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2013


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Hybrid nanocolloids with programmed three-dimensional shape and material composition

Mark, A. G., Gibbs, J. G., Lee, T., Fischer, P.

NATURE MATERIALS, 12(9):802-807, 2013, Max Planck Press Release. (article)

Abstract
Tuning the optical(1,2), electromagnetic(3,4) and mechanical properties of a material requires simultaneous control over its composition and shape(5). This is particularly challenging for complex structures at the nanoscale because surface-energy minimization generally causes small structures to be highly symmetric(5). Here we combine low-temperature shadow deposition with nanoscale patterning to realize nanocolloids with anisotropic three-dimensional shapes, feature sizes down to 20 nm and a wide choice of materials. We demonstrate the versatility of the fabrication scheme by growing three-dimensional hybrid nanostructures that contain several functional materials with the lowest possible symmetry, and by fabricating hundreds of billions of plasmonic nanohelices, which we use as chiral metafluids with record circular dichroism and tunable chiroptical properties.

Max Planck Press Release.

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Video - Fabrication of Designer Nanostructures DOI [BibTex]


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Chiral Colloidal Molecules And Observation of The Propeller Effect

Schamel, D., Pfeifer, M., Gibbs, J. G., Miksch, B., Mark, A. G., Fischer, P.

JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 135(33):12353-12359, 2013 (article)

Abstract
Chiral molecules play an important role in biological and chemical processes, but physical effects due to their symmetry-breaking are generally weak. Several physical chiral separation schemes which could potentially be useful, including the propeller effect, have therefore not yet been demonstrated at the molecular scale. However, it has been proposed that complex nonspherical colloidal particles could act as ``colloidal molecules{''} in mesoscopic model systems to permit the visualization of molecular phenomena that are otherwise difficult to observe. Unfortunately, it is difficult to synthesize such colloids because surface minimization generally favors the growth of symmetric particles. Here we demonstrate the production of large numbers of complex colloids with glancing angle physical vapor deposition. We use chiral colloids to demonstrate the Baranova and Zel'dovich (Baranova, N. B.; Zel'dovich, B. Y. Chem. Phys. Lett. 1978, 57, 435) propeller effect: the separation of a racemic mixture by application of a rotating field that couples to the dipole moment of the enantiomers and screw propels them in opposite directions. The handedness of the colloidal suspensions is monitored with circular differential light scattering. An exact solution for the colloid's propulsion is derived, and comparisons between the colloidal system and the corresponding effect at the molecular scale are made.

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Video - Nanospropellers DOI [BibTex]

Video - Nanospropellers DOI [BibTex]


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Indirect absorption spectroscopy using quantum cascade lasers: mid-infrared refractometry and photothermal spectroscopy

Pfeifer, M., Ruf, A., Fischer, P.

OPTICS EXPRESS, 21(22):25643-25654, 2013 (article)

Abstract
We record vibrational spectra with two indirect schemes that depend on the real part of the index of refraction: mid-infrared refractometry and photothermal spectroscopy. In the former, a quantum cascade laser (QCL) spot is imaged to determine the angles of total internal reflection, which yields the absorption line via a beam profile analysis. In the photothermal measurements, a tunable QCL excites vibrational resonances of a molecular monolayer, which heats the surrounding medium and changes its refractive index. This is observed with a probe laser in the visible. Sub-monolayer sensitivities are demonstrated. (C) 2013 Optical Society of America

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DOI [BibTex]


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Plasmonic nanohelix metamaterials with tailorable giant circular dichroism

Gibbs, J. G., Mark, A. G., Eslami, S., Fischer, P.

APPLIED PHYSICS LETTERS, 103(21), 2013, Featured cover article. (article)

Abstract
Plasmonic nanohelix arrays are shown to interact with electromagnetic fields in ways not typically seen with ordinary matter. Chiral metamaterials (CMMs) with feature sizes small with respect to the wavelength of visible light are a promising route to experimentally achieve such phenomena as negative refraction without the need for simultaneously negative e and mu. Here we not only show that giant circular dichroism in the visible is achievable with hexagonally arranged plasmonic nanohelix arrays, but that we can precisely tune the optical activity via morphology and lattice spacing. The discrete dipole approximation is implemented to support experimental data. (C) 2013 AIP Publishing LLC.

Featured cover article.

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DOI [BibTex]

DOI [BibTex]


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AGILITY – Dynamic Full Body Locomotion and Manipulation with Autonomous Legged Robots

Hutter, M., Bloesch, M., Buchli, J., Semini, C., Bazeille, S., Righetti, L., Bohg, J.

In 2013 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), pages: 1-4, IEEE, Linköping, Sweden, 2013 (inproceedings)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Objective Functions for Manipulation

Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S.

In 2013 IEEE International Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

Abstract
We present an approach to learning objective functions for robotic manipulation based on inverse reinforcement learning. Our path integral inverse reinforcement learning algorithm can deal with high-dimensional continuous state-action spaces, and only requires local optimality of demonstrated trajectories. We use L 1 regularization in order to achieve feature selection, and propose an efficient algorithm to minimize the resulting convex objective function. We demonstrate our approach by applying it to two core problems in robotic manipulation. First, we learn a cost function for redundancy resolution in inverse kinematics. Second, we use our method to learn a cost function over trajectories, which is then used in optimization-based motion planning for grasping and manipulation tasks. Experimental results show that our method outperforms previous algorithms in high-dimensional settings.

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link (url) DOI [BibTex]

link (url) DOI [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.

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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]


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Controlled Reduction with Unactuated Cyclic Variables: Application to 3D Bipedal Walking with Passive Yaw Rotation

Gregg, R., Righetti, L.

IEEE Transactions on Automatic Control, 58(10):2679-2685, October 2013 (article)

Abstract
This technical note shows that viscous damping can shape momentum conservation laws in a manner that stabilizes yaw rotation and enables steering for underactuated 3D walking. We first show that unactuated cyclic variables can be controlled by passively shaped conservation laws given a stabilizing controller in the actuated coordinates. We then exploit this result to realize controlled geometric reduction with multiple unactuated cyclic variables. We apply this underactuated control strategy to a five-link 3D biped to produce exponentially stable straight-ahead walking and steering in the presence of passive yawing.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Task Error Models for Manipulation

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

In 2013 IEEE Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

Abstract
Precise kinematic forward models are important for robots to successfully perform dexterous grasping and manipulation tasks, especially when visual servoing is rendered infeasible due to occlusions. A lot of research has been conducted to estimate geometric and non-geometric parameters of kinematic chains to minimize reconstruction errors. However, kinematic chains can include non-linearities, e.g. due to cable stretch and motor-side encoders, that result in significantly different errors for different parts of the state space. Previous work either does not consider such non-linearities or proposes to estimate non-geometric parameters of carefully engineered models that are robot specific. We propose a data-driven approach that learns task error models that account for such unmodeled non-linearities. We argue that in the context of grasping and manipulation, it is sufficient to achieve high accuracy in the task relevant state space. We identify this relevant state space using previously executed joint configurations and learn error corrections for those. Therefore, our system is developed to generate subsequent executions that are similar to previous ones. The experiments show that our method successfully captures the non-linearities in the head kinematic chain (due to a counterbalancing spring) and the arm kinematic chains (due to cable stretch) of the considered experimental platform, see Fig. 1. The feasibility of the presented error learning approach has also been evaluated in independent DARPA ARM-S testing contributing to successfully complete 67 out of 72 grasping and manipulation tasks.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2012


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Fourier-transform photocurrent spectroscopy using a supercontinuum light source

Petermann, C., Beigang, R., Fischer, P.

APPLIED PHYSICS LETTERS, 100(6), 2012 (article)

Abstract
We demonstrate an implementation of frequency-encoded photocurrent spectroscopy using a super-continuum light source. The spectrally broad light is spatially dispersed and modulated with a special mechanical chopper design that permits a continuous wavelength-dependent modulation. After recombination, the light beam contains a frequency encoded spectrum which enables us to map the spectral response of a given sample in 60 ms and with a lateral resolution of 10 mu m. (C) 2012 American Institute of Physics.

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DOI [BibTex]

2012


DOI [BibTex]


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Eine neue Form von Cavity Enhanced Absorption Spectroscopy

Petermann, C., Fischer, P.

DE Gruyter, 79(1), 2012, Best paper award OPTO 2011 (article)

Abstract
Wir stellen eine Kopplungsmethode für resonatorgestützte Absorptionsmessungen vor, bei der Licht durch einen im Resonator platzierten akustooptischen Modulator aktiv ein- und ausgekoppelt wird. Dies ermöglicht es Cavity-Ring-Down-Spektroskopie (CRDS) mit breitbandigen und zeitlich inkohärenten Lichtquellen niedriger spektraler Leistungsdichte durchzuführen. Das Verfahren wird zum ersten Mal mit einer breitbandigen Superkontinuum-Quelle demonstriert.

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A new coupling scheme for cavity enhanced absorption spectroscopy makes use of an intracavity acousto-optical modulator to actively switch light into (and out of) a resonator. This allows cavity ringdown spectroscopy (CRDS) to be implemented with broadband temporally incoherent light sources with low spectral power densities. The method is demonstrated for the first time using a broadband supercontinuum source. Best paper award OPTO 2011.

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link (url) [BibTex]

link (url) [BibTex]


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Encoding of Periodic and their Transient Motions by a Single Dynamic Movement Primitive

Ernesti, J., Righetti, L., Do, M., Asfour, T., Schaal, S.

In 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012), pages: 57-64, IEEE, Osaka, Japan, November 2012 (inproceedings)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Force Control Policies for Compliant Robotic Manipulation

Kalakrishnan, M., Righetti, L., Pastor, P., Schaal, S.

In ICML’12 Proceedings of the 29th International Coference on International Conference on Machine Learning, pages: 49-50, Edinburgh, Scotland, 2012 (inproceedings)

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[BibTex]

[BibTex]


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Quadratic programming for inverse dynamics with optimal distribution of contact forces

Righetti, L., Schaal, S.

In 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012), pages: 538-543, IEEE, Osaka, Japan, November 2012 (inproceedings)

Abstract
In this contribution we propose an inverse dynamics controller for a humanoid robot that exploits torque redundancy to minimize any combination of linear and quadratic costs in the contact forces and the commands. In addition the controller satisfies linear equality and inequality constraints in the contact forces and the commands such as torque limits, unilateral contacts or friction cones limits. The originality of our approach resides in the formulation of the problem as a quadratic program where we only need to solve for the control commands and where the contact forces are optimized implicitly. Furthermore, we do not need a structured representation of the dynamics of the robot (i.e. an explicit computation of the inertia matrix). It is in contrast with existing methods based on quadratic programs. The controller is then robust to uncertainty in the estimation of the dynamics model and the optimization is fast enough to be implemented in high bandwidth torque control loops that are increasingly available on humanoid platforms. We demonstrate properties of our controller with simulations of a human size humanoid robot.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Towards Associative Skill Memories

Pastor, P., Kalakrishnan, M., Righetti, L., Schaal, S.

In 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012), pages: 309-315, IEEE, Osaka, Japan, November 2012 (inproceedings)

Abstract
Movement primitives as basis of movement planning and control have become a popular topic in recent years. The key idea of movement primitives is that a rather small set of stereotypical movements should suffice to create a large set of complex manipulation skills. An interesting side effect of stereotypical movement is that it also creates stereotypical sensory events, e.g., in terms of kinesthetic variables, haptic variables, or, if processed appropriately, visual variables. Thus, a movement primitive executed towards a particular object in the environment will associate a large number of sensory variables that are typical for this manipulation skill. These association can be used to increase robustness towards perturbations, and they also allow failure detection and switching towards other behaviors. We call such movement primitives augmented with sensory associations Associative Skill Memories (ASM). This paper addresses how ASMs can be acquired by imitation learning and how they can create robust manipulation skill by determining subsequent ASMs online to achieve a particular manipulation goal. Evaluation for grasping and manipulation with a Barrett WAM/Hand illustrate our approach.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Template-based learning of grasp selection

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

In 2012 IEEE International Conference on Robotics and Automation, pages: 2379-2384, IEEE, Saint Paul, USA, 2012 (inproceedings)

Abstract
The ability to grasp unknown objects is an important skill for personal robots, which has been addressed by many present and past research projects, but still remains an open problem. A crucial aspect of grasping is choosing an appropriate grasp configuration, i.e. the 6d pose of the hand relative to the object and its finger configuration. Finding feasible grasp configurations for novel objects, however, is challenging because of the huge variety in shape and size of these objects. Moreover, possible configurations also depend on the specific kinematics of the robotic arm and hand in use. In this paper, we introduce a new grasp selection algorithm able to find object grasp poses based on previously demonstrated grasps. Assuming that objects with similar shapes can be grasped in a similar way, we associate to each demonstrated grasp a grasp template. The template is a local shape descriptor for a possible grasp pose and is constructed using 3d information from depth sensors. For each new object to grasp, the algorithm then finds the best grasp candidate in the library of templates. The grasp selection is also able to improve over time using the information of previous grasp attempts to adapt the ranking of the templates. We tested the algorithm on two different platforms, the Willow Garage PR2 and the Barrett WAM arm which have very different hands. Our results show that the algorithm is able to find good grasp configurations for a large set of objects from a relatively small set of demonstrations, and does indeed improve its performance over time.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Probabilistic depth image registration incorporating nonvisual information

Wüthrich, M., Pastor, P., Righetti, L., Billard, A., Schaal, S.

In 2012 IEEE International Conference on Robotics and Automation, pages: 3637-3644, IEEE, Saint Paul, USA, 2012 (inproceedings)

Abstract
In this paper, we derive a probabilistic registration algorithm for object modeling and tracking. In many robotics applications, such as manipulation tasks, nonvisual information about the movement of the object is available, which we will combine with the visual information. Furthermore we do not only consider observations of the object, but we also take space into account which has been observed to not be part of the object. Furthermore we are computing a posterior distribution over the relative alignment and not a point estimate as typically done in for example Iterative Closest Point (ICP). To our knowledge no existing algorithm meets these three conditions and we thus derive a novel registration algorithm in a Bayesian framework. Experimental results suggest that the proposed methods perform favorably in comparison to PCL [1] implementations of feature mapping and ICP, especially if nonvisual information is available.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Chiral molecules split light: Reflection and refraction in a chiral liquid

Ghosh, A., Fischer, P.

PHYSICAL REVIEW LETTERS, 97(17), 2006, Featured highlight ‘Fundamental optical physics: Refraction’ Nature Photonics, Nov. 2006. (article)

Abstract
A light beam changes direction as it enters a liquid at an angle from another medium, such as air. Should the liquid contain molecules that lack mirror symmetry, then it has been predicted by Fresnel that the light beam will not only change direction, but will actually split into two separate beams with a small difference in the respective angles of refraction. Here we report the observation of this phenomenon. We also demonstrate that the angle of reflection does not equal the angle of incidence in a chiral medium. Unlike conventional optical rotation, which depends on the path-length through the sample, the reported reflection and refraction phenomena arise within a few wavelengths at the interface and thereby suggest a new approach to polarimetry that can be used in microfluidic volumes.

Featured highlight ‘Fundamental optical physics: Refraction’ Nature Photonics, Nov. 2006.

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DOI [BibTex]

DOI [BibTex]


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Direct chiral discrimination in NMR spectroscopy

Buckingham, A., Fischer, P.

CHEMICAL PHYSICS, 324(1):111-116, 2006 (article)

Abstract
Conventional nuclear magnetic resonance spectroscopy is unable to distinguish between the two mirror-image forms (enantiomers) of a chiral molecule. This is because the NMR spectrum is determined by the chemical shifts and spin-spin coupling constants which - in the absence of a chiral solvent - are identical for the two enantiomers. We discuss how chirality may nevertheless be directly detected in liquid-state NMR spectroscopy: In a chiral molecule, the rotating nuclear magnetic moment induces an electric dipole moment in the direction perpendicular to itself and to the permanent magnetic field of the spectrometer. We present computations of the precessing electric polarization following a pi/2 pulse. Our estimates indicate that the electric polarization should be detectable in favourable cases. We also predict that application of an electrostatic field induces a chirally sensitive magnetization oscillating in the direction of the permanent magnetic field. We show that the electric-field-perturbed chemical shift tensor, the nuclear magnetic shielding polarizability, underlies these chiral NMR effects. (c) 2005 Elsevier B.V. All rights reserved.

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DOI [BibTex]

DOI [BibTex]


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NONLINEAR OPTICAL PROPERTIES OF CHIRAL LIQUIDS Electric-dipolar pseudoscalars in nonlinear optics

Fischer, P., Champagne, B.

In NON-LINEAR OPTICAL PROPERTIES OF MATTER: FROM MOLECULES TO CONDENSED PHASES, 1, pages: 359-381, Challenges and Advances in Computational Chemistry and Physics, 2006 (incollection)

Abstract
We give all overview of linear and nonlinear optical processes that can be specific to chiral molecules in isotropic media. Specifically, we discuss the pseudoscalars that underlie nonlinear optical activity and chiral frequency conversion processes in fluids. We show that nonlinear optical techniques open entirely new ways of exploring chirality: Sum-frequency-generation (SFG) at second-order and BioCARS at fourth-order arise in the electric-dipole approximation and do not require circularly polarized light to detect chiral molecules in solution. Here the frequency conversion in itself is a measure of chirality. This is in contrast to natural optical activity phenomena which are based on the interference of radiation from induced oscillating electric and magnetic dipoles, and which are observed as a differential response to right and left circularly polarized light. We give examples from our SFG experiments in optically active solutions and show how the application of an additional static electric field to sum-frequency generation allows the absolute configuration of the chiral solute to be determined via all electric-dipolar process. Results from ab initio calculations of the SFG pseudoscalar are presented for a number of chiral molecules

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[BibTex]

[BibTex]


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Ring-resonator-based frequency-domain optical activity measurements of a chiral liquid

Vollmer, F., Fischer, P.

OPTICS LETTERS, 31(4):453-455, 2006 (article)

Abstract
Chiral liquids rotate the plane of polarization of linearly polarized light and are therefore optically active. Here we show that optical rotation can be observed in the frequency domain. A chiral liquid introduced in a fiber-loop ring resonator that supports left and right circularly polarized modes gives rise to relative frequency shifts that are a direct measure of the liquid's circular birefringence and hence of its optical activity. The effect is in principle not diminished if the circumference of the ring is reduced. The technique is similarly applicable to refractive index and linear birefringence measurements. (c) 2006 Optical Society of America.

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DOI [BibTex]


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Sign of the refractive index in a gain medium with negative permittivity and permeability

Chen, Y., Fischer, P., Wise, F.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 23(1):45-50, 2006 (article)

Abstract
We show how the sign of the refractive index in any medium may be derived using a rigorous analysis based on Einstein causality. In particular, we consider left-handed materials, i.e., media that have negative permittivities and permeabilities at the frequency of interest. We find that the consideration of gain in such media can give rise to a positive refractive index. (c) 2006 Optical Society of America.

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DOI [BibTex]

DOI [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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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]