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Matthias Mayr

Publications and source records attributed to Matthias Mayr.

35 records · Page 2Linked to original sources

Learning of Parameters in Behavior Trees for Movement Skills

Reinforcement Learning (RL) is a powerful mathematical framework that allows robots to learn complex skills by trial-and-error. Despite numerous successes in many applications, RL algorithms still require thousands of trials to converge to high-performing policies, can produce dangerous behaviors while learning, and the optimized policies (usually modeled as neural networks) give almost zero explanation when they fail to perform the task. For these reasons, the adoption of RL in industrial settings is not common. Behavior Trees (BTs), on the other hand, can provide a policy representation that a) supports modular and composable skills, b) allows for easy interpretation of the robot actions, and c) provides an advantageous low-dimensional parameter space. In this paper, we present a novel algorithm that can learn the parameters of a BT policy in simulation and then generalize to the physical robot without any additional training. We leverage a physical simulator with a digital twin of our workstation, and optimize the relevant parameters with a black-box optimizer. We showcase the efficacy of our method with a 7-DOF KUKA-iiwa manipulator in a task that includes obstacle avoidance and a contact-rich insertion (peg-in-hole), in which our method outperforms the baselines.

cs.RO↗

Skill-based Multi-objective Reinforcement Learning of Industrial Robot Tasks with Planning and Knowledge Integration

In modern industrial settings with small batch sizes it should be easy to set up a robot system for a new task. Strategies exist, e.g. the use of skills, but when it comes to handling forces and torques, these systems often fall short. We introduce an approach that provides a combination of task-level planning with targeted learning of scenario-specific parameters for skill-based systems. We propose the following pipeline: (1) the user provides a task goal in the planning language PDDL, (2) a plan (i.e., a sequence of skills) is generated and the learnable parameters of the skills are automatically identified. An operator then chooses (3) reward functions and hyperparameters for the learning process. Two aspects of our methodology are critical: (a) learning is tightly integrated with a knowledge framework to support symbolic planning and to provide priors for learning, (b) using multi-objective optimization. This can help to balance key performance indicators (KPIs) such as safety and task performance since they can often affect each other. We adopt a multi-objective Bayesian optimization approach and learn entirely in simulation. We demonstrate the efficacy and versatility of our approach by learning skill parameters for two different contact-rich tasks. We show their successful execution on a real 7-DOF KUKA-iiwa manipulator and outperform the manual parameterization by human robot operators.

cs.RO↗

Scalable computational kernels for mortar finite element methods

Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling conditions at high accuracy, but come with considerable numerical effort and cost for the evaluation of the mortar integrals to compute the coupling operators. In this paper, we identify bottlenecks in parallel data layout and domain decomposition that hinder an efficient evaluation of the mortar integrals. We then propose a set of computational strategies to restore optimal parallel communication and scalability for the core kernels devoted to the evaluation of mortar terms. We exemplarily study the proposed algorithmic components in the context of three-dimensional large-deformation contact mechanics, both for cases with fixed and dynamically varying interface topology, yet these concepts can naturally and easily be transferred to other mortar applications, e.g. classical meshtying problems. To restore parallel scalability, we employ overlapping domain decompositions of the interface discretization independent from the underlying volumes and then tackle parallel communication for the mortar evaluation by a geometrically motivated reduction of ghosting data. Using three-dimensional contact examples, we demonstrate strong and weak scalability of the proposed algorithms up to 480 parallel processes as well as study and discuss improvements in parallel communication related to mortar finite element methods. For the first time, dynamic load balancing is applied to mortar contact problems with evolving contact zones, such that the computational work is well balanced among all parallel processors independent of the current state of the simulation.

math.NA↗

Fluid-beam interaction: Capturing the effect of embedded slender bodies on global fluid flow and vice versa

This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to model the behavior of slender structures while leading to rather well-posed problem descriptions. In particular, we propose a mixed-dimensional embedded finite element approach for the coupling of one-dimensional geometrically exact beam equations to a three-dimensional background fluid mesh, referred to as fluid-beam interaction (FBI) in analogy to the well-established notion of FSI. Here, the fluid is described by the incompressible isothermal Navier-Stokes equations for Newtonian fluids. In particular, we present algorithmic aspects regarding the solution of the resulting one-way coupling schemes and, through selected numerical examples, analyze their spatial convergence behavior as well as their suitability not only as stand-alone methods but also for an extension to a full two-way coupling scheme.

cs.CE↗

Algebraic multigrid methods for saddle point systems arising from mortar contact formulations

In this paper, a fully aggregation-based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach. While the idea of extending multigrid methods to saddle point systems can already be found, e.g., in the context of Stokes and Oseen equations in literature, the main contributions of this work are (i) the development and open-source implementation of an interface aggregation strategy specifically suited for generating Lagrange multiplier aggregates that are required for coupling structural equilibrium equations with contact constraints and (ii) a review of saddle point smoothers in the context of constrained interface problems. The new interface aggregation strategy perfectly fits into an aggregation-based multigrid framework and can easily be combined with segregated transfer operators, which allow to preserve the saddle point structure on the coarse levels. Further analysis provides insight into saddle point smoothers applied to contact problems, while numerical experiments illustrate the robustness of the new method. We have implemented the proposed algorithm within the MueLu package of the open-source Trilinos project. Numerical examples demonstrate the robustness of the proposed method in complex dynamic contact problems as well as its scalability up to 23.9 million unknowns on 480 MPI ranks.

cs.CE↗

Non-invasive multigrid for semi-structured grids

Multigrid solvers for hierarchical hybrid grids (HHG) have been proposed to promote the efficient utilization of high performance computer architectures. These HHG meshes are constructed by uniformly refining a relatively coarse fully unstructured mesh. While HHG meshes provide some flexibility for unstructured applications, most multigrid calculations can be accomplished using efficient structured grid ideas and kernels. This paper focuses on generalizing the HHG idea so that it is applicable to a broader community of computational scientists, and so that it is easier for existing applications to leverage structured multigrid components. Specifically, we adapt the structured multigrid methodology to significantly more complex semi-structured meshes. Further, we illustrate how mature applications might adopt a semi-structured solver in a relatively non-invasive fashion. To do this, we propose a formal mathematical framework for describing the semi-structured solver. This formalism allows us to precisely define the associated multigrid method and to show its relationship to a more traditional multigrid solver. Additionally, the mathematical framework clarifies the associated software design and implementation. Numerical experiments highlight the relationship of the new solver with classical multigrid. We also demonstrate the generality and potential performance gains associated with this type of semi-structured multigrid.

math.NA↗

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to capture for the reinforcements, while still being able to account for complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance.

cs.CE↗

A multi-scale FEM-BEM formulation for contact mechanics between rough surfaces

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface interactions at the macro-scale with a boundary element method (BEM) for the solution of the contact problem at the micro-scale. The BEM is used at each integration point to determine the normal contact traction and the normal contact stiffness, allowing to take into account any desirable kind of rough topology, either real, e.g. obtained from profilometric data, or artificial, evaluated with the most suitable numerical or analytical approach. Different numerical strategies to accelerate coupling between FEM and BEM are discussed in relation to a selected benchmark test.

cs.CE↗

A Temporal Consistent Monolithic Approach to Fluid-Structure Interaction Enabling Single Field Predictors

We present a monolithic approach to large-deformation fluid-structure interaction (FSI) problems that allows for choosing fully implicit, single-step and single-stage time integration schemes in the structure and fluid field independently, and hence is tailored to the needs of the individual field. The independent choice of time integration schemes is achieved by temporal consistent interpolation of the interface traction. To reduce computational costs, we introduce the possibility of field specific predictors in both structure and fluid field. These predictors act on the single fields only. Possible violations of the interface coupling conditions during the predictor step are dealt with within the monolithic solution procedure. We present full detail of such a generalized monolithic solution procedure, which is fully consistent in its non-conforming temporal and spatial discretization. The incorporated mortar approach allows for non-matching spatial discretizations of the fluid and solid domain at the FSI interface and is fully integrated in the resulting monolithic system of equations. The method is applied to a variety of numerical examples. Thereby, temporal convergence rates, the special role of essential boundary conditions at the fluid-structure interface, and the positive effect of predictors are demonstrated and discussed. Emphasis is put on the comparison of different time integration schemes in fluid and structure field, for what the achieved freedom of choice of time integrators is fully exploited.

math.NA↗

The influence of proximity effects in inhomogeneous electronic states

We describe the high-temperature superconductor La$_{2-x}$Sr$_x$CuO$_4$ in the underdoped regime in terms of a mixed-phase model, which consists of superconducting clusters embedded in the antiferromagnetic matrix. Our work is motivated by a series of recent angle-resolved photoemission experiments, which have significantly enhanced our understanding of the electronic structure in single-layer cuprates, and we show that those results can be fully reproduced once a reasonable set of parameters is chosen and disorder is properly taken into account. Close to half-filling, many nominally hole-rich and superconducting sites have comparatively large excitation gaps due to the ubiquitous proximity of the insulating phase. No other competing states or any further assumptions are necessary to account for a satisfying description of the underdoped phase, including the notorious pseudogap, which emerges as a natural consequence of a mixed-phase state. Close to optimal doping, the resulting gap distribution mirrors the one found in tunneling experiments. The scenario presented is also compelling because the existence of an optimal doping is intrinsically linked to the presence of electronic inhomogeneity, as is the transition from the highly mysterious to the rather conventional nature of the metallic state above $T_c$ in the overdoped regime. The phase diagram that emerges bears strong similarity to the canonical cuprate phase diagram, it explains quantitatively the rapid loss of long-range antiferromagnetic order, and also provides for a ``superconducting fluctuating'' regime just above $T_c$ as recently proposed in the context of resistance measurements. Implications for manganites are briefly discussed.

cond-mat.str-el↗

Domain-wall excitons and optical conductivity in one-dimensional Wigner lattices

Motivated by the recent finding that doped edge-sharing Cu-O chain compounds like Na$_3$Cu$_2$O$_4$ and Na$_8$Cu$_5$O$_{10}$ are realizations of one-dimensional Wigner crystals, we study the optical spectra of such systems. Charge excitations in 1D Wigner crystals are described in terms of domain wall excitations with fractional charge. We investigate analytically and numerically the domain-wall excitations that dominate the optical absorption, and analyse the dispersion and the parameter range of exciton states characteristic for the long-ranged Coulomb attraction between domain walls. Here we focus on the Wigner lattice at quarter-filling relevant for Na$_3$Cu$_2$O$_4$ and analyze in particular the role of second neighbor hopping $t_2$ which is important in edge-sharing chain compounds. Large $t_2$ drives an instability of the Wigner lattice via a soft domain-wall exciton towards a charge-density wave with a modulation period distinct from that of the Wigner lattice. Furthermore we calculate the temperature dependence of the DC-conductivity and show that it can be described by activated behavior combined with a $T^{-α}$ dependent mobility.

cond-mat.str-el↗

Phase Diagram of a Model for Diluted Magnetic Semiconductors Beyond Mean-Field Approximations

A lattice spin-fermion model for diluted magnetic semiconductors (DMS) is investigated numerically, improving on previously used mean-field (MF) approximations. Curie temperatures are obtained varying the Mn-spin x and hole n densities, and the impurity-hole exchange J in units of the hopping amplitude t. Optimal values are found in the subtle intermediate regime between itinerant and localized carriers. Our main result is the behavior of the Curie temperature at large J/t, where a "clustered" state is observed and ferromagnetism is suppressed. Formal analogies between DMS and manganites are also discussed.

cond-mat.str-el↗

Global versus Local Ferromagnetism in a Model for Diluted Magnetic Semiconductors Studied with Monte Carlo Techniques

A model recently introduced for diluted magnetic semiconductors by Berciu and Bhatt (PRL 87, 107203 (2001)) is studied with a Monte Carlo technique, and the results are compared to Hartree-Fock calculations. For doping rates close to the experimentally observed metal-insulator transition, a picture dominated by ferromagnetic droplets formed below a T* scale emerges. The moments of these droplets align as the temperature is lowered below a critical value Tc<T*. Our Monte Carlo investigations provide critical temperatures considerably smaller than Hartree-Fock predictions. Disorder does not seem to enhance ferromagnetism substantially. The inhomogeneous droplet state should be strongly susceptible to changes in doping and external fields.

cond-mat.dis-nn↗

Resistivity of Mixed-Phase Manganites

The resistivity $ρ_{dc}$ of manganites is studied using a random-resistor-network, based on phase-separation between metallic and insulating domains. When percolation occurs, both as chemical composition and temperature vary, results in good agreement with experiments are obtained. Similar conclusions are reached using quantum calculations and microscopic considerations. Above the Curie temperature, it is argued that ferromagnetic clusters should exist in Mn-oxides. Small magnetic fields induce large $ρ_{dc}$ changes and a bad-metal state with (disconnected) insulating domains.

cond-mat.str-el↗

Explanation of Giant Cluster Coexistence in Doped Manganites and Other Compounds

Computational studies show the generation of large coexisting metallic and insulating clusters with equal electronic density in models for manganites. The clusters are induced by disorder on exchange and hopping amplitudes near first-order transitions of the non-disordered strongly coupled system. The random-field Ising model is used to explain the qualitative aspects of our results. Percolative characteristics are natural in this context. Our results explain the recently experimentally discovered micrometer size inhomogeneities in manganites. The conclusions are general and apply to a variety of compounds.

cond-mat.str-el↗

A-type Antiferromagnetic and C-type Orbital-Ordered State in LaMnO$_3$ Using Cooperative Jahn-Teller Phonons

The effect of Jahn-Teller phonons on the magnetic and orbital structure of LaMnO$_3$ is investigated using a combination of relaxation and Monte Carlo techniques on three-dimensional clusters of MnO$_6$ octahedra. In the physically relevant region of parameter space for LaMnO$_3$, and after including small corrections due to tilting effects, the A-type antiferromagnetic and C-type orbital structures were stabilized, in agreement with experiments.

cond-mat.str-el↗

Pseudogap Formation in an Electronic System with d-wave Attraction at Low-density

On the basis of an electronic model with separable attractive interaction, the precursors at high temperature and strong coupling of the d-wave superconducting state are investigated in the one-particle spectral function $A({\bf k},ω)$ and the total density of states $ρ(ω)$, with the use of the self-consistent $t$-matrix approximation. In the low-density region, it is found that a gap-like structure at the Fermi level appears in $A({\bf k},ω)$ and $ρ(ω)$ above the superconducting transition temperature. It is shown that the pseudogap energy scale is determined by the binding energy of the Cooper-pair.

cond-mat↗