arXiv subjects

Mathias Bürger

Publications and source records attributed to Mathias Bürger.

12 recordsLinked to original sources

arXiv2023

The e-Bike Motor Assembly: Towards Advanced Robotic Manipulation for Flexible Manufacturing

Robotic manipulation is currently undergoing a profound paradigm shift due to the increasing needs for flexible manufacturing systems, and at the same time, because of the advances in enabling technologies such as sensing, learning, optimization, and hardware. This demands for robots that can observe and reason about their workspace, and that are skillfull enough to complete various assembly processes in weakly-structured settings. Moreover, it remains a great challenge to enable operators for teaching robots on-site, while managing the inherent complexity of perception, control, motion planning and reaction to unexpected situations. Motivated by real-world industrial applications, this paper demonstrates the potential of such a paradigm shift in robotics on the industrial case of an e-Bike motor assembly. The paper presents a concept for teaching and programming adaptive robots on-site and demonstrates their potential for the named applications. The framework includes: (i) a method to teach perception systems onsite in a self-supervised manner, (ii) a general representation of object-centric motion skills and force-sensitive assembly skills, both learned from demonstration, (iii) a sequencing approach that exploits a human-designed plan to perform complex tasks, and (iv) a system solution for adapting and optimizing skills online. The aforementioned components are interfaced through a four-layer software architecture that makes our framework a tangible industrial technology. To demonstrate the generality of the proposed framework, we provide, in addition to the motivating e-Bike motor assembly, a further case study on dense box packing for logistics automation.

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arXiv2021

Geometric Task Networks: Learning Efficient and Explainable Skill Coordination for Object Manipulation

Complex manipulation tasks can contain various execution branches of primitive skills in sequence or in parallel under different scenarios. Manual specifications of such branching conditions and associated skill parameters are not only error-prone due to corner cases but also quickly untraceable given a large number of objects and skills. On the other hand, learning from demonstration has increasingly shown to be an intuitive and effective way to program such skills for industrial robots. Parameterized skill representations allow generalization over new scenarios, which however makes the planning process much slower thus unsuitable for online applications. In this work, we propose a hierarchical and compositional planning framework that learns a Geometric Task Network (GTN) from exhaustive planners, without any manual inputs. A GTN is a goal-dependent task graph that encapsulates both the transition relations among skill representations and the geometric constraints underlying these transitions. This framework has shown to improve dramatically the offline learning efficiency, the online performance and the transparency of decision process, by leveraging the task-parameterized models. We demonstrate the approach on a 7-DoF robot arm both in simulation and on hardware solving various manipulation tasks.

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arXiv2019

Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromised when the parameter space is high-dimensional. A way to tackle this problem is to introduce domain knowledge into the BO framework. We propose to exploit the geometry of non-Euclidean parameter spaces, which often arise in robotics (e.g. orientation, stiffness matrix). Our approach, built on Riemannian manifold theory, allows BO to properly measure similarities in the parameter space through geometry-aware kernel functions and to optimize the acquisition function on the manifold as an unconstrained problem. We test our approach in several benchmark artificial landscapes and using a 7-DOF simulated robot to learn orientation and impedance parameters for manipulation skills.

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arXiv2017

Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems

In this paper, we study parameter-independent stability in qualitatively heterogeneous passive networked systems containing damped and undamped nodes. Given the graph topology and a set of damped nodes, we ask if output consensus is achieved for all system parameter values. For given parameter values, an eigenspace analysis is used to determine output consensus. The extension to parameter-independent stability is characterized by a coloring problem, named the richly balanced coloring (RBC) problem. The RBC problem asks if all nodes of the graph can be colored red, blue and black in such a way that (i) every damped node is black, (ii) every black node has blue neighbors if and only if it has red neighbors, and (iii) not all nodes in the graph are black. Such a colored graph is referred to as a richly balanced colored graph. Parameter-independent stability is guaranteed if there does not exist a richly balanced coloring. The RBC problem is shown to cover another well-known graph coloring scheme known as zero forcing sets. That is, if the damped nodes form a zero forcing set in the graph, then a richly balanced coloring does not exist and thus, parameter-independent stability is guaranteed. However, the full equivalence of zero forcing sets and parameter-independent stability holds only true for tree graphs. For more general graphs with few fundamental cycles an algorithm, named chord node coloring, is proposed that significantly outperforms a brute-force search for solving the NP-complete RBC problem.

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arXiv2016

Stability Analysis of Networked Systems Containing Damped and Undamped Nodes

This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the damped nodes will always converge to a steady-state value, the convergence of the undamped nodes is much more delicate and depends on the parameter values of the network as well as on the topology of the graph. A complete stability analysis is presented based on an eigenvector analysis involving the mass values and the topology of both the original graph and the reduced graph obtained by a Kron reduction that eliminates the damped nodes.

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arXiv2015

An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages

This paper studies the problem of frequency regulation in power grids under unknown and possible time-varying load changes, while minimizing the generation costs. We formulate this problem as an output agreement problem for distribution networks and address it using incremental passivity and distributed internal-model-based controllers. Incremental passivity enables a systematic approach to study convergence to the steady state with zero frequency deviation and to design the controller in the presence of time-varying voltages, whereas the internal-model principle is applied to tackle the uncertain nature of the loads.

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arXiv2015

On the Robustness of Uncertain Consensus Networks

This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in the graph, or any single negative edge weight has magnitude less than the inverse of the effective resistance between the two incident nodes, then the resulting network is unstable. These results are then applied to analyze the robustness properties of the consensus network with additive but bounded perturbations of the edge weights. It is shown that the small-gain condition is related again to cuts in the graph and effective resistance. For the single edge case, the small-gain condition is also shown to be exact. The results are then extended to consensus networks with non-linear couplings.

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arXiv2014

On the Definiteness of the Weighted Laplacian and its Connection to Effective Resistance

This work explores the definiteness of the weighted graph Laplacian matrix with negative edge weights. The definiteness of the weighted Laplacian is studied in terms of certain matrices that are related via congruent and similarity transformations. For a graph with a single negative weight edge, we show that the weighted Laplacian becomes indefinite if the magnitude of the negative weight is less than the inverse of the effective resistance between the two incident nodes. This result is extended to multiple negative weight edges. The utility of these results are demonstrated in a weighted consensus network where appropriately placed negative weight edges can induce a clustering behavior for the protocol.

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arXiv2014

Optimal pricing control in distribution networks with time-varying supply and demand

This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost functions of Legendre-type, is formalized and solved. The time-varying optimal flow is characterized in terms of the time-varying dual variables of a corresponding network optimization problem. A dynamic feedback controller is proposed that regulates the flows asymptotically to the optimal flows and achieves in addition a balancing of all storage levels.

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arXiv2013

Dynamic coupling design for nonlinear output agreement and time-varying flow control

This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances, using dynamic diffusive couplings. Necessary conditions are derived for general networks of nonlinear systems, and these conditions are explicitly interpreted as conditions relating the node dynamics and the network topology. For the class of incrementally passive systems, necessary and sufficient conditions for output agreement are derived. The approach proposed in the paper lends itself to solve flow control problems in distribution networks. As a first case study, the internal model approach is used for designing a controller that achieves an optimal routing and inventory balancing in a dynamic transportation network with storage and time-varying supply and demand. It is in particular shown that the time-varying optimal routing problem can be solved by applying an internal model controller to the dual variables of a certain convex network optimization problem. As a second case study, we show that droop-controllers in microgrids have also an interpretation as internal model controllers.

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arXiv2013

Duality and Network Theory in Passivity-based Cooperative Control

This paper presents a class of passivity-based cooperative control problems that have an explicit connection to convex network optimization problems. The new notion of maximal equilibrium independent passivity is introduced and it is shown that networks of systems possessing this property asymptotically approach the solutions of a dual pair of network optimization problems, namely an optimal potential and an optimal flow problem. This connection leads to an interpretation of the dynamic variables, such as system inputs and outputs, to variables in a network optimization framework, such as divergences and potentials, and reveals that several duality relations known in convex network optimization theory translate directly to passivity-based cooperative control problems. The presented results establish a strong and explicit connection between passivity-based cooperative control theory on the one side and network optimization theory on the other, and they provide a unifying framework for network analysis and optimal design. The results are illustrated on a nonlinear traffic dynamics model that is shown to be asymptotically clustering.

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arXiv2013

A Polyhedral Approximation Framework for Convex and Robust Distributed Optimization

In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to compute the optimizer of a linear cost function subject to the constraints. We propose a novel fully distributed algorithm, named cutting-plane consensus, to solve the problem, based on an outer polyhedral approximation of the constraint sets. Processors running the algorithm compute and exchange linear approximations of their locally feasible sets. Independently of the number of processors in the network, each processor stores only a small number of linear constraints, making the algorithm scalable to large networks. The cutting-plane consensus algorithm is presented and analyzed for the general framework. Specifically, we prove that all processors running the algorithm agree on an optimizer of the global problem, and that the algorithm is tolerant to node and link failures as long as network connectivity is preserved. Then, the cutting plane consensus algorithm is specified to three different classes of distributed optimization problems, namely (i) inequality constrained problems, (ii) robust optimization problems, and (iii) almost separable optimization problems with separable objective functions and coupling constraints. For each one of these problem classes we solve a concrete problem that can be expressed in that framework and present computational results. That is, we show how to solve: position estimation in wireless sensor networks, a distributed robust linear program and, a distributed microgrid control problem.

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