arXiv subjects

Andreas Muller

Publications and source records attributed to Andreas Muller.

13 recordsLinked to original sources

arXiv2019

Inducing Multi-Convexity in Path Constrained Trajectory Optimization for Mobile Manipulators

In this paper, we propose a novel trajectory optimization algorithm for mobile manipulators under end-effector path, collision avoidance and various kinematic constraints. Our key contribution lies in showing how this highly non-linear and non-convex problem can be solved as a sequence of convex unconstrained quadratic programs (QPs). This is achieved by reformulating the non-linear constraints that arise out of manipulator kinematics and its coupling with the mobile base in a multi-affine form. We then use techniques from Alternating Direction Method of Multipliers (ADMM) to formulate and solve the trajectory optimization problem. The proposed ADMM has two similar non-convex steps. Importantly, a convex surrogate can be derived for each of them. We show how large parts of our optimization can be solved in parallel providing the possibility of exploiting multi-core CPUs/GPUs. We validate our trajectory optimization on different benchmark examples. Specifically, we highlight how it solves the cyclicity bottleneck and provides a holistic approach where diverse set of trajectories can be obtained by trading-off different aspects of manipulator and mobile base motion.

cs.RO↗

arXiv2018

Combining Method of Alternating Projections and Augmented Lagrangian for Task Constrained Trajectory Optimization

Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization problem with non-linear equality constraints which can be solved by general non-linear optimization techniques. In this paper, we present a novel custom optimizer which exploits the underlying structure present in many task constraints. At the core of our approach are some simple reformulations, which when coupled with the \emph{method of alternating projection}, leads to an efficient convex optimization based routine for computing a feasible solution to the task constraints. We subsequently build on this result and use the concept of Augmented Lagrangian to guide the feasible solutions towards those which also minimize the user defined cost function. We show that the proposed optimizer is fully distributive and thus, can be easily parallelized. We validate our formulation on some common robotic benchmark problems. In particular, we show that the proposed optimizer achieves cyclic motion in the joint space corresponding to a similar nature trajectory in the task space. Furthermore, as a baseline, we compare the proposed optimizer with an off-the-shelf non-linear solver provide in open source package SciPy. We show that for similar task constraint residuals and smoothness cost, it can be upto more than three times faster than the SciPy alternative.

cs.RO↗

arXiv2014

Machine Learning for Neuroimaging with Scikit-Learn

Statistical machine learning methods are increasingly used for neuroimaging data analysis. Their main virtue is their ability to model high-dimensional datasets, e.g. multivariate analysis of activation images or resting-state time series. Supervised learning is typically used in decoding or encoding settings to relate brain images to behavioral or clinical observations, while unsupervised learning can uncover hidden structures in sets of images (e.g. resting state functional MRI) or find sub-populations in large cohorts. By considering different functional neuroimaging applications, we illustrate how scikit-learn, a Python machine learning library, can be used to perform some key analysis steps. Scikit-learn contains a very large set of statistical learning algorithms, both supervised and unsupervised, and its application to neuroimaging data provides a versatile tool to study the brain.

cs.LG↗

arXiv2012

Feedback-controlled laser fabrication of micromirror substrates

Short (40-200 microseconds) single focused CO2 laser pulses of energy of about 100 microJ were used to fabricate high quality concave micromirror templates on silica and fluoride glass. The ablated features have diameters of 20-100 microns and average root-mean-square (RMS) surface microroughness near their center of less than 0.2 nm. Temporally monitoring the fabrication process revealed that it proceeds on a time scale shorter than the laser pulse duration. We implement a fast feedback control loop (20 kHz bandwidth) based on the light emitted by the sample that ensures an RMS size dispersion of less than 5 percent in arrays on chips or in individually fabricated features on an optical fiber tip, a significant improvement over previous approaches using longer pulses and open loop operation.

physics.optics↗

arXiv2012

Approximate Message Passing under Finite Alphabet Constraints

In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which the sparse original signal is drawn from a finite alphabet. To solve this problem we propose an iterative message passing algorithm, which capitalises not only on the sparsity but by means of a prior distribution also on the discrete nature of the original signal. In our numerical experiments we test this algorithm in combination with a Rademacher measurement matrix and a measurement matrix derived from the random demodulator, which enables compressive sampling of analogue signals. Our results show in both cases significant performance gains over a linear programming based approach to the considered BPDN problem. We also compare the proposed algorithm to a similar message passing based algorithm without prior knowledge and observe an even larger performance improvement.

cs.IT↗

arXiv2011

Coalescence of Single Photons Emitted by Disparate Single Photon Sources: The Example of InAs Quantum Dots and Parametric Down-Conversion Sources

Single photons produced by fundamentally dissimilar physical processes will in general not be indistinguishable. We show how photons produced from a quantum dot and by parametric down-conversion in a nonlinear crystal can be manipulated to be indistinguishable. The measured two-photon coalescence probability is 16%, and is limited by quantum-dot decoherence. Temporal filtering to the quantum dot coherence time and accounting for detector time response increases this to 61% while retaining 25% of the events. This technique can connect different elements in a scalable quantum network.

quant-ph↗

arXiv2010

Resolved Sideband Emission of InAs/GaAs Quantum Dots Strained by Surface Acoustic Waves

The dynamic response of InAs/GaAs self-assembled quantum dots (QDs) to strain is studied experimentally by periodically modulating the QDs with a surface acoustic wave and measuring the QD fluorescence with photoluminescence and resonant spectroscopy. When the acoustic frequency is larger than the QD linewidth, we resolve phonon sidebands in the QD fluorescence spectrum. Using a resonant pump laser, we have demonstrated optical frequency conversion via the dynamically modulated QD, which is the physical mechanism underlying laser sideband cooling a nanomechanical resonator by means of an embedded QD.

cond-mat.mes-hall↗

arXiv2010

Active feedback of a Fabry-Perot cavity to the emission of a single InAs/GaAs quantum dot

We present a detailed study of the use of Fabry-Perot (FP) cavities for the spectroscopy of single InAs quantum dots (QDs). We derive optimal cavity characteristics and resolution limits, and measure photoluminescence linewidths as low as 0.9 GHz. By embedding the QDs in a planar cavity, we obtain a sufficiently large signal to actively feed back on the length of the FP to lock to the emission of a single QD with a stability below 2% of the QD linewidth. An integration time of approximately two seconds is found to yield an optimum compromise between shot noise and cavity length fluctuations.

cond-mat.mes-hall↗

arXiv2010

Interference of Single Photons from Two Separate Semiconductor Quantum Dots

We demonstrate and characterize interference between discrete photons emitted by two separate semiconductor quantum dot states in different samples excited by a pulsed laser. Their energies are tuned into resonance using strain. The photons have a total coalescence probability of 18.1% and the coincidence rate is below the classical limit. Post-selection of coincidences within a narrow time window increases the coalescence probability to 47%. The probabilities are reduced from unity because of dephasing and the postselection value is also reduced by the detector time response.

quant-ph↗

arXiv2009

Coupling an epitaxial quantum dot to a fiber-based external-mirror microcavity

We report the coupling of individual InAs quantum dots (QDs) to an external-mirror microcavity. The external mirror is bonded to a fiber and positioned above a semiconductor sample consisting of a QD-containing GaAs layer on top of a distributed Bragg reflector (DBR). This open cavity can be rapidly tuned with a piezoelectric actuator without negatively affecting the QD linewidth. A mirror radius of curvature of 42 microns and a cavity length of 10 microns enable good mode-matching and thus high collection efficiency directly into the fiber. With an improved finesse this system may enter the strong coupling regime.

cond-mat.mes-hall↗

arXiv2008

Emission spectrum of a dressed exciton-biexciton complex in a semiconductor quantum dot

The photoluminescence spectrum of a single quantum dot was recorded as a secondary resonant laser optically dressed either the vacuum-to-exciton or the exciton-to-biexciton transitions. High-resolution polarization-resolved measurements using a scanning Fabry-Perot interferometer reveal splittings of the linearly-polarized fine-structure states that are non-degenerate in an asymmetric quantum dot. These splittings manifest as either triplets or doublets and depend sensitively on laser intensity and detuning. Our approach realizes complete resonant control of a multi-excitonic system in emission, which can be either pulsed or continuous-wave, and offers direct access to the emitted photons.

cond-mat.mes-hall↗

arXiv2007

Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity

We show that resonance fluorescence, i.e. the resonant emission of a coherently driven two-level system, can be realized with a semiconductor quantum dot. The dot is embedded in a planar optical micro-cavity and excited in a wave-guide mode so as to discriminate its emission from residual laser scattering. The transition from the weak to the strong excitation regime is characterized by the emergence of oscillations in the first-order correlation function of the fluorescence, g(t), as measured by interferometry. The measurements correspond to a Mollow triplet with a Rabi splitting of up to 13.3 micro eV. Second-order-correlation measurements further confirm non-classical light emission.

cond-mat.mtrl-sci↗

arXiv2005

Coherent control of a V-type three-level system in a single quantum dot

In a semiconductor quantum dot, the Px and Py transitions to the polarization eigenstates, |x> and |y>, naturally form a three-level V-type system. Using low-temperature polarized photoluminescence spectroscopy, we have investigated the exciton dynamics arising under strong laser excitation. We also explicitly solved the density matrix equations for comparison with the experimental data. The polarization of the exciting field controls the coupling between the otherwise orthogonal states. In particular, when the system is initialized into |y>, a polarization-tailored pulse can swap the population into |x>, and vice-versa, effectively operating on the exciton spin.

cond-mat.mtrl-sci↗