-time inference of hand kinematics from a population of motor cortical neurons. Firing rates are modeled as a Gaussian mixture where the mean of each Gaussian component is a linear function of hand kinematics. A “hidden state” models the probability of each mixture component and evolves over time in a Markov chain. The model generalizes previous encoding and decoding methods, addresses the non-Gaussian nature of firing rates, and can cope with crudely sorted neural data common in on-line prosthetic applications.

ps

pdf pdf from publisher [BibTex]

pdf pdf from publisher [BibTex]


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E. Coli Inspired Propulsion for Swimming Microrobots

Behkam, Bahareh, Sitti, Metin

pages: 1037–1041, 2004 (article)

Abstract
Medical applications are among the most fascinating areas of microrobotics. For long, scientists have dreamed of miniature smart devices that can travel inside the human body and carry out a host of complex operations such as minimally invasive surgery (MIS), highly localized drug delivery, and screening for diseases that are in their very early stages. Still a distant dream, significant progress in micro and nanotechnology brings us closer to materializing it. For such a miniature device to be injected into the body, it has to be 800 μm or smaller in diameter. Miniature, safe and energy efficient propulsion systems hold the key to maturing this technology but they pose significant challenges. Scaling the macroscale natation mechanisms to micro/nano length scales is unfeasible. It has been estimated that a vibrating-fin driven swimming robot shorter than 6 mm can not overcome the viscous drag forces in water. In this paper, the authors propose a new type of propulsion inspired by the motility mechanism of bacteria with peritrichous flagellation, such as Escherichia coli, Salmonella typhimurium and Serratia marcescens. The perfomance of the propulsive mechanism is estimated by modeling the dynamics of the motion. The motion of the moving organelle is simulated and key parameters such as velocity, distribution of force and power requirments for different configurations of the tail are determined theoretically. In order to validate the theoretical result, a scaled up model of the swimming robot is fabricated and characterized in silicone oil using the Buckingham PI theorem for scaling. The results are compared with the theoretically computed values. These robots are intended to swim in stagnation/low velocity biofluid and reach currently inaccessible areas of the human body for disease inspection and possibly treatment. Potential target regions to use these robots include eyeball cavity, cerebrospinal fluid and the urinary system.

pi

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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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]

[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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Atomic force microscope probe based controlled pushing for nanotribological characterization

Sitti, M.

IEEE/ASME Transactions on mechatronics, 9(2):343-349, IEEE, 2004 (article)

pi

[BibTex]

[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]