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Christoph Böhm

Publications and source records attributed to Christoph Böhm.

At least 19 recordsLinked to original sources

Autonomous Control of Redundant Hydraulic Manipulator Using Reinforcement Learning with Action Feedback

This article presents an entirely data-driven approach for autonomous control of redundant manipulators with hydraulic actuation. The approach only requires minimal system information, which is inherited from a simulation model. The non-linear hydraulic actuation dynamics are modeled using actuator networks from the data gathered during the manual operation of the manipulator to effectively emulate the real system in a simulation environment. A neural network control policy for autonomous control, based on end-effector (EE) position tracking is then learned using Reinforcement Learning (RL) with Ornstein-Uhlenbeck process noise (OUNoise) for efficient exploration. The RL agent also receives feedback based on supervised learning of the forward kinematics which facilitates selecting the best suitable action from exploration. The control policy directly provides the joint variables as outputs based on provided target EE position while taking into account the system dynamics. The joint variables are then mapped to the hydraulic valve commands, which are then fed to the system without further modifications. The proposed approach is implemented on a scaled hydraulic forwarder crane with three revolute and one prismatic joint to track the desired position of the EE in 3-Dimensional (3D) space. With the emulated dynamics and extensive learning in simulation, the results demonstrate the feasibility of deploying the learned controller directly on the real system.

cs.RO↗

Automated Code Generation and Validation for Software Components of Microcontrollers

This paper proposes a method for generating software components for embedded systems, integrating seamlessly into existing implementations without developer intervention. We demonstrate this by automatically generating hardware abstraction layer (HAL) code for GPIO operations on the STM32F407 microcontroller. Using Abstract Syntax Trees (AST) for code analysis and Retrieval-Augmented Generation (RAG) for component generation, our approach enables autonomous code completion for embedded applications.

cs.SE↗

UGV-CBRN: An Unmanned Ground Vehicle for Chemical, Biological, Radiological, and Nuclear Disaster Response

Robotic search and rescue (SAR) supports response teams by accelerating disaster assessment and by keeping operators away from hazardous environments. In the event of a chemical, biological, radiological, and nuclear (CBRN) disaster, robots are deployed to identify and locate radiation sources. Human responders then assess the situation and neutralize the danger. The presented system takes a step toward enhanced integration of robots into SAR teams. Integrating autonomous radiation mapping with semi-autonomous substance sampling and online analysis of the CBRN threat lets the human operator localize and assess the threat from a safe distance. Two LiDARs, an IMU, and a Geiger counter are used for mapping the surrounding area and localizing potential radiation sources. A mobile manipulator with six Degrees of Freedom manipulates valves and samples substances that are analyzed by an onboard Raman spectrometer. The human operator monitors the mission's progression from a remote location defining target locations and directing the semi-autonomous manipulation processes. Diverse recovery behaviours aid robot deployment, system state monitoring, as well as recovery of hard- and software. Field tests showcase the capabilities of the presented system during trials at the CBRN disaster response challenge European Robotics Hackathon (EnRicH). We provide recorded sensor data and implemented software through a GitHub repository: https://github.com/TW-Robotics/search-and-rescue-robot-2024.

cs.RO↗

Moment map flow on real reductive Lie groups and GIT estimates

A finite dimensional real vector space carrying an action of a real reductive group possesses a moment map and a stratification as defined by Kirwan and Ness. In this article we investigate the properties of the moment map, the Kirwan-Ness stratification, and Lauret's application from a more functorial, algebraic point of view.

math.DG↗

Scalar curvature along Ebin geodesics

Let $M$ be a smooth, compact manifold and let $\mathcal{N}_μ$ denote the set of Riemannian metrics on $M$ with smooth volume density $μ$. For a given $g_0\in \mathcal{N}_μ$, we show that if $\dim(M)\ge 5$, then there exists an open and dense subset $\mathcal{Y}_{g_0} \subset T_{g_0} \mathcal{N}_μ$ (in the $C^{\infty}$ topology) so that for each $h\in \mathcal{Y}_{g_0}$, the $(\mathcal{N}_μ,L^2)$ Ebin geodesic $γ_h(t)$ with $γ_h(0)=g_0$ and $γ_h'(0)=h$ satisfies $\lim_{t \to \infty}$ $R(γ_h(t))=-\infty$, uniformly.

math.DG↗

Non-compact Einstein manifolds with unimodular isometry group

We show that a negative Einstein manifold admitting a proper isometric action of a connected unimodular Lie group with compact, possibly singular, orbit space splits isometrically as a product of a symmetric space and a compact negative Einstein manifold. The proof involves the theory of polar actions, Lie-theoretic arguments and maximum principles.

math.DG↗

Homogeneous Einstein Metrics and Butterflies

M.~M.~Graev associated in \cite{Gr} to a compact homogeneous space $G/H$ a nerve $\XGH$, whose non-contractibility implies the existence of a $G$-invariant Einstein metric on $G/H$. The nerve $\XGH$ is a compact semi-algebraic set, defined purely Lie theoretically by intermediate subgroups. In this paper we present a detailed description of the work of Graev and the curvature estimates of \cite{Bo}.

math.DG↗

Non-compact Einstein manifolds with symmetry

For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie group G with compact, smooth orbit space, we show the following rigidity result: The nilradical N of G acts polarly, and the N-orbits can be extended to minimal Einstein submanifolds. As an application, we prove the Alekseevskii conjecture: Any homogeneous Einstein manifold with negative scalar curvature is diffeomorphic to a Euclidean space.

math.DG↗

Overcoming Bias: Equivariant Filter Design for Biased Attitude Estimation with Online Calibration

Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system's capability. Both asymptotic behavior (e.g.,~for regular operation) and transient response (e.g.,~for fast initialization and reset) of such filters are of crucial importance in guaranteeing robust operation of autonomous systems. This paper introduces a new generic formulation for a gyroscope aided attitude estimator using N direction measurements including both body-frame and reference-frame direction type measurements. The approach is based on an integrated state formulation that incorporates navigation, extrinsic calibration for all direction sensors, and gyroscope bias states in a single equivariant geometric structure. This newly proposed symmetry allows modular addition of different direction measurements and their extrinsic calibration while maintaining the ability to include bias states in the same symmetry. The subsequently proposed filter-based estimator using this symmetry noticeably improves the transient response, and the asymptotic bias and extrinsic calibration estimation compared to state-of-the-art approaches. The estimator is verified in statistically representative simulations and is tested in real-world experiments.

cs.RO↗

COP: Control & Observability-aware Planning

In this research, we aim to answer the question: How to combine Closed-Loop State and Input Sensitivity-based with Observability-aware trajectory planning? These possibly opposite optimization objectives can be used to improve trajectory control tracking and, at the same time, estimation performance. Our proposed novel Control & Observability-aware Planning (COP) framework is the first that uses these possibly opposing objectives in a Single-Objective Optimization Problem (SOOP) based on the Augmented Weighted Tchebycheff method to perform the balancing of them and generation of Bézier curve-based trajectories. Statistically relevant simulations for a 3D quadrotor unmanned aerial vehicle (UAV) case study produce results that support our claims and show the negative correlation between both objectives. We were able to reduce the positional mean integral error norm as well as the estimation uncertainty with the same trajectory to comparable levels of the trajectories optimized with individual objectives.

cs.RO↗

Depth-aware Object Segmentation and Grasp Detection for Robotic Picking Tasks

In this paper, we present a novel deep neural network architecture for joint class-agnostic object segmentation and grasp detection for robotic picking tasks using a parallel-plate gripper. We introduce depth-aware Coordinate Convolution (CoordConv), a method to increase accuracy for point proposal based object instance segmentation in complex scenes without adding any additional network parameters or computation complexity. Depth-aware CoordConv uses depth data to extract prior information about the location of an object to achieve highly accurate object instance segmentation. These resulting segmentation masks, combined with predicted grasp candidates, lead to a complete scene description for grasping using a parallel-plate gripper. We evaluate the accuracy of grasp detection and instance segmentation on challenging robotic picking datasets, namely Siléane and OCID_grasp, and show the benefit of joint grasp detection and segmentation on a real-world robotic picking task.

cs.CV↗

The impact of climate change on astronomical observations

Climate change is affecting and will increasingly affect astronomical observations. In this paper, we investigated the role some key weather parameters play in the quality of astronomical observations, and analysed their long-term trends (longer than 30 years) in order to grasp the impact of climate change on current and future observations. In this preliminary study, we specifically analysed four parameters, the temperature, the surface layer turbulence, the wind speed at the jetstream layer and the humidity. The analyses is conducted with data from the Very Large Telescope (VLT), operated by the European Southern Observatory (ESO), located at Cerro Paranal in the Atacama desert, Chile, which is one of the driest places on Earth. To complete the data from the various sensors installed at Paranal, we used the fifth generation and 20th century European Centre Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis of the global climate, ERA5 (from 1980 to now) and ERA20C (from 1900 to 2010), which we interpolated at the Paranal observatory location. In addition, we also explored climate projections in this region, using the Coupled Model Intercomparison Project Phase 6 (CMIP6) multi-model ensemble, under the worst-case climate change Shared Socio-Economic Pathways (SSP5-8.5) scenario. Further investigation is needed to better understand the underlying mechanisms of change, as well as to assess the severity of the impact.

astro-ph.IM↗

Electro-magneto-mechanically response of polycrystalline materials: Computational Homogenization via the Virtual Element Method

This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties of heterogeneous polycrystalline microstructures with anisotropic grains. The flexibility in element shapes can be exploited for creating VE-mesh with a significant lower number of degrees of freedom if compared to finite element (FE) meshes, while maintaining a high accuracy. Evidence that VE-approaches outperform FEM are available in the literature, but only addressing purely-mechanic problems (i.e. elastic properties) and transversely anisotropic materials. The aim of this work is twofold. On one hand, the study compares VE-and FE-based numerical homogenization schemes for electro-mechanically coupled problems for different crystal lattice structures and degrees of elastic anisotropy. Within all considered materials, the VE-approach outperforms the FE-approach for the same number of nodes. On the other hand a hybrid microstructure made up by both electro-mechanical and magneto-mechanical grains is investigated resulting in a electro-magneto-mechanically coupled microstructure. Again, VEM provides a more accurate solution strategy.

cs.CE↗

Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds

We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit-Einstein condition, we construct a Lyapunov function based on curvature estimates which come from real GIT.

math.DG↗

Immortal homogeneous Ricci flows

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.

math.DG↗

The Ricci flow on solvmanifolds of real type

We show that for any solvable Lie group of real type, any homogeneous Ricci flow solution converges in Cheeger-Gromov topology to a unique non-flat solvsoliton, which is independent of the initial left-invariant metric. As an application, we obtain results on the isometry groups of non-flat solvsoliton metrics and Einstein solvmanifolds.

math.DG↗

Real geometric invariant theory

For linear actions of real reductive Lie groups we prove the Kempf-Ness Theorem about closed orbits and the Kirwan-Ness Stratification Theorem of the null cone. Since our completely self-contained proof focuses strongly on geometric and analytic methods, essentially avoiding any deep algebraic result, it applies also to non-rational linear actions.

math.DG↗

Optimal curvature estimates for homogeneous Ricci flows

We prove uniform curvature estimates for homogeneous Ricci flows: For a solution defined on $[0,t]$ the norm of the curvature tensor at time $t$ is bounded by the maximum of $C(n)/t$ and $C(n) ( scal(g(t)) - scal(g(0)) )$. This is used to show that solutions with finite extinction time are Type I, immortal solutions are Type III and ancient solutions are Type I, where all the constants involved depend only on the dimension $n$. A further consequence is that a non-collapsed homogeneous ancient solution on a compact homogeneous space emerges from a unique Einstein metric on the same space. The above curvature estimates are proved using a gap theorem for Ricci-flatness on homogeneous spaces. The proof of this gap theorem is by contradiction and uses a local $W^{2,p}$ convergence result, which holds without symmetry assumptions.

math.DG↗