Intelligent Systems
Note: This research group has relocated.

33 results (View BibTeX file of all listed publications)

2022

The Wheelbot: A Jumping Reaction Wheel Unicycle
The Wheelbot: A Jumping Reaction Wheel Unicycle

Geist, A. R., Fiene, J., Tashiro, N., Jia, Z., Trimpe, S.

IEEE Robotics and Automation Letters, 7(4):9683-9690, IEEE, 2022 (article)

Abstract
Combining off-the-shelf components with 3D- printing, the Wheelbot is a symmetric reaction wheel unicycle that can jump onto its wheels from any initial position. With non-holonomic and under-actuated dynamics, as well as two coupled unstable degrees of freedom, the Wheelbot provides a challenging platform for nonlinear and data-driven control research. This letter presents the Wheelbot's mechanical and electrical design, its estimation and control algorithms, as well as experiments demonstrating both self-erection and disturbance rejection while balancing.

link (url) DOI [BibTex]

2022

Geist, A. R., Fiene, J., Tashiro, N., Jia, Z., Trimpe, S. The Wheelbot: A Jumping Reaction Wheel Unicycle IEEE Robotics and Automation Letters, 7(4):9683-9690, IEEE, 2022 (article)

link (url) DOI [BibTex]

Structured learning of rigid-body dynamics: A survey and unified view from a robotics perspective
Structured learning of rigid-body dynamics: A survey and unified view from a robotics perspective

Geist, A. R., Trimpe, S.

GAMM-Mitteilungen, 44(2):e202100009, Special Issue: Scientific Machine Learning, 2021 (article)

Abstract
Accurate models of mechanical system dynamics are often critical for model-based control and reinforcement learning. Fully data-driven dynamics models promise to ease the process of modeling and analysis, but require considerable amounts of data for training and often do not generalize well to unseen parts of the state space. Combining data-driven modeling with prior analytical knowledge is an attractive alternative as the inclusion of structural knowledge into a regression model improves the model's data efficiency and physical integrity. In this article, we survey supervised regression models that combine rigid-body mechanics with data-driven modeling techniques. We analyze the different latent functions (such as kinetic energy or dissipative forces) and operators (such as differential operators and projection matrices) underlying common descriptions of rigid-body mechanics. Based on this analysis, we provide a unified view on the combination of data-driven regression models, such as neural networks and Gaussian processes, with analytical model priors. Furthermore, we review and discuss key techniques for designing structured models such as automatic differentiation.

DOI [BibTex]

Geist, A. R., Trimpe, S. Structured learning of rigid-body dynamics: A survey and unified view from a robotics perspective GAMM-Mitteilungen, 44(2):e202100009, Special Issue: Scientific Machine Learning, 2021 (article)

DOI [BibTex]

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Robot Learning with Crash Constraints

Marco, A., Baumann, D., Khadiv, M., Hennig, P., Righetti, L., Trimpe, S.

IEEE Robotics and Automation Letters, 6(2):1439-1446, IEEE, February 2021 (article)

Abstract
In the past decade, numerous machine learning algorithms have been shown to successfully learn optimal policies to control real robotic systems. However, it is common to encounter failing behaviors as the learning loop progresses. Specifically, in robot applications where failing is undesired but not catastrophic, many algorithms struggle with leveraging data obtained from failures. This is usually caused by (i) the failed experiment ending prematurely, or (ii) the acquired data being scarce or corrupted. Both complicate the design of proper reward functions to penalize failures. In this paper, we propose a framework that addresses those issues. We consider failing behaviors as those that violate a constraint and address the problem of learning with crash constraints, where no data is obtained upon constraint violation. The no-data case is addressed by a novel GP model (GPCR) for the constraint that combines discrete events (failure/success) with continuous observations (only obtained upon success). We demonstrate the effectiveness of our framework on simulated benchmarks and on a real jumping quadruped, where the constraint threshold is unknown a priori. Experimental data is collected, by means of constrained Bayesian optimization, directly on the real robot. Our results outperform manual tuning and GPCR proves useful on estimating the constraint threshold.

link (url) DOI [BibTex]

Marco, A., Baumann, D., Khadiv, M., Hennig, P., Righetti, L., Trimpe, S. Robot Learning with Crash Constraints IEEE Robotics and Automation Letters, 6(2):1439-1446, IEEE, February 2021 (article)

link (url) DOI [BibTex]

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Joint State and Dynamics Estimation With High-Gain Observers and Gaussian Process Models

Buisson-Fenet, M., Morgenthaler, V., Trimpe, S., Di Meglio, F.

IEEE Control Systems Letters, 5(5):1627-1632, 2021 (article)

Abstract
With the rising complexity of dynamical systems generating ever more data, learning dynamics models appears as a promising alternative to physics-based modeling. However, the data available from physical platforms may be noisy and not cover all state variables. Hence, it is necessary to jointly perform state and dynamics estimation. In this letter, we propose interconnecting a high-gain observer and a dynamics learning framework, specifically a Gaussian process state-space model. The observer provides state estimates, which serve as the data for training the dynamics model. The updated model, in turn, is used to improve the observer. Joint convergence of the observer and the dynamics model is proved for high enough gain, up to the measurement and process perturbations. Simultaneous dynamics learning and state estimation are demonstrated on simulations of a mass-spring-mass system.

DOI [BibTex]

Buisson-Fenet, M., Morgenthaler, V., Trimpe, S., Di Meglio, F. Joint State and Dynamics Estimation With High-Gain Observers and Gaussian Process Models IEEE Control Systems Letters, 5(5):1627-1632, 2021 (article)

DOI [BibTex]

Wireless Control for Smart Manufacturing: Recent Approaches and Open Challenges
Wireless Control for Smart Manufacturing: Recent Approaches and Open Challenges

Baumann, D., Mager, F., Wetzker, U., Thiele, L., Zimmerling, M., Trimpe, S.

Proceedings of the IEEE, 109(4):441-467, 2021 (article)

arXiv DOI [BibTex]

Baumann, D., Mager, F., Wetzker, U., Thiele, L., Zimmerling, M., Trimpe, S. Wireless Control for Smart Manufacturing: Recent Approaches and Open Challenges Proceedings of the IEEE, 109(4):441-467, 2021 (article)

arXiv DOI [BibTex]

Learning Event-triggered Control from Data through Joint Optimization
Learning Event-triggered Control from Data through Joint Optimization

Funk, N., Baumann, D., Berenz, V., Trimpe, S.

IFAC Journal of Systems and Control, 16, pages: 100144, 2021 (article)

Abstract
We present a framework for model-free learning of event-triggered control strategies. Event-triggered methods aim to achieve high control performance while only closing the feedback loop when needed. This enables resource savings, e.g., network bandwidth if control commands are sent via communication networks, as in networked control systems. Event-triggered controllers consist of a communication policy, determining when to communicate, and a control policy, deciding what to communicate. It is essential to jointly optimize the two policies since individual optimization does not necessarily yield the overall optimal solution. To address this need for joint optimization, we propose a novel algorithm based on hierarchical reinforcement learning. The resulting algorithm is shown to accomplish high-performance control in line with resource savings and scales seamlessly to nonlinear and high-dimensional systems. The method’s applicability to real-world scenarios is demonstrated through experiments on a six degrees of freedom real-time controlled manipulator. Further, we propose an approach towards evaluating the stability of the learned neural network policies.

arXiv link (url) DOI [BibTex]

Event-triggered Learning for Linear Quadratic Control
Event-triggered Learning for Linear Quadratic Control

Schlüter, H., Solowjow, F., Trimpe, S.

IEEE Transactions on Automatic Control, 66(10):4485-4498, 2021 (article)

arXiv DOI [BibTex]

Schlüter, H., Solowjow, F., Trimpe, S. Event-triggered Learning for Linear Quadratic Control IEEE Transactions on Automatic Control, 66(10):4485-4498, 2021 (article)

arXiv DOI [BibTex]

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Controller Design via Experimental Exploration With Robustness Guarantees

Holicki, T., Scherer, C. W., Trimpe, J. S.

IEEE Control Systems Letters, 5(2):641-646, 2021 (article)

DOI [BibTex]

Holicki, T., Scherer, C. W., Trimpe, J. S. Controller Design via Experimental Exploration With Robustness Guarantees IEEE Control Systems Letters, 5(2):641-646, 2021 (article)

DOI [BibTex]

2020

A Learnable Safety Measure
A Learnable Safety Measure

Heim, S., Rohr, A. V., Trimpe, S., Badri-Spröwitz, A.

Proceedings of the Conference on Robot Learning, 100, pages: 627-639, Proceedings of Machine Learning Research, (Editors: Kaelbling, Leslie Pack and Kragic, Danica and Sugiura, Komei), PMLR, Conference on Robot Learning, October 2020 (article)

Arxiv [BibTex]

2020

Heim, S., Rohr, A. V., Trimpe, S., Badri-Spröwitz, A. A Learnable Safety Measure Proceedings of the Conference on Robot Learning, 100, pages: 627-639, Proceedings of Machine Learning Research, (Editors: Kaelbling, Leslie Pack and Kragic, Danica and Sugiura, Komei), PMLR, Conference on Robot Learning, October 2020 (article)

Arxiv [BibTex]

A little damping goes a long way: a simulation study of how damping influences task-level stability in running
A little damping goes a long way: a simulation study of how damping influences task-level stability in running

Heim, S., Millard, M., Le Mouel, C., Badri-Spröwitz, A.

Biology Letters, 16(9):20200467, September 2020 (article)

Abstract
It is currently unclear if damping plays a functional role in legged locomotion, and simple models often do not include damping terms. We present a new model with a damping term that is isolated from other parameters: that is, the damping term can be adjusted without retuning other model parameters for nominal motion. We systematically compare how increased damping affects stability in the face of unexpected ground-height perturbations. Unlike most studies, we focus on task-level stability: instead of observing whether trajectories converge towards a nominal limit-cycle, we quantify the ability to avoid falls using a recently developed mathematical measure. This measure allows trajectories to be compared quantitatively instead of only being separated into a binary classification of ‘stable' or ‘unstable'. Our simulation study shows that increased damping contributes significantly to task-level stability; however, this benefit quickly plateaus after only a small amount of damping. These results suggest that the low intrinsic damping values observed experimentally may have stability benefits and are not simply minimized for energetic reasons. All Python code and data needed to generate our results are available open source.

link (url) DOI Project Page [BibTex]

Event-triggered Learning
Event-triggered Learning

Solowjow, F., Trimpe, S.

Automatica, 117, pages: 109009, Elsevier, July 2020 (article)

arXiv PDF DOI [BibTex]

Solowjow, F., Trimpe, S. Event-triggered Learning Automatica, 117, pages: 109009, Elsevier, July 2020 (article)

arXiv PDF DOI [BibTex]

Data-efficient Autotuning with Bayesian Optimization: An Industrial Control Study
Data-efficient Autotuning with Bayesian Optimization: An Industrial Control Study

Neumann-Brosig, M., Marco, A., Schwarzmann, D., Trimpe, S.

IEEE Transactions on Control Systems Technology, 28(3):730-740, May 2020 (article)

Abstract
Bayesian optimization is proposed for automatic learning of optimal controller parameters from experimental data. A probabilistic description (a Gaussian process) is used to model the unknown function from controller parameters to a user-defined cost. The probabilistic model is updated with data, which is obtained by testing a set of parameters on the physical system and evaluating the cost. In order to learn fast, the Bayesian optimization algorithm selects the next parameters to evaluate in a systematic way, for example, by maximizing information gain about the optimum. The algorithm thus iteratively finds the globally optimal parameters with only few experiments. Taking throttle valve control as a representative industrial control example, the proposed auto-tuning method is shown to outperform manual calibration: it consistently achieves better performance with a low number of experiments. The proposed auto-tuning framework is flexible and can handle different control structures and objectives.

arXiv (PDF) DOI Project Page [BibTex]

Neumann-Brosig, M., Marco, A., Schwarzmann, D., Trimpe, S. Data-efficient Autotuning with Bayesian Optimization: An Industrial Control Study IEEE Transactions on Control Systems Technology, 28(3):730-740, May 2020 (article)

arXiv (PDF) DOI Project Page [BibTex]

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Sliding Mode Control with Gaussian Process Regression for Underwater Robots

Lima, G. S., Trimpe, S., Bessa, W. M.

Journal of Intelligent & Robotic Systems, 99(3-4):487-498, January 2020 (article)

DOI [BibTex]

Lima, G. S., Trimpe, S., Bessa, W. M. Sliding Mode Control with Gaussian Process Regression for Underwater Robots Journal of Intelligent & Robotic Systems, 99(3-4):487-498, January 2020 (article)

DOI [BibTex]

Hierarchical Event-triggered Learning for Cyclically Excited Systems with Application to Wireless Sensor Networks
Hierarchical Event-triggered Learning for Cyclically Excited Systems with Application to Wireless Sensor Networks

Beuchert, J., Solowjow, F., Raisch, J., Trimpe, S., Seel, T.

IEEE Control Systems Letters, 4(1):103-108, January 2020 (article)

arXiv PDF DOI [BibTex]

Beuchert, J., Solowjow, F., Raisch, J., Trimpe, S., Seel, T. Hierarchical Event-triggered Learning for Cyclically Excited Systems with Application to Wireless Sensor Networks IEEE Control Systems Letters, 4(1):103-108, January 2020 (article)

arXiv PDF DOI [BibTex]

Control-guided Communication: Efficient Resource Arbitration and Allocation in Multi-hop Wireless Control Systems
Control-guided Communication: Efficient Resource Arbitration and Allocation in Multi-hop Wireless Control Systems

Baumann, D., Mager, F., Zimmerling, M., Trimpe, S.

IEEE Control Systems Letters, 4(1):127-132, January 2020 (article)

arXiv PDF DOI [BibTex]

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Online learning with stability guarantees: A memory-based warm starting for real-time MPC

Schwenkel, L., Gharbi, M., Trimpe, S., Ebenbauer, C.

Automatica, 122, pages: 109247, 2020 (article)

DOI [BibTex]

Spatial Scheduling of Informative Meetings for Multi-Agent Persistent Coverage
Spatial Scheduling of Informative Meetings for Multi-Agent Persistent Coverage

Haksar, R. N., Trimpe, S., Schwager, M.

IEEE Robotics and Automation Letters, 5(2):3027-3034, 2020 (article)

DOI [BibTex]

Haksar, R. N., Trimpe, S., Schwager, M. Spatial Scheduling of Informative Meetings for Multi-Agent Persistent Coverage IEEE Robotics and Automation Letters, 5(2):3027-3034, 2020 (article)

DOI [BibTex]

Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control
Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Nubert, J., Koehler, J., Berenz, V., Allgower, F., Trimpe, S.

IEEE Robotics and Automation Letters, 5(2):3050-3057, 2020 (article)

Abstract
Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.

arXiv PDF DOI [BibTex]

Nubert, J., Koehler, J., Berenz, V., Allgower, F., Trimpe, S. Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control IEEE Robotics and Automation Letters, 5(2):3050-3057, 2020 (article)

arXiv PDF DOI [BibTex]

2019

Fast Feedback Control over Multi-hop Wireless Networks with Mode Changes and Stability Guarantees
Fast Feedback Control over Multi-hop Wireless Networks with Mode Changes and Stability Guarantees

Baumann, D., Mager, F., Jacob, R., Thiele, L., Zimmerling, M., Trimpe, S.

ACM Transactions on Cyber-Physical Systems, 4(2):18, November 2019 (article)

arXiv PDF DOI [BibTex]

2019

Baumann, D., Mager, F., Jacob, R., Thiele, L., Zimmerling, M., Trimpe, S. Fast Feedback Control over Multi-hop Wireless Networks with Mode Changes and Stability Guarantees ACM Transactions on Cyber-Physical Systems, 4(2):18, November 2019 (article)

arXiv PDF DOI [BibTex]

Resource-aware IoT Control: Saving Communication through Predictive Triggering
Resource-aware IoT Control: Saving Communication through Predictive Triggering

Trimpe, S., Baumann, D.

IEEE Internet of Things Journal, 6(3):5013-5028, June 2019 (article)

Abstract
The Internet of Things (IoT) interconnects multiple physical devices in large-scale networks. When the 'things' coordinate decisions and act collectively on shared information, feedback is introduced between them. Multiple feedback loops are thus closed over a shared, general-purpose network. Traditional feedback control is unsuitable for design of IoT control because it relies on high-rate periodic communication and is ignorant of the shared network resource. Therefore, recent event-based estimation methods are applied herein for resource-aware IoT control allowing agents to decide online whether communication with other agents is needed, or not. While this can reduce network traffic significantly, a severe limitation of typical event-based approaches is the need for instantaneous triggering decisions that leave no time to reallocate freed resources (e.g., communication slots), which hence remain unused. To address this problem, novel predictive and self triggering protocols are proposed herein. From a unified Bayesian decision framework, two schemes are developed: self triggers that predict, at the current triggering instant, the next one; and predictive triggers that check at every time step, whether communication will be needed at a given prediction horizon. The suitability of these triggers for feedback control is demonstrated in hardware experiments on a cart-pole, and scalability is discussed with a multi-vehicle simulation.

PDF arXiv DOI [BibTex]

2018

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Learning an Approximate Model Predictive Controller with Guarantees

Hertneck, M., Koehler, J., Trimpe, S., Allgöwer, F.

IEEE Control Systems Letters, 2(3):543-548, July 2018 (article)

Abstract
A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding’s Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.

arXiv PDF DOI [BibTex]

2018

Hertneck, M., Koehler, J., Trimpe, S., Allgöwer, F. Learning an Approximate Model Predictive Controller with Guarantees IEEE Control Systems Letters, 2(3):543-548, July 2018 (article)

arXiv PDF DOI [BibTex]

2017

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Event-based State Estimation: An Emulation-based Approach

Trimpe, S.

IET Control Theory & Applications, 11(11):1684-1693, July 2017 (article)

Abstract
An event-based state estimation approach for reducing communication in a networked control system is proposed. Multiple distributed sensor agents observe a dynamic process and sporadically transmit their measurements to estimator agents over a shared bus network. Local event-triggering protocols ensure that data is transmitted only when necessary to meet a desired estimation accuracy. The event-based design is shown to emulate the performance of a centralised state observer design up to guaranteed bounds, but with reduced communication. The stability results for state estimation are extended to the distributed control system that results when the local estimates are used for feedback control. Results from numerical simulations and hardware experiments illustrate the effectiveness of the proposed approach in reducing network communication.

arXiv Supplementary material PDF DOI Project Page [BibTex]

2017

Trimpe, S. Event-based State Estimation: An Emulation-based Approach IET Control Theory & Applications, 11(11):1684-1693, July 2017 (article)

arXiv Supplementary material PDF DOI Project Page [BibTex]

2016

A New Perspective and Extension of the Gaussian Filter
A New Perspective and Extension of the Gaussian Filter

Wüthrich, M., Trimpe, S., Garcia Cifuentes, C., Kappler, D., Schaal, S.

The International Journal of Robotics Research, 35(14):1731-1749, December 2016 (article)

Abstract
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. The GF represents the belief of the current state by a Gaussian distribution, whose mean is an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF as the solution to a constrained optimization problem. From this new perspective, the GF is seen as a special case of a much broader class of filters, obtained by relaxing the constraint on the form of the approximate posterior. On this basis, we outline some conditions which potential generalizations have to satisfy in order to maintain the computational efficiency of the GF. We propose one concrete generalization which corresponds to the standard GF using a pseudo measurement instead of the actual measurement. Extending an existing GF implementation in this manner is trivial. Nevertheless, we show that this small change can have a major impact on the estimation accuracy.

PDF DOI Project Page [BibTex]

2016

Wüthrich, M., Trimpe, S., Garcia Cifuentes, C., Kappler, D., Schaal, S. A New Perspective and Extension of the Gaussian Filter The International Journal of Robotics Research, 35(14):1731-1749, December 2016 (article)

PDF DOI Project Page [BibTex]

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Event-based Sampling for Reducing Communication Load in Realtime Human Motion Analysis by Wireless Inertial Sensor Networks

Laidig, D., Trimpe, S., Seel, T.

Current Directions in Biomedical Engineering, 2(1):711-714, De Gruyter, 2016 (article)

PDF DOI [BibTex]

Laidig, D., Trimpe, S., Seel, T. Event-based Sampling for Reducing Communication Load in Realtime Human Motion Analysis by Wireless Inertial Sensor Networks Current Directions in Biomedical Engineering, 2(1):711-714, De Gruyter, 2016 (article)

PDF DOI [BibTex]

2014

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Wenn es was zu sagen gibt

(Klaus Tschira Award 2014 in Computer Science)

Trimpe, S.

Bild der Wissenschaft, pages: 20-23, November 2014, (popular science article in German) (article)

PDF Project Page [BibTex]

2014

Trimpe, S. Wenn es was zu sagen gibt Bild der Wissenschaft, pages: 20-23, November 2014, (popular science article in German) (article)

PDF Project Page [BibTex]

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A Limiting Property of the Matrix Exponential

Trimpe, S., D’Andrea, R.

IEEE Transactions on Automatic Control, 59(4):1105-1110, 2014 (article)

PDF DOI [BibTex]

Trimpe, S., D’Andrea, R. A Limiting Property of the Matrix Exponential IEEE Transactions on Automatic Control, 59(4):1105-1110, 2014 (article)

PDF DOI [BibTex]

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Event-Based State Estimation With Variance-Based Triggering

Trimpe, S., D’Andrea, R.

IEEE Transactions on Automatic Control, 59(12):3266-3281, 2014 (article)

PDF Supplementary material DOI Project Page [BibTex]

Trimpe, S., D’Andrea, R. Event-Based State Estimation With Variance-Based Triggering IEEE Transactions on Automatic Control, 59(12):3266-3281, 2014 (article)

PDF Supplementary material DOI Project Page [BibTex]

2012

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The Balancing Cube: A Dynamic Sculpture as Test Bed for Distributed Estimation and Control

Trimpe, S., D’Andrea, R.

IEEE Control Systems Magazine, 32(6):48-75, December 2012 (article)

DOI [BibTex]

2012

Trimpe, S., D’Andrea, R. The Balancing Cube: A Dynamic Sculpture as Test Bed for Distributed Estimation and Control IEEE Control Systems Magazine, 32(6):48-75, December 2012 (article)

DOI [BibTex]