arXiv subjects

Florian Beck

Publications and source records attributed to Florian Beck.

18 recordsLinked to original sources

arXiv2025

BoundPlanner: A convex-set-based approach to bounded manipulator trajectory planning

Online trajectory planning enables robot manipulators to react quickly to changing environments or tasks. Many robot trajectory planners exist for known environments but are often too slow for online computations. Current methods in online trajectory planning do not find suitable trajectories in challenging scenarios that respect the limits of the robot and account for collisions. This work proposes a trajectory planning framework consisting of the novel Cartesian path planner based on convex sets, called BoundPlanner, and the online trajectory planner BoundMPC. BoundPlanner explores and maps the collision-free space using convex sets to compute a reference path with bounds. BoundMPC is extended in this work to handle convex sets for path deviations, which allows the robot to optimally follow the path within the bounds while accounting for the robot's kinematics. Collisions of the robot's kinematic chain are considered by a novel convex-set-based collision avoidance formulation independent on the number of obstacles. Simulations and experiments with a 7-DoF manipulator show the performance of the proposed planner compared to state-of-the-art methods. The source code is available at github.com/TU-Wien-ACIN-CDS/BoundPlanner and videos of the experiments can be found at www.acin.tuwien.ac.at/42d4.

cs.RO↗

arXiv2024

Language-Driven Closed-Loop Grasping with Model-Predictive Trajectory Replanning

Combining a vision module inside a closed-loop control system for a \emph{seamless movement} of a robot in a manipulation task is challenging due to the inconsistent update rates between utilized modules. This task is even more difficult in a dynamic environment, e.g., objects are moving. This paper presents a \emph{modular} zero-shot framework for language-driven manipulation of (dynamic) objects through a closed-loop control system with real-time trajectory replanning and an online 6D object pose localization. We segment an object within $\SI{0.5}{\second}$ by leveraging a vision language model via language commands. Then, guided by natural language commands, a closed-loop system, including a unified pose estimation and tracking and online trajectory planning, is utilized to continuously track this object and compute the optimal trajectory in real-time. Our proposed zero-shot framework provides a smooth trajectory that avoids jerky movements and ensures the robot can grasp a non-stationary object. Experiment results exhibit the real-time capability of the proposed zero-shot modular framework for the trajectory optimization module to accurately and efficiently grasp moving objects, i.e., up to \SI{30}{\hertz} update rates for the online 6D pose localization module and \SI{10}{\hertz} update rates for the receding-horizon trajectory optimization. These advantages highlight the modular framework's potential applications in robotics and human-robot interaction; see the video in https://www.acin.tuwien.ac.at/en/6e64/.

cs.RO↗

arXiv2024

Model Predictive Trajectory Optimization With Dynamically Changing Waypoints for Serial Manipulators

Systematically including dynamically changing waypoints as desired discrete actions, for instance, resulting from superordinate task planning, has been challenging for online model predictive trajectory optimization with short planning horizons. This paper presents a novel waypoint model predictive control (wMPC) concept for online replanning tasks. The main idea is to split the planning horizon at the waypoint when it becomes reachable within the current planning horizon and reduce the horizon length towards the waypoints and goal points. This approach keeps the computational load low and provides flexibility in adapting to changing conditions in real time. The presented approach achieves competitive path lengths and trajectory durations compared to (global) offline RRT-type planners in a multi-waypoint scenario. Moreover, the ability of wMPC to dynamically replan tasks online is experimentally demonstrated on a KUKA LBR iiwa 14 R820 robot in a dynamic pick-and-place scenario.

cs.RO↗

arXiv2024

BoundMPC: Cartesian path following with error bounds based on model predictive control in the joint space

This work introduces the BoundMPC strategy, an innovative online model-predictive path-following approach for robot manipulators. This joint-space trajectory planner allows the following of Cartesian reference paths in the end-effector's position and orientation, including via-points, within the desired asymmetric bounds of the orthogonal path error. These bounds encode the obstacle-free space and additional task-specific constraints in Cartesian space. Contrary to traditional path-following concepts, BoundMPC purposefully deviates from the Cartesian reference path in position and orientation to account for the robot's kinematics, leading to more successful task executions for Cartesian reference paths. Furthermore the simple reference path formulation is computationally efficient and allows for replanning during the robot's motion. This feature makes it possible to use this planner for dynamically changing environments and varying goals. The flexibility and performance of BoundMPC are experimentally demonstrated by five scenarios on a 7-DoF Kuka LBR iiwa 14 R820 robot. The first scenario shows the transfer of a larger object from a start to a goal pose through a confined space where the object must be tilted. The second scenario deals with grasping an object from a table where the grasping point changes during the robot's motion, and collisions with other obstacles in the scene must be avoided. The adaptability of BoundMPC is showcased in scenarios such as the opening of a drawer, the transfer of an open container, and the wiping of a table, where it effectively handles task-specific constraints. The last scenario highlights the possibility of accounting for collisions with the entire robot's kinematic chain. The code is readily available at https://github.com/thieso/boundmpc, inspiring you to explore its potential and adapt it to your specific robotic tasks.

cs.RO↗

arXiv2023

Special geometry, quasi-modularity and attractor flow for BPS structures

We study mathematical structures on the moduli spaces of BPS structures of $\mathcal{N}=2$ theories. Guided by the realization of BPS structures within type IIB string theory on non-compact Calabi-Yau threefolds, we develop a notion of BPS variation of Hodge structure which gives rise to special K\"ahler geometry as well as to Picard-Fuchs equations governing the central charges of the BPS structure. We focus our study on cases with complex one dimensional moduli spaces and charge lattices of rank two including Argyres-Douglas $A_2$ as well as Seiberg-Witten $SU(2)$ theories. In these cases the moduli spaces are identified with modular curves and we determine the expressions of the central charges in terms of quasi-modular forms of the corresponding duality groups. We furthermore determine the curves of marginal stability and study the attractor flow in these examples, showing that it provides another way of determining the complete BPS spectrum in these cases.

hep-th↗

arXiv2023

Efficient learning of large sets of locally optimal classification rules

Conventional rule learning algorithms aim at finding a set of simple rules, where each rule covers as many examples as possible. In this paper, we argue that the rules found in this way may not be the optimal explanations for each of the examples they cover. Instead, we propose an efficient algorithm that aims at finding the best rule covering each training example in a greedy optimization consisting of one specialization and one generalization loop. These locally optimal rules are collected and then filtered for a final rule set, which is much larger than the sets learned by conventional rule learning algorithms. A new example is classified by selecting the best among the rules that cover this example. In our experiments on small to very large datasets, the approach's average classification accuracy is higher than that of state-of-the-art rule learning algorithms. Moreover, the algorithm is highly efficient and can inherently be processed in parallel without affecting the learned rule set and so the classification accuracy. We thus believe that it closes an important gap for large-scale classification rule induction.

cs.LG↗

arXiv2022

Two-Step Online Trajectory Planning of a Quadcopter in Indoor Environments with Obstacles

This paper presents a two-step algorithm for online trajectory planning in indoor environments with unknown obstacles. In the first step, sampling-based path planning techniques such as the optimal Rapidly exploring Random Tree (RRT*) algorithm and the Line-of-Sight (LOS) algorithm are employed to generate a collision-free path consisting of multiple waypoints. Then, in the second step, constrained quadratic programming is utilized to compute a smooth trajectory that passes through all computed waypoints. The main contribution of this work is the development of a flexible trajectory planning framework that can detect changes in the environment, such as new obstacles, and compute alternative trajectories in real time. The proposed algorithm actively considers all changes in the environment and performs the replanning process only on waypoints that are occupied by new obstacles. This helps to reduce the computation time and realize the proposed approach in real time. The feasibility of the proposed algorithm is evaluated using the Intel Aero Ready-to-Fly (RTF) quadcopter in simulation and in a real-world experiment.

cs.RO↗

arXiv2022

Machine Learning-based Framework for Optimally Solving the Analytical Inverse Kinematics for Redundant Manipulators

Solving the analytical inverse kinematics (IK) of redundant manipulators in real time is a difficult problem in robotics since its solution for a given target pose is not unique. Moreover, choosing the optimal IK solution with respect to application-specific demands helps to improve the robustness and to increase the success rate when driving the manipulator from its current configuration towards a desired pose. This is necessary, especially in high-dynamic tasks like catching objects in mid-flights. To compute a suitable target configuration in the joint space for a given target pose in the trajectory planning context, various factors such as travel time or manipulability must be considered. However, these factors increase the complexity of the overall problem which impedes real-time implementation. In this paper, a real-time framework to compute the analytical inverse kinematics of a redundant robot is presented. To this end, the analytical IK of the redundant manipulator is parameterized by so-called redundancy parameters, which are combined with a target pose to yield a unique IK solution. Most existing works in the literature either try to approximate the direct mapping from the desired pose of the manipulator to the solution of the IK or cluster the entire workspace to find IK solutions. In contrast, the proposed framework directly learns these redundancy parameters by using a neural network (NN) that provides the optimal IK solution with respect to the manipulability and the closeness to the current robot configuration. Monte Carlo simulations show the effectiveness of the proposed approach which is accurate and real-time capable ($\approx$ \SI{32}{\micro\second}) on the KUKA LBR iiwa 14 R820.

cs.RO↗

arXiv2022

Singularity Avoidance with Application to Online Trajectory Optimization for Serial Manipulators

This work proposes a novel singularity avoidance approach for real-time trajectory optimization based on known singular configurations. The focus of this work lies on analyzing kinematically singular configurations for three robots with different kinematic structures, i.e., the Comau Racer 7-1.4, the KUKA LBR iiwa R820, and the Franka Emika Panda, and exploiting these configurations in form of tailored potential functions for singularity avoidance. Monte Carlo simulations of the proposed method and the commonly used manipulability maximization approach are performed for comparison. The numerical results show that the average computing time can be reduced and shorter trajectories in both time and path length are obtained with the proposed approach

cs.RO↗

arXiv2021

An Investigation into Mini-Batch Rule Learning

We investigate whether it is possible to learn rule sets efficiently in a network structure with a single hidden layer using iterative refinements over mini-batches of examples. A first rudimentary version shows an acceptable performance on all but one dataset, even though it does not yet reach the performance levels of Ripper.

cs.LG↗

arXiv2021

An Empirical Investigation into Deep and Shallow Rule Learning

Inductive rule learning is arguably among the most traditional paradigms in machine learning. Although we have seen considerable progress over the years in learning rule-based theories, all state-of-the-art learners still learn descriptions that directly relate the input features to the target concept. In the simplest case, concept learning, this is a disjunctive normal form (DNF) description of the positive class. While it is clear that this is sufficient from a logical point of view because every logical expression can be reduced to an equivalent DNF expression, it could nevertheless be the case that more structured representations, which form deep theories by forming intermediate concepts, could be easier to learn, in very much the same way as deep neural networks are able to outperform shallow networks, even though the latter are also universal function approximators. In this paper, we empirically compare deep and shallow rule learning with a uniform general algorithm, which relies on greedy mini-batch based optimization. Our experiments on both artificial and real-world benchmark data indicate that deep rule networks outperform shallow networks.

cs.LG↗

arXiv2021

Geometry of the Space of Sections of Twistor Spaces with Circle Action

We study the holomorphic symplectic geometry of (the smooth locus of) the space of holomorphic sections of a twistor space with rotating circle action. The twistor space carries a line bundle with meromorphic connection constructed by Hitchin. We give an interpretation of Hitchin's meromorphic connection in the context of the Atiyah-Ward transform of the corresponding hyperholomorphic line bundle. It is shown that the residue of the meromorphic connection serves as a moment map for the induced circle action, and furthermore the critical points of this moment map are studied. Particular emphasis is given to the example of Deligne-Hitchin moduli spaces.

math.DG↗

arXiv2020

Parabolic Higgs bundles, $tt^*$ connections and opers

The non-abelian Hodge correspondence identifies complex variations of Hodge structures with certain Higgs bundles. In this work we analyze this relationship, and some of its ramifications, when the variations of Hodge structures are determined by a (complete) one-dimensional family of compact Calabi-Yau manifolds. This setup enables us to apply techniques from mirror symmetry. For example, the corresponding Higgs bundles extend to parabolic Higgs bundles to the compactification of the base of the families. We determine the parabolic degrees of the underlying parabolic bundles in terms of the exponents of the Picard-Fuchs equations obtained from the variations of Hodge structure. Moreover, we prove in this setup that the flat non-abelian Hodge or $tt^*$-connection is gauge equivalent to an oper which is determined by the corresponding Picard-Fuchs equations. This gauge equivalence puts forward a new derivation of non-linear differential relations between special functions on the moduli space which generalize Ramanujan's relations for the differential ring of quasi-modular forms.

math.AG↗

arXiv2020

Folding of Hitchin systems and crepant resolutions

Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of ABCDEFG-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of ADE-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi--Yau orbifold stacks constructed by the first author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi--Yau threefolds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.

math.AG↗

arXiv2020

Energy of sections of the Deligne-Hitchin twistor space

We study a natural functional on the space of holomorphic sections of the Deligne-Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We give a link to a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. Moreover, we prove that for a certain class of real holomorphic sections of the Deligne-Hitchin moduli space, the functional is basically given by the Willmore energy of corresponding (equivariant) conformal map to the 3-sphere. As an application we use the functional to distinguish new components of real holomorphic sections of the Deligne-Hitchin moduli space from the space of twistor lines.

math.DG↗

arXiv2019

Hitchin and Calabi-Yau integrable systems via variations of Hodge structures

A complex integrable system determines a family of complex tori over a Zariski-open and dense subset in its base. This family in turn yields an integral variation of Hodge structures of weight $\pm 1$. In this paper, we study the converse of this procedure. Starting from an integral variation of Hodge structures of weight $\pm 1$, we give a criterion for when its associated family of complex tori carries a Lagrangian structure, i.e. for when it can be given the structure of an integrable system. This sheaf-theoretic approach to (the smooth parts of) complex integrable systems enables us to apply powerful tools from Hodge and sheaf theory to study complex integrable systems. We exemplify the usefulness of this viewpoint by proving that the degree zero component of the Hitchin system for any simple adjoint or simply-connected complex Lie group $G$ is isomorphic to a non-compact Calabi-Yau integrable system over a Zariski-open and dense subset in the corresponding Hitchin base. In particular, we recover previously known results for the case where $G$ has a Dynkin diagram of type ADE and extend them to the remaining Dynkin types $\mathrm{B}_k$, $\mathrm{C}_k$, $\mathrm{F}_4$ and $\mathrm{G}_2$.

math.AG↗

arXiv2019

Aspects of Calabi-Yau Integrable and Hitchin Systems

In the present notes we explain the relationship between Calabi-Yau integrable systems and Hitchin systems based on work by Diaconescu-Donagi-Pantev and the author. Besides a review of these integrable systems, we highlight related topics, for example variations of Hodge structures, cameral curves and Slodowy slices, along the way.

math.AG↗

arXiv2018

Calabi-Yau orbifolds over Hitchin bases

Any irreducible Dynkin diagram $Δ$ is obtained from an irreducible Dynkin diagram $Δ_h$ of type $\mathrm{ADE}$ by folding via graph automorphisms. For any simple complex Lie group $G$ with Dynkin diagram $Δ$ and compact Riemann surface $Σ$, we give a Lie-theoretic construction of families of quasi-projective Calabi-Yau threefolds together with an action of graph automorphisms over the Hitchin base associated to the pair $(Σ, G)$ . These give rise to Calabi-Yau orbifolds over the same base. Their intermediate Jacobian fibration, constructed in terms of equivariant cohomology, is isomorphic to the Hitchin system of the same type away from singular fibers.

math.AG↗